Carl Friedrich Göschel: Hegel and his time: with regard to Goethe (1832)

The last time we met Göschel, he was busy defending Hegelian philosophy against the reinterpretation of a single philosopher, but now we see him arguing for Hegel against all his contemporaries in the work Hegel und seine Zeit, mit Rücksicht auf Goethe. The look toward Goethe mentioned in the title refers to Göschel’s belief that Goethe and Hegel were essentially on the same side in this battle, Indeed, at various points of the work, Göschel quotes Goethe’s poems, to indicate correspondences with Hegelian and Goethean ideas. Even more, Göschel begins with a description of Goethe’s take on Leibnizian monadology – we are a collection of monads, soul being a central monad, ruling over a body made out of other monads, and after our death, the monads disperse, only to come together during resurrection, only with more heightened awareness – just to make the fancy remark that the two recently deceased philosophers must now be conversing in a heaven of monads, waiting for their return to the world of living.

The main text of the work is dedicated to describing the relations between Hegelian philosophy – or as Göschel prefers to call it most of the time, speculative philosophy – and the contemporary culture of the times. He begins with what he calls Umsicht – literally, a look from outside. In other words, he is interested in what the contemporaries who are not Hegelians think of Hegelian philosophy.

Göschel begins from the end of Hegel’s philosophical system or religion (one could point out that Hegel continues with philosophy after religion, but Göschel may be betraying his interests here somewhat). He notes that Hegelianism sits squarely in the middle between two major factions in the philosophy of religion: rationalism, which emphasises the role of reason in deciding what to believe, and supernaturalism, which endorses divine revelation as the foundation of religious certainty. Just like rationalism, Göschel says, Hegelian philosophy thinks that reason should be used as the “form” or method for studying religion by the subject, while the content or object of this method Hegel takes to agree in its essentials with Lutheranism, just like supernaturalists state.

Göschel thinks the position he describes as Hegelian is reasonable, if we just assume that the two sides – the investigating subject or individual human reason and the investigated object or divine revelation – are in a sense identical or connected to one another, even when they are seen as different. More particularly, Göschel adds, we should, firstly, assume that both these opposites have their worth, secondly, admit that this coexistence involves some contradiction or tension between the two poles, and finally, solve this tension by noting that opposites share something in common – human reason agrees with divine revelation, since the latter is also caused by reason, just that of divinity. Göschel at once points out that this mediating stance doesn’t still satisfy the extremes, which question the justifiability of the other extreme, but not of themselves: for rationalists, Hegelian philosophy of religion appears irrational in accepting orthodox dogmas, while for supernaturalists, it seems blasphemous in subjugating Bible to standards of human reason.

Göshcel considers similarly contemporary evaluations of other parts of Hegelian system (more particularly, he goes through it in reverse, continuing from philosophy of religion to philosophy of state, then to philosophy of religion, philosophy of nature, particularly medicine, and mathematics, ending finally with what philologists, historians and other philosophers have to say about Hegelianism), but his main point is clear from the first example. Hegelian philosophy often takes a mediating position between two extreme positions, of which one usually corresponds to subjective, human reason ready for revolution, while the other extreme then corresponds to objective, divine reason upholding traditions. Hegelianism solves the seeming contradiction of these two positions by noting their interconnectedness and essential unity, leading it to endorse moderation between radicalism and conservatism, which just makes the extreme positions reject this middle stance.

From different standpoints, Göschel concludes, Hegel’s system could be taken as too eclectic – in combining all systems – or too exclusive – as taking itself as the final truth; too poetic and mystic – as upholding contradictions as truth – or as too pedantic and scholastic – as using hierarchic classifications; as too realistic – as dealing only with the world around us – or as too idealistic – as seeing material world as a mere appearance of reason; as too pantheistic – as seeing God everywhere – or as too atheistic – as seeing God nowhere.

After this look from outside, Göschel moves to Einsicht or a look inside the Hegelian system. As we noted in the previous post about him, Göschel knows his Hegelian liturgy. He also shares some basic faults common to many so-called Hegelians. Thus, after quite correctly insisting that Hegel wants to develop the basic structures of his philosophy from a standpoint where we abstract from everything given – indeed, he wants to begin from nothing definite at all – but then when the truly interesting question how this development occurs at crucial points of the system is presented, Göschel merely answers with the general consideration that it happens “by immanent negation”, which in Hegelese really says nothing more than “by finding out how the matter at hand shows how to arrive at the next step”.

Göschel even makes the comparison – even if not outright identification – of the supposed steps of Hegelian method with the trivison of thesis, antithesis and synthesis at the beginning of the first version of Fichtean Wissenschaftslehre. In this often criticised comparison that loses the distinctness of Hegelian philosophy, Göschel also errs in not noting that this Fichtean trivision is rather different in holding the thesis (positing of an existing I) as higher than the two others, because in its pure form it describes what an absolute or divine I would be like, while the antithesis (positing I against not-I) describes the standpoint of human I and the resulting synthesis (I and not-I being divisible and thus able to share the consciousness of I) just tries to explain how the human standpoint could be possible from the standpoint of divine consciousness.

Moving back to his take on Hegelianism, Göschel makes the very common error of immediately assuming that the supposed three steps in Hegel’s method (abstraction of pure starting point, “negation” or development of new structures out of the first and “second negation” or consideration of this string of structures as forming a unified system) agree literally with the various trivisions of Hegel’s system. This assumption makes then possible to just ignore the question how the individual transitions in Hegel’s system work, although Göschel does at one place admit that the trivisions might sometimes appear arbitrary (no wonder, as Hegel himself reworked them from time to time and suggested they were more to help the reader than anything else).

We need not thus go in any detail to Göschel’s reconstruction of Hegelian logic, which is really just a summary of its table of contents. We can therefore skip at once to his peculiar understanding of its end, where Göschel outright assumes that the absolute idea concluding the book simply is God, not in any metaphorical sense, but as the same personality as described by orthodox Lutheranism. The development of pure thinking in Hegelian philosophy should then end with faith in the certainty of a personal God, who unites e.g. subject and object or infinite and finite by showing that the former has the power to “overreach” into the latter – in other words, to be the controlling and even creating principle in their organic fusion.

Göschel then continues to summarise the Hegelian philosophy of the concrete, or as Göschel emphasises, created nature and created spirit (we could say, humanity), which we for the just mentioned reason can also skip and jump into his take on absolute spirit. The final point of Göschel’s interpretation is that nature and humanity are not independent, but exist merely in relation to absolute spirit, which is then again God, but as related to their creations. The structures of logic were supposedly just developments of divine thought, which then in the concrete world appear as distinct and seemingly independent entities. World is thus, in a sense, fuller than logic, but it also mirrors the latter’s structure, showing analogies between different levels of the natural and the human world.

Another major point in the latter part of Hegel’s philosophy, according to Göschel, is that it shows the divine to be present in the here and now of the world we are living: just like theology said, God is omnipresent. Furthermore, Göschel adds, it also shows that these individual heres and nows form a larger continuity, where individuals unite into an organic whole.

Finally, Göschel presents as mediating between the Umsicht and the Einsicht the Aussicht – literally, a look toward the outside. In other words, he wants to deal with various problems that hinder the contemporary reader from understanding Hegelian philosophy, as he understands it. The central obstacle, he thinks, is our natural thinking, which as natural is still moored in some immediate presuppositions, which the absolute thinking has learned to put aside. Göschel admits this change of standpoint is difficult, since it involves us resisting the stubborn independence of concrete individuals in order that we can recognise that the light of reason is able to penetrate the essence of all things.

A particularly interesting shape of this stubborn attitude is found in the objection that what is actual seems not always reasonable, especially when this actual is evil and sinful. Göschel can quite correctly point out that this objection involves just a misunderstanding of Hegelian terminology. Actual does not mean for Hegel just anything that exists, but only the lawlike structures upholding what exists. Evil and sin, on the other hand, are mere existences, which may or may not appear – they are contingent. Then again, Göschel adds with conviction, such non-actual or contingent existences are then bound to be destroyed by the divine necessity and thus evil and sin are fated to find their retribution.

Quite characteristic is also Göschel’s answer to the question whether the absolute idea and the absolute spirit are just symbolic names for what is human. Göschel affirms this, but with a twist: it is not just any individual human Hegel is talking about, but the universal humanity embodied in Christ. Thus, he continues, while Father of the Christian Trinity is the exemplary infinite, Christ is the exemplary finite, in whose image the individual humans are then created. With this move Göschel reveals his cards: the Hegelian system is just a cover for quite a literal understanding of Christianity.

Ludwig Feuerbach: Pierre Bayle. Article on history of philosophy and humanity (1839)

While Leibniz was a natural continuation of Feuerbach’s work on the history of philosophy, Pierre Bayle seems an odd choice. Indeed, Feuerbach himself finally concludes his Pierre Bayle. Ein Beitrag zur Geschichte der Philosophie und Menschheit by noting that Bayle never really brought anything positive to philosophy, and indeed, failed to understand the worth of thinkers like Spinoza, confusing in his criticism of latter the level of sense individuals with the level of one substance behind these individuals.

Yet, what was of worth in Bayle’s writings, Feuerbach says, is the contradiction of faith and reason – a question which appears to haunt Feuerbach himself more and more in his writings. Feuerbach begins again from the consideration of Christianity, which he sees as characterised by dualism. True, Feuerbach admits, the pre-Christian culture did also speak of oppositions, but only of natural oppositions, while Christianity added to these certain metaphysical dualisms, like that of God and world, of heaven and earth, of spirit and flesh and of faith and reason, all of which were externally expressed in the battle between the Church and the state.

Characteristic dualism in Catholicism, Feuerbach notes, was the opposition between sensuous flesh and supersensous spirit, where the latter was placed above the former. Thus, the highest virtue for the Catholic Church was not natural love, but unnatural chastity, and although the Church seemingly allowed marriage, the practice of the saints showed the true preference. Catholic artists, like Dante and Petrarca, appeared to value natural love as the highest shape in which heavenly can appear on earth, but, Feuerbach says, these artists were for Church mere adopted children in comparison to real children or saints. Even a Christian artist must do beautiful works that appeal also to non-Christians, because a true work of art belongs to no specific religion, but unites the whole humanity, and therefore religion is just an external covering to an artist. Thus, beautiful Catholic works of art are contrary to the very idea of Catholicism, and seeing sensual Madonnas pictured in cloisters just shows that monks were never truly able to leave their earthly lusts behind.

Just as the Catholic Church related to art, similarly it related to science, Feuerbach insists. True, Catholic monks did develop science, but this was opposed to the original spirit of Catholicism, which appreciated only devotional books. Scientific spirit contradicts Catholicism, Feuerbach thinks, and therefore it will either turn against Catholicism or be suppressed as mere means for spreading faith.

Protestantism rebelled against the practical contradiction of flesh and spirit, Feuerbach continues, but retained the theoretical opposition between faith and reason. Feuerbach thinks that the battle of the reformers against celibacy was not just based on the Bible, but the true reason justifying this turn was human understanding. Thus, Feuerbach finds it even more puzzling why Protestantism then turned against reason. A Catholic saint can at least cut away tempting organs – Feuerbach is probably referring to the famous rumour of Origen castrating himself – but a Protestant cannot cut away their reason.

It is this opposition of reason and faith that Feuerbach thinks is the most interesting aspect of Bayle. Feuerbach thinks it particularly poignant that Bayle was no professional theologian, since that showed him to start his criticism from a standpoint of freedom. Theology, Feuerbach states, thinks it has a monopoly over other sciences. The interest of theology is not to study anything scientifically, but to interpret and comment on the truth of faith. Doubts, on the other hand, are a sin for it and science is a mere means for the goal of faith. In other words, Feuerbach concludes, the spirit of theology is not the spirit of science, since science is universal for both Christians and non-Christians, while theology limits itself to the former.

When theology reigned, Feuerbach continues, other sciences were considered only as means for theology and subservient to it. Nature was studied for the sake of finding signs of God in nature and was thus regarded in a mechanical fashion as a mere external means for a goal. Thus, humans were forcefully turned toward heaven by theologians arguing teleologically from various phenomena of nature, and only Giordano Bruno and Spinoza understood that nature has its own reason. Theology, Feuerbach thinks, opposes science, because the main principle of theology is miracle and arbitrary will, which is opposed to reason as the principle of science. Thus, philosophy regards moral principles as laws of reason, while theology sees them as commands of God. More generally, theology derives everything from the will of God, while philosophy tries to explain it.

Feuerbach regards Bayle as an antitheologian and thus a person of reason. For instance, Bayle saw comets as natural phenomena and not as divine signs and argued for this by noting that by using comets as signs God would have just increased superstition, which Bayle regarded as worse than atheism. Indeed, Bayle went even so far as to note that atheists often lived better lives than Christians.

Bayle’s criticism, Feuerbach says, concerned religion as differing from morality and philosophy, in other words, positive religion like Catholicism that had solidified into a church and was limited by certain articles of faith. In such a positive religion the believer does not need to do anything else, but what its dogmas say to be sanctified (the official sacraments). Although Protestantism was a sort of liberation from Catholicism, it also became a positive religion. Thus, even Protestantism makes God into an object of devotion that demands service, while duties toward humans become subservient to this and filled only because so God is also served. Protestantism, Feuerbach concludes, binds itself to a specific time and place – church Sundays, when the priest is preaching – and religion becomes a mere custom one has to regularly follow.

Feuerbach thus agrees with Bayle that it is not the positive religion that has combined barbarians into society, but that humans have done it themselves, because of their conscience. Christians do not do good because they are Christians, but because they are humans. On the other hand, a bad person remains a bad person, even if Christianity would frighten him not to do bad things. Furthermore, paradoxically the belief in the dogma of the original evil in human nature just shows that the believer of this dogma does not believe themselves to be good.

Feuerbach notes that Bayle endorsed the independency of ethics from religion and criticised the habit of explaining away the immoralities of Biblical figures. Feuerbach regards Bayle’s endeavour to separate ethics from religion as noble. According to Feuerbach, it is foolish to try to ground ethics on the notion of God. True, one could try to base ethics on the idea of God as the epitome of goodness, but actually, it is not the goodness as the goodness of God that is here important, but merely goodness as such. Furthermore, Feuerbach continues, although the goodness of God might be in line with ethics, the notion of divine omnipotence contradicts the idea of goodness, since it is just a notion of a magical demon capable of anything. Indeed, he adds, even the devil seems capable of miracles, which then are just an unethical and immoral concept.

Scholastic theology could not do proper ethics, Feuerbach explains, since it founded everything on the will of God. Truly independent ethics didn’t appear, Feuerbach thinks, before the Kantian categorical imperative, which gave ethics a sacred and independent position. Feuerbach praises Fichte for raising ethics even further to an ideal that an empirical human being could never fully achieve, but still has to strive to for its own sake, while in comparison, a theologian does good only for the sake of God and paradise. If one does not do good for its own sake, one is merely seeking for one’s own interest and making good serve as a means for one’s pious goal, Feuerbach insists and adds that only ethics is the true religion and true love of God is the love of humanity.

According to Feuerbach, separation of ethics from theology shows most strikingly that spirit has broken away from theology. He thinks that Bayle expounded this contradiction especially in discussion with rationalists theologians, who thought that dogmas could not contradict reason. Against them, Bayle argued that especially original sin was an unreasonable dogma: the Biblical story of the fall of humankind makes God into a literal instigator of sin. Leibniz had argued against Bayle that God had other ends beyond human virtue (perhaps the preservation of certain plants, as the Bible story suggests), but Feuerbach thinks this justification is not available to the theological standpoint, which sees God working only for humanity. Leibniz and rational theologians objected also that divine goodness and justice meant no ordinary human goodness and justice, but Bayle could answer that they must still be recognisable as goodness and justice. Indeed, Bayle was only holding on to a philosophical ideal of good and just God, while the theologian’s God was very passionate and deceived humans into sin, although this God also wanted to retain the appearance of not doing so.

Bayle found dogmas of religion problematic, Feuerbach continues, not because they contradicted lower passions, but because they contradicted natural reason. While for an orthodox theologian reason was just a concubine, for Bayle it was a life companion. Feuerbach sees Bayle’s relation to faith as exhibiting a more general sign of his time: faith was not anymore natural, but felt as contradictory to reason or as a mere object, first of reflection, then of doubt and criticism and finally of denial.

Feuerbach notes that Descartes had particularly shared a similar idea of faith: both Descartes and Bayle knew objectively the contradiction of positive faith with reason, while their own faith was subjectively contradicting their reason. Descartes did not doubt his own faith, but just with this lack of doubt he showed that it contradicted the universal reason. Philosophy cannot exist, when assertions have to be just assumed as true, which Feuerbach thinks is true of Church dogmas. Thus, if Descartes had been a good Catholic, he would have just accepted dogmas and not thought of anything. Yet, as an instigator of modern philosophy he could not accept any determined fundament or limitation for thinking, but had to follow its own necessity.

Descartes, Feuerbach thinks, had based his philosophy on self-certainty, which is something completely antidogmatic. Positive effects of any philosophy, Feuerbach says, are not visible to the senses and do not limit to mere formal consequences, but to change of spirit. Cartesian philosophy especially taught us to think, Feuerbach insists, and to distinguish material from spiritual and to reduce study of nature to mechanism.

A particular point where Feuerbach sees Descartes contradicting the dogmas of Catholicism was his idea of body as characterised by extension. Feuerbach thinks that this notion of extension cannot be reconciled with the idea of transsubstantiation, where the same extension of bread supposedly changes its very substance into the flesh of Christ. By ignoring such dogmas, Feurbach notes, Cartesian thinking showed its lack of interest in matters of faith. Faith was thus not anymore based on self-consciousness, but was only an external addition or historical faith. Historical matters can be believed only historically, that is without any further justification, since while present facts we are forced to believe, historical facts of past lack this feeling of necessity and are something we must always doubt. Similarly, Feuerbach suggests, true faith in dogmatic facts could occur only when these facts were felt as a living part of human self-consciousness, while from Descartes onward such living faith was more and more just a thing of the past.

Feuerbach admits that there was still something making faith very much a living force at the time of Descartes, namely, the community of believers or the Church representing faith in the actual world. Because of the Church, faith was a universal opinion, while reason was in comparison a mere subjective opinion. Feuerbarch notes that Bayle also was a part of such a community, although in his case it was not Catholic, but Reformed church. Still, Feuerbach insists, Bayle’s faith was an act of self-denial: Bayle rejected reason in favour of historically grounded faith, or after placing doubts on dogmas he still leaped to faith.

Feuerbach sees Bayle as an intellectual ascetic, abstaining from the use of reason, but at the same time contradicting himself. For Feuerbach, Bayle was a sophist in defending faith. Feuerbach considers earthly satisfaction to be truly more divine than mere blind faith, which is just human invention. Indeed, Feuerbach says, even the believers understand this, because they think God is the most blessed and happiest of all beings, who does not require any faith at all, but knows everything with full clarity.

Although Feuerbach thus is ultimately let down by Bayle’s choice of faith over reason, he congratulates Bayle for his otherwise impartial polemics against all positive forms of religion. He is especially fond of Bayle’s criticism against all religious authority and particularly the Catholic reliance on the power of tradition. Bayle was correct, Feuerbach says, in rejecting the idea that the Church could force the conscience of individual people into believing something. Instead, Bayle demanded unlimited tolerance of all creeds, which Feuerbarch wholeheartedly agrees with: truth is tolerant, because it is always sure of itself.

Ludwig Feuerbach: History of newer philosophy. Exposition, development and critique of Leibnizian philosophy (1837)

Feuerbach continued his work on the history of philosophy with the book Geschichte der neueren Philosophie. Darstellung, Entwicklung und Kritik der Leibnizschen Philosophie. As the title outright says, this time he has decided to concentrate on a single thinker, Leibniz. Feuerbach argues for his choice by noting that Leibniz is the most important philosopher in the time succeeding that of Descartes and Spinoza. Furthermore, ideas of the contemporaries, like Locke, Feuerbach thinks, are easily understood from their own writings, while this is not true for Leibniz. This difficulty, Feuerbach adds, is made even more complex by the fact that Feuerbach is trying to not just superficially expound and criticise Leibniz’s texts, but also to find their hidden implications by revealing the organic connections in his system.

Feuerbach begins with a summary of previous movements in the history of modern philosophy, presenting its developments in terms of nationalities. Thus, he places the beginning of modern philosophy in Italy, where, he thinks, the natural temperament of the people could not be satisfied by dryness of scholasticism, but notes that the philosophy could not develop there, but had to move to more northerly countries. From Italy philosophy at first moved to England, and Feuerbach suggests that the mercantile nature of English nation restricted philosophy to crude empiricism, while more metaphysical philosophy appeared only with thinkers engaged with ancient philosophical systems (Feuerbach is probably thinking of the so-called Cambridge Platonists).

The more metaphysical needs of philosophy were satisfied in France, because French people, Feuerbach thinks, are more acquainted with the loftier side of life than English and thus more capable of thinking instead of just perceiving. Where French – or more specifically, Cartesians – failed was to find empirical content matching their metaphysical idea. Therefore French philosophy eventually reverted to English materialism. From France philosophy then moved to Netherlands, but not really to Dutch people, since Netherlands merely served as a place where a person living between different cultures could thrive. Feuerbach is, of course, speaking of Spinoza, who disclaimed his Jewish heritage, but still never converted to Christianity. Spinoza, Feuerbach thinks, created proper philosophy, but his system was too lifeless to gain any followers.

The final destination of modern philosophy thus far was German, Feuerbach suggests. Indeed, he insists that philosophy became even a national characteric of Germans, although it first looked like a foreign import. Indeed, Feuerbach notes that German reformers had eventually accepted philosophy, but only grudgingly, as a formal tool for bolstering the freedom of religion and removing it from the shackles of foreign Catholicism. Unlike in France or England, in Germany philosophy was then intricately combined with religion, which became apparent in mystical thinkers like Jacob Böhme.

The first German thinker with a properly philosophical outlook was, according to Feuerbach, Leibniz. The central notion of his philosophy, Feuerbach says, was substance. This makes Leibniz resemble Spinoza, but Feuerbach notes that Leibniz defined the concept in a radically different manner as active force or self-activity. This means that unlike Spinoza, Leibniz could accept the existence of many different substances, as long as they actively differentiated themselves from one another. Feuerbach thus sees Spinoza’s unity replaced by Leibnizian distinction and suggests the comparison that while Spinoza looked through a telescope and saw nothing but colourless heaven, Leibniz looked through a microscope to discover life within life.

Feuerbach’s remark about Leibniz discovering life is connected to earlier philosophical discussions. Descartes had distinguished mind and body sharply and insisted that bodies are mindless machines. Many thinkers had responded that matter has something more in it that makes it more alive, but none of them could replace mechanism with anything definite. This was true until Leibniz came along. Leibniz noticed, Feuerbach suggests, that mere geometry could not explain all in nature, but something more was required. This something more was identified by Leibniz as force. Force meant for him nothing material, but simple and indivisible and therefore soul-like principle. This soul-like principle Leibniz had also called monads. For Leibniz, only forces or monads existed and they were also souls, without which no multiplicity nor individuation could have existed.

For Leibniz, Feuerbach continues, all things were then ultimately souls, but a soul was not necessarily conscious, but just spontaneous. By this spontaneity Leibniz had meant that nothing, beyond God, could affect the monads. For Leibniz, change then required differentiation of monads through internal qualities, which were activities determined by monads themselves. In other words, Feuerbach reads Leibniz, they were representations or perceptions: all the multiplicity of the universe was present for monads only through representations of this multiplicity in unity. Furthermore, such a representation was not passive, but an active drive causing continual movement in the monad.

Feuerbach notes that Leibnizian monads differed through their representations, which had an infinity of grades. The major classification of these grades were the two divisions of representation, firstly, into distinct and confused, and secondly, into clear and obscure. Obscure representation or concept Leibniz had explained to be not enough for recognising something, while clear concept was. Clear representations Leibniz had then divided into confused and distinct representations, confused being such where the signs used for recognising something were not themselves recognisable: an example would be representations of colours, since we can distinguish e.g. blue from red, but we cannot define what distinguishes them. Now, Leibniz had added that confused representations were generated by a multiplicity of too insignificant representations that we are not conscious of – for instance, a representation of green had been generated by an unconscious representation of blue being added to an unconscious representation of yellow. Thus, Feuerbach explains, the difference between the grades of representations was not very sharp for Leibniz, because even our distinct representations consisted of many small confused representations.

These confused representations, Feuerbach explains, were for Leibniz a sign of the infinite content within monads. For Leibniz, monads were like complete independent worlds. As worlds, monads mirrored the whole infinite system of monads from their own viewpoint. This viewpoint was always in some measure confused, because of the infinity of the content. This essential confusion then formed the materiality of monads, which also glued the monads together into a universe. Feuerbach notes that this thought radically separates Leibniz from more sentimental spiritualists who thought that matter only hindered the connection of souls.

For Leibniz, Feurbach suggests, what a monad represented as matter were the other monads taken as others, that is, the limits of the first monad itself. More precisely, matter was a confused representation, since only confusion limited monads. Feuerbach also emphasises that representation was for Leibniz no sign of irreality, but of life and thus calling matter a representation  was not meant to suggest matter did not exist, but only that it was also spiritual in nature. Feuerbach also notes that Leibniz argued for his understanding of matter by noting that even our sensual representations of matter, such as pressure and resistance, had no other distinguishing marks beyond inclarity and restriction of our freedom. Soul and matter then required nothing more to connect them, because matter just meant the limitedness inherent in the finite souls and thus their necessary counterpart.

The idea of matter as the inherent restrictedness of substances or monads was only the first concept of matter Leibniz had, Feuerbach explains. In addition, when Leibniz was speaking of matter as an object of representation, he meant an aggregate of countless monads. Thus, when people were speaking of extension, Leibniz had thought they actually meant just diffusion of certain quality over such a group of monads, like when whiteness was said to be extended over a whole glass of milk. Extension, for Leibniz, was then a property belonging to a complex thing, while space meant just a relation between things.

In addition to all these passive properties, Leibniz admitted that matter had an active force, which explained, for instance, why material things resisted when someone tried to move them. This active force, he explained, was either primitive force – the soul of the thing – or derivative force arising from limitation of this primitive force in contact with other things: qualities of a body, for example, were in Leibniz’s opinion just such modifications or limitations of the primitive force. Ultimately, this primitive force was, of course, the internal activity or representation, while derivative forces were kinds of movement or external activity. Movement was then, for Leibniz, nothing truly real, but moving force was, and against Descartes Leibniz insisted that not the quantity of the motion, but the quantity of this force remained constant in the force.

Although not a fiction or illusion, Feuerbach writes, the ordinary material world just described was for Leibniz not the ultimate reality, but merely a phenomenon founded on the ultimate reality or the monads. What was particularly real in the material world was its regularity and laws. Indeed, Leibniz saw monads as intrinsically connected to one another and thus thought every monad naturally had their own corresponding matter or body. Like all material things in Leibnizian philosophy, this body consisted of other monads and the central monad was their soul. Again, Leibniz emphasised that although these bodies were phenomena, they were no deceptions, because they were well grounded and cohered with one another.

For Leibnizian monads, bodies were like their organs, that is, monads represented the world from the perspective of their bodies, so that the world was mirrored in all of its parts. Feuerbach notes that Leibniz distinguished monads from Epicurean atoms, because atoms had only a single drive, but monads had an infinity of representations, since they mirrored an infinite universe. Because all monads had their own bodies, organic bodies would consist of further organic bodies, and the whole universe formed a continuous hierarchy of all levels of organisation and consciousness.

Feuerbach notes that because in Leibnizian philosophy every monad was a microcosm, monads had no need to affect one another. In other words, because a monad reflected all the other monads and especially its body and their respective changes, it could change its state instantly, say, from joy to sadness. Feuerbach therefore suggests that Leibniz’s monads were not actors, but only observers, and the only reason why anyone would say that one monad caused something in another was that they found in the first reasons for something happening in the second.

Just like two monads, a monad (soul) and a group of monads (body) could not affect one another, but just changed their states in harmony. Leibniz explained that this correspondence was caused by a pre-established harmony. Although Leibniz was particularly fond of this idea, Feuerbach considers it misleading, because it suggests that harmony would be based on nothing else but an unreasoning and arbitrary act of will by a being external to monads. Such an act, Feuerbach insists, would ground the harmony of monads to a mere miracle, although its true reason in Leibnizian system should be the nature of the monad as representing everything and especially its body. In effect, Feuerbach claims, the notion of pre-established harmony was a return to occasionalism that emphasised the difference of soul and body and made their correspondence a miracle. The main fault Feuerbach sees in the notion of pre-established harmony is that it contradicts the supposed independence of monads.

Feuerbach also points out a similar problem concerning the originator of monads. On the one hand, Leibniz appeared to have said that the individual monads were emanations from God as the original monad, which should thus be nothing but the truth behind the individual monads. On the other hand, Leibniz also seemed to speak of God as something distinct from concrete monads and thus completely unlike them or a mere abstraction. Leibniz’s most famous work, Theodicy, tried to sort the notion of God, but in the eyes of Feuerbach, it managed merely to confuse things more. In that book, Leibniz tried to give a philosophically respectable account of God, but at once applied also theological notions, like God’s wisdom and goodness.

For theology, Feuerbach explains, God is a being just like us, but just way more powerful: God of a theologian lives outside us and thus in some place and is therefore finite. For the theologian, God is infinite only in being free and separate from the world and in having purely arbitrary capacity to choose what is good and righteous. For philosophy, Feuerbach insists, world is a necessary product of God, while for theology, the world is a contingent creation of God. Feuerbach explains this distinction further by saying that theology takes the practical standpoint of will and philosophy the theoretical standpoint of reason. Practical standpoint belongs to a living, contingent individual, while the theoretical standpoint is something that an individual requires great effort to reach. In theory, Feuerbach continues, we regard an object objectively or for the sake of the object itself, while in practice, we regard it subjectively or for our own sake.

As belonging to the theoretical standpoint, philosophy tries to learn the essence of all things and to perceive the infinite as infinite, while religion, belonging to the practical standpoint, perceives infinite from the standpoint of finite – in other words, it perceives God in its relation to humanity. Theology then makes the norm of religion into the norm of knowledge and turns God into a personal being. A true mediation of philosophy and theology, Feuerbach thinks, would recognise their differing viewpoints by showing that theology regards God practically as goodness, but trying to combine these two conflicting standpoints would lead to mere ridiculous monstrosities.

Feuerbach sees Leibnizian theodicy as an example of such a monstrosity. Leibniz started from theological properties of God, like righteousness, and restricted them through reason. Thus he created as an amalgamation of the concept of necessary (what the essence of the world is for reason) and the concept of contingent (what the existence of the world is for religion) the concept of moral necessity, and then announced that the world, as created by God, was morally, but not metaphysically necessary. A further monstrosity, Feuerbach notes, lies in the fact that Leibnizian God appeared to be just a name for the intrinsic ordering of monads, realising their inner possibilities of connection, but also an external power apart from monads.

Moving to the topic of self-conscious souls or monads, Feuerbach states that Leibniz started from the Cartesian viewpoint, believing in innate principles, such as the principle of contradiction and the principle of sufficient reason, and therefore opposed Lockean empiricism. Feuerbach notes that Locke had been correct, if innate principles were regarded in a literal sense, as principles readymade in the human mind, but Leibniz was correct in the sense that they should be regarded as necessary potentials of self-consciousness. In the Lockean sense, Feuerbach continues, nothing is innate to our mind, except a hunger to fill our mind, yet, even this hunger already presupposes that the mind can be filled with something and has thus some innate capacities. Empiricism does not recognise this truth and thinks it can derive all knowledge from sensations. Yet, Feuerbach retorts, the possibility of sensation is already one capacity of consciousness and thus a form of thinking, although not yet self-conscious thinking. Furthermore, he continues, although humans do sense, they also have a theoretical capacity to use senses as means for thinking.

Feuerbach does congratulate empiricism for emphasising the role of ordinary consciousness and for freeing the human spirit from chains of superstition. Still, he emphasises, empiricism has forgotten its limits and made conditioned or empirical consciousness into unconditioned, while even Leibniz and after him Kant and Fichte had understood that self-thinking is essential to spirit.

In the concluding chapter of the book, Feuerbach characterises Leibnizian philosophy as idealism. Its basic idea was that soul was not a particular kind of substance, in addition to material substance, but that all existence was activity and thus soul-like, while matter was just something caused by limitation and differentiation of monads. Feuerbach immediately adds that there are many other kinds of idealism. Indeed, he believes that humankind has been idealistic from its very steps and that even materialism is really idealism: although materialism denies the existence of soul or spirit, the matter it speaks of is not an object of senses, but of thinking, and spirit can really think only of itself.

The historically first standpoint of idealism that Feuerbach mentions is poetic or anthropological idealism of the renaissance philosophers, where humans did not separate themselves from nature and saw life everywhere. The second standpoint after that Feuerbach calls the standpoint of reflection, where humans separated themselves from natural things, which they regarded as the other of spirit or as mere dead matter. The problem in this essentially Cartesian standpoint was the required mediation of the spirit and the matter.

The solution for this dualistic problem would be, Feuerbach says, finding differences and gradations in the spirit itself and taking this principle of self-distinction or representation as a link between the spirit and the world – this was essentially what Leibniz did, when he regarded monads as mirrors representing the universe. Feuerbach admits that materialists might take Leibnizian idealism as mere subjective idealism, which would try to look at nature through human lenses. Feuerbach answers the materialists by saying that other living beings beyond humans also have their own forms of representation and that even the seemingly inorganic nature truly might be an aggregate of organisms, although imperceptible ones, since we can observe small animals through a microscope.

Going further to deficiencies in the Leibnizian system, Feuerbach notes that it was still tainted by the dualism of his time. This dualism appeared firstly in the conflict between religion and philosophy. At the beginning of the modern time, Feuerbach says, philosophers restricted religion to their personal lives: true in philosopher’s life, he insists, is what has importance to others or their public writing, and thus the personal faith of thinkers like Descartes and Bacon is of no importance. Ultimately this estranged marriage of reason and faith could not last, but led to either antireligious attitude of freethinkers or to scepticism toward reason, combined with a devotion to faith, as exemplified e.g. by Pierre Bayle.

Leibniz had to live during this time of strife and was therefore forced to divide his loyalty between reason and faith. A good example of the influence of theology, Feuerbach notes, is Leibniz’s idea of God as an all-powerful entity who can choose anything, not restricted even by reason or morality. Such an idea of God as a demonic, arbitrarily free decision maker was, on Feuerbach’s opinion, already vanquished by Spinoza, who purged divinity from all anthropomorphism, although in a very grey and lifeless manner. Leibniz, on the other hand, could do it only partially and thus remained like Tycho Brahe between two systems

Feuerbach continues that Leibniz lived also in a time of dualism of spirit and matter, which inevitably led to mechanistic understanding of nature. Indeed, Leibniz himself was a mechanistic thinker and said that even the soul was another kind of mechanism. Furthermore, he related soul as a simple substance to body as a complex substance in a mechanistic manner: he regarded them as two distinct and separate entities so that the material world works with its own laws, without any sign of soulfulness. Leibniz did explain, Feuerbach admits, that the material world was just a phenomenon or appearance of monads, but like mechanistic atoms, monads were completely separate and in no intrinsic manner connected to one another. Although Feuerbach considers it good that Leibniz did this separation in order to emphasise that soul is always active and never controllable by external forces, Feuerbach thinks it was a failing on Leibniz’s part that he did not see that spirit could be described elastic in the sense that it retains its independence when and even because it interacts with others.

Continuing with this criticism from another angle, Feuerbach notes that the universe does not just individualise and distinguish, like monads were individualised in the Leibnizian systems, but also connects things. Indeed, he immediately adds, paradoxically, the more individualised objects are, the more similar and indistinct they seem: all water drops look the same. Thus, he finally concludes, it was necessary to move away from Leibnizian polytheism to transcendental idealism, where individual quirks of monads or souls were subjugated to more general ideals of morality.

Lubwig Feuerbach: History of newer philosophy (1832)

When we first saw Feuerbach, the overwhelming impression was that his ideas were very close to what Hegel himself had thought. This impression does not change when reading Feuerbach’s Geschichte der neueren Philosophie, a work of a history of philosophy. Although the topic of the book is the philosophy of modern philosophy, Feuerbach does give a short summary of ancient and medieval philosophy. Thus, beginning from pre-Christian times, he notes that then state, religion and art formed an organic unity, but only a particular unity for particular people. This particularity was universalised in the philosophy, but as philosophers were still individuals of their own nation, this universalisation remained only ideal.

A realisation of this ideal, Feuerbach says, was Christianity, where Christ symbolised the awareness of humanity being divine and of reason becoming flesh – that is, each human having a universal reason. While Christ as such was still an individual, his death enabled anyone to understand their own divinity. Still, in the Christian religion, this new truth appeared only as an immediate belief to Christ as the road to salvation and to God as the father of all humanity. Furthermore, this belief was still only spiritual and the church denied that it had any relation to the world.

This antiworldly attitude, Feuerbach thinks, led to the dismissal of sciences and to the fall of the Roman empire. Nature was especially ignored, except as a means for God’s purposes. Thus, light of natural reason was replaced with light of devotion or only faintly reached the minds of mediaeval thinkers through the lens of Aristotelian philosophy, which was adapted to the needs of religion. Some philosophers did study nature, but it was clearly a distraction from more important matters. Hence, the only science left was theology, which studied the content of Christian faith. Still, even in scholasticism, thought became its own object and theology turned so into philosophy, but only stiltedly, as formal logic. The church also literally conquered the world by becoming a worldly power battling with states and repressing sciences. Yet, Feuerbach thinks, the scholastic endeavours at least led to a certain autonomy of reason or thinking, which even in its most fruitless controversies showed an interest to rationally test the tenets of faith. Similarly art, which at first served church, became autonomous endeavour interested in beauty as such. The religious spirit that acted negatively toward the world thus led naturally to modern universal and scientific spirit.

This new spirit awakened at first, Feuerbach suggests, as protestantism, which affected a liberation from external authorities and hierarchies to free communal life. Luther endorsed the principle, Feuerbach thinks, that what I believe in exists and also initiated a scepticism toward dogmas of Catholicism. In protestantism, Logos became truly flesh, not just within the mind of a believer, but as the world spirit. By simplifying religion and removing historical additions from it, protestantism freed room for thinking to move to scientific endeavours.

At first this new scientific spirit appeared, Feuerbach recounts, as a study of external material, that is, the arts and sciences of the ancient world. Thus, only through reproduction it could step toward spontaneous production. Nature was then once more taken as an essential object of study, with experience of the whole of humanity as the key method of research. Only with the start of the modern age begins the interest in natural or experiential sciences, which are an expression of the freedom of thinking. Experience is not just naive perception, but an interest in nature, generated from sceptical distrust of all presuppositions. While Descartes with his doubt of everything, Feuerbach says, was then the spiritual father for the standpoint of experience, Francis Bacon was the immediate or sensuous father, who gave the experiential sciences their method, and from him Feuerbach begins the tale of the modern philosophy.

The importance of Bacon’s philosophy, for Feuerbach, lies in taking experience as the primary object of study, while earlier it was just of random interest, although he managed to merely explicate the experiential method, but not really apply it to any topic. Experience for Bacon meant a combination of thinking and perception and it was to be used as means for the goal of philosophical knowledge, that is, finding forms of each thing: Bacon’s example of such a form was warmth as expansive movement. Through the idea of such materialised forms, Bacon managed to liberate philosophy from scholastic abstractions, and for this reason he was taken solely as an empiricist, although his notion of experience also included the use of thinking.

Although Bacon was more of a traditionalist when it came to notions like soul and God, Feuerbach considers his philosophy as a route from mediaeval scholasticism to Hobbesian materialism. Just like a student coming from school to real life, he says Bacon opposed mediaeval philosophy, which went beyond nature and sensuous reality to mystical intuition of divinity and to scholastic consideration of abstractions, and took material and sensuous as the proper object. It was just natural, Feuerbach thinks, that entranced by sensuous reality humanity would be interested in materialism. This materialism was then embodied in Hobbesian philosophy, which had nothing self-moving and was thus no real system. Indeed, Feuerbach says, it was just a mechanistic, lifeless machine, where everything was finite, relative and conditioned, but although it was lifeless, it was still a necessary step in the development of philosophy.

This mechanistic nature of Hobbesian philosophy can be seen, Feuerbach thinks, in his understanding of thinking as a mere mechanical operation. Similarly, nature for Hobbes was not living and his philosophy of nature was mere philosophy of moving bodies and especially their quantities: movement of bodies was not immanent to them, but only caused by movement of other bodies, while sensuous qualities were just phantasms caused by bodies having an effect on subject. On Feuerbach’s opinion, Hobbes was right in thinking that motion was the principle of nature – even Aristotle knew that – but his fault was to restrict nature only to one type of movement, namely, mechanical movement, where mathematics prevails, but quality and life are missing.

Just as little as about life, Hobbesian philosophy knew about soul and spirit, Feuerbach insists. Thus, instead of psychology, Hobbes could speak only of anthropology and the only basis of his ethics could be a sensuous individual. Hence, when Hobbes spoke of will, he meant only sensuous desire and even this as something determined and dependent and object of this will or good could be only individual and relative.

Feuerbach continues that similarly, state could be for Hobbes only something generated either by oppression of individuals or by their free contract. The Hobbesian state presupposed a free state of nature, while the state itself was violent oppression and external combination. Thus, although individuals became citizens in the state, they still in a sense remained outside and independent of it and merely forced to submission – while in the condition of nature everyone had been free, in a state, the natural freedom lied only with the ruler. For Hobbes, right meant only natural freedom, while the state merely restricted this freedom. The supposed aim of the Hobbesian state was the wellbeing of people, but it did not improve the quality of humans, who essentially remained similar animals as in the state of nature.

In other words, Feuerbach concludes, Hobbesian state did make good and bad absolute by making one will universal, but this universalisation was based on mere arbitrary choice. State truly is a unity and morality and reason exist only in state, Feuerbach says, but with Hobbes this unity was not organic, but merely based on exclusive will. Hobbesian universal will was just formal and its content or morality was completely arbitrary. Hobbesian state did nothing to the individuals or did not educate them to be true citizens, but merely preserved them, as they were in the state of nature.

After Hobbes, Feuerbach next considers Pierre Gassendi, whom he regards important mostly as a restorer of Epicurean philosophy, but not as an independent thinker. In his methodology, Feuerbach thinks, Gassendi fell to the mistake of all empiricists that true universality cannot be really discovered through individual instances. Instead, Feuerbach insists, we as individuals can jump to universality only through reason. Thus, as an empiricist Gassendi couldn’t even explain where humans received the ability to make deductions.

Feuerbach also sees Gassendi’s theory of atoms as full of contradictions. Gassendian atom should have been simple and independent, but according to Feuerbach, we can only think of a group of atoms. As simple, the Gassendian atoms could be distinguished only through their movement, which should thus be implicit to them, but Gassendi thought they needed God to move them. Feuerbach notes that combinations of atoms should be accidental, while atoms should be eternal, but Gassendi still suggested that God had created and ordered them. Feuerbach makes the colourful analogy that Gassendi’s philosophy also externally combined in the void of Gassendi’s head independent and even contradictory things: physical system of atoms and theological notions like God and immortal soul.

Gassendi’s philosophy was, in Feuerbach’s opinion, an example of how unsatisfactory empiricism ultimately is. From this dedication of the external, he continues, philosophy moves to the internal with Jacob Böhme, who mystically saw God as a conscious, living spirit. One might think that this idea had been common to all Christian thinkers, but Feuerbach insists they had not really understood what that means, except implicitly in the idea of a trinity. In other words, they had not understood that God themselves also contained negativity and self-differentiation and was not just negative to nature. Although Feuerbach admits Böhme to be a muddled thinker, he is clear about Böhme’s basic idea: spirit, consciousness, life and sensation are born through self-doubling and opposition, where the opposite is still essentially identical with what it opposes. Purified from mysticism, Feuerbarch says, Böhme is seen to simply describe the nature of self-consciousness, which is the basic idea of Cartesian philosophy.

Descartes famously began his philosophy with doubt, and while this doubt may seem a mere subjective beginning, Feuerbach thinks there is an important reason why Descartes had to choose that beginning: the self-conscious I could find itself only through doubting and by separating itself from e.g. sensuousness. Descartes saw that even if I doubted everything, I could not doubt my own existence, because I was the one thinking these doubts. Existence of mind was then the principle of Cartesian philosophy, while everything distinguishable from mind or object was doubtful and less real. Cartesian doubt, Feuerbach concludes, was then not just doubt, but distinguishing oneself from objects. Mind at this point in history meant just this self-distinguishing from objects and denial of their reality, while existence of self did not mean sensuous existence that would have made it doubtful, but just thinking or consciousness. Feuerbach points out that for Descartes, cogito ergo cum was no deduction, and that therefore Gassendi missed the point when he insisted that our existence could be deduced even from our sensuous existence: in cogito ergo sum, Descartes was describing the essence of self-consciousness.

Cartesian mind was then a self or I as a self-relation distinguishing itself from body, Feuerbach states, and although Descartes himself did not understand it, doubt and cogito ergo sum formed the essence of the mind: living distinguishing oneself from bodies and the resulting self-certainty. Immateriality is then not the essence of mind, but only the result of this distinguishing, that is, we are immaterial, because we distinguish ourselves from bodies. The fault of Descartes, Feuerbach suggests, was to think that mind is only such self-relating subjectivity, which makes the opposition of mind and body permanent.

Feuerbach continues the exposition of Cartesian philosophy by recounting how the mind knows itself certainly and has in clarity and distinctness a criterion for certainty. Yet, as Descartes added, this was a criterion only for certainty and not for knowledge and truth. In other words, the Cartesian mind or soul could not know whether bodies exist, except through the medium of certainty of absolute reality or infinite being without any opposition. Feuerbach suggests that Descartes confused this infinite being with the popular idea of God: without showing how self-consciousness could be developed into objective thinking of ideas he just found an inborn concept of God that he thought had been implanted by God himself.

Descartes used here the ontological proof of God’s existence. He began from the idea of God, which should not have been just a necessary and universal idea, but also the most real and thus distinguished from all other ideas. Idea of God, Descartes said, contained only necessary existence, so that in thinking God we were necessarily thinking of their existence, while with other things, ideas were distinct from their existence. Feuerbach notes that this Cartesian proof of God is not really a proof, but an immediate grasping of God’s existence. Furthermore, God is not the starting point for the certainty of our cognition – this is our own self-thinking – but its perfection or objective authorisation. In other words, Cartesian God merely authorised as true what we as subjects already had regarded as certain.

Feuerbach notes that nature was the most interesting object for the Cartesian mind, because it was distinguished from the mind as being a mere object. Thus, it was inevitable, Feuerbach thinks, that Descartes regarded nature as mere matter. Certain in this Cartesian notion of matter was not what we sensed or qualities, but extension or intuition of externality, which as an abstraction from sense qualities was a further affirmation of our self-certainty. Indeed, Descartes allowed in physics only geometry, where bodies were not regarded through senses or imagination, but through intelligence. The main defect of Cartesian philosophy of nature, in Feuerbach's opinion, was that he made matter completely inert and thus was unable to show how movement could develop from it: that is, he thought God had imparted motion to matter, although matter itself should have had an urge to move. Still, Feuerbach admits, Descartes at least managed to start modern physics, which in its fundamentals still follows Cartesian ideas.

With God, Descartes found the opposition of mind and body removed. Yet, Feuerbach insists, Descartes failed to show their unity without the help of God and therefore mind and body remained in his philosophy completely separate. Thus, they could form no organic unity, although he inconsistently accepted their unification from experience. This fault in Cartesian philosophy was caused, Feuerbach suggests, by his seeing mind as mere distinction from body, and following old metaphysics, as a mere simple, immaterial unity. Since Descartes regarded only mind as living, he saw animals as mere machines and also human bodies as mere automatons.

After Descartes, Feuerbach turns briefly to Arnold Geulincx, who, he thinks, developed Cartesian philosophy into its logical, but one-sided conclusion. Geulincx, as the founder of the so-called occasionalism, suggested that the interaction of the mind and the body was reliant on God doing continuous miracles. Relying on wonder as an explanation, Feuerbach says, means really that there is something definitely wrong in one’s fundamental concepts. With Geulincx, like with Descartes, this basic fault was the assumption that mind was just a knowing self in separation from matter.

Feuerbach sees Nikolaus Malebranche and Baruch Spinoza as the true fulfillers of Cartesian philosophy. Mind as simple self, distinct from matter, was the principle of Cartesian philosophy, and the opposition of the mind and matter was resolved only through infinite being, which provided for Descartes the only certainty of the existence of things and truth of representations, but ideas as immaterial objects could not really have any connection with material things. Malebranche, Feuerbach suggests, took the next necessary step that because the mind as just an affirmation of oneself could not develop any ideas of external things and even less matter could make itself visible to mind, we could perceive things only in God and our ideas were really ideas of God. While Descartes contradictorily thought that spirit could move its body through pineal gland, Malebranche understood that only an omnipotent infinite being could achieve this. Like Descartes, Malebranche immediately confused this solution with theological notions, although implicitly God with him was the unification of all minds and the true cause of all individual material movements.

Feuerbach thinks that Malebranche’s philosophy did not just bridge the opposition of mind and body through God, but also saw finite minds as aspects of God. Then again, because of his theological leanings, Malebranche did not understand this and spoke only of individual minds as different from God. Thus, when Malebranche insisted that we cannot know, but only feel ourselves, he was speaking merely of individual humans. God was then for Malebranche just the universal reason which went beyond mere individual humanity and where we could see universal ideas. Extension, particularly, was a universal idea common to all humanity, while sensations filling it belonged only to individual humans. Both individual soul and material objects were in Malebranche’s philosophy dark and obscure objects that we saw only in the light of universal reason. Feuerbach concludes that while God is the spirit or reason in us, Malebranche confused this with theological notions, for instance, by saying that God let us see things because of his goodness. Furthermore, because Malebranche’s God was immaterial, nature remained outside them as a negation of God: true, nature was seen in God, but only in an idealised manner.

Malebranche was already on his way from Descartes to Spinoza, since he emphasised the still just subjective middle point of Cartesian philosophy or God. While with Malebranche the mind and the matter still had objective reality, he at least raised the importance of God as the unity of minds. Yet, Feuerbach notes, beyond Malebranche’s God still remained the material world, although it already was under the power of God. The next step is then to make nature into a mere modification of God, which was achieved in Spinoza’s philosophy: last system dealt in Feuerbach’s book.

Feuerbach returns for a moment to Descartes, who already admitted that God was really the true substance, because other things were dependent on them. Still, Descartes had regarded matter and mind as substances in the sense of having distinct attributes or extension and thinking. Thus, Cartesian matter and mind could be thought independently of God’s concept, although they were in their existence dependent on God: Feuerbach thinks Descartes the philosopher and Descartes the theologian contradicted here one another. Instead of relying on such external notions like creation, Feuerbach suggests Spinoza improved the equation by showing that God was internally necessary for matter and mind by making the two mere attributes of God. Spinoza also saw matter and mind as independent of one another, but just by this independence they showed themselves to be mere aspects of one substance: what was positive in them was not their opposition, but substance. Spinoza’s substance thus solved all the contradictions involved in Cartesian dualism of matter and mind. Individual bodies and spirits were then mere limitations of matter and mind as such, which were the only positive thing in these individuals. Spinozan substance was so the necessary consequence of the notion of God as the highest reality, which could have no personal existence in addition to it.

Like Descartes, Feuerbach notes, Spinoza used the ontological proof to show the existence of his substance. Feuerbach notes that Kant would not have accepted Spinoza’s conclusions, because according to Kant, through mere thought one cannot arrive at existence, which would have required sensations to confirm it. For Spinoza, Feuerbach adds, this objection would have been beside the point, because sensuous existence was for him just unreal, finite and ultimately negative existence and substance as mere object of thought still had more reality than determinate things. Feuerbach notes that again the form of argument is misleading and describes just how we individual minds can come to know the true reality behind finite entities.

Feuerbach explains that matter was necessarily an attribute of Spinozan God, because both were infinite. Individual bodies were then mere limitations of extension, which as such had no negativity and was thus a cause of itself. Sensuous extended bodies were divisible, but matter as such was simple and thus indivisible, unified and unique existence. Matter expressed thus the essence of God, but was still only one attribute of God, since God expressed itself also as thinking. Indeed, Feuerbach notes, Spinoza spoke of an infinity of attributes, although we humans knew only of two of them. Thinking and extension differed and thus in their difference were unreal, but this duality seemed arbitrary to Spinoza and thus in need of increase to infinity. Yet, Feuerbach thinks, this arbitrary nature of their opposition was just a defect in Spinoza’s philosophy, since determination should be more than just negation.

Feuerbach thinks that it would be an inappropriate, theological question to ask how finite things were generated from Spinozan infinity. Indeed, Feuerbach says, really true for Spinoza was only infinite existence and finite things had only a negative existence or existed as mere modes of substance: substance did not temporally precede finite entities, but was their internal power holding the finite chains of causation together, while time was just a finite mode of understanding the true reality or God. For Spinoza, all finite things were modes of God, which had thinking and extension as their attributes. Thus Feuerbach explains, Spinoza could conclude that finite things all had body and soul, which were just two aspects of the same finite thing: extended body thought and thinking soul extended itself.

Feuerbach opposes the common idea that Spinoza’s philosophy would be identical with naive pantheism or atheism, where finite is just identified with infinite, because Spinoza has ascribed to God more power and reality than anyone. Feuerbach notes that Spinoza is also attacked for destroying morality, but while he did show that good was mere utility, his morality was still very sublime by making intelligence the highest good. Feuerbach admits that Spinoza did deny freedom of will, but thinks he was no fatalist, since Spinozan God was not determined by anything outside itself. The main fault Feuerbach sees in Spinoza’s philosophy is the one he has already mentioned: Spinoza did not really determine God, that is, he did not explain the difference of thinking and extension, just like Descartes did not explain their identity. True, Spinoza’s God did think, but he did not understood thinking God as a self-developing spirit, which, Feuerbach thinks, would have given Spinoza a principle of differentiation for his substance.

Carl Friedrich Göschel: Monism of thought (1832)

(1784–1861)

Right after Hegel’s death in 1831, the interpreters dashed like vultures to feed on the carcass of Hegel’s system – for what was left of Hegel’s philosophy after his death was certainly not anymore a living, developing organism, but a mere dead corpse that could be used by other thinkers as nutriments for developing their own philosophies. After a while, two broad extremes of Hegel-interpretation rose: the so-called Young or Left Hegelians and the opposing Old or Right Hegelians, the dividing line being roughly determined by the political stances

An example of the Right Hegelianism is provided by Göschel’s Der Monismus des Gedankens, which is a perfect example of an interpreter reading more into a philosopher’s texts than could be gleaned from the text itself. The occasion for Göschel’s text is provided by Christian Hermann Weisse, whose Hegel-inspired book on aesthetics we have considered. Weisse did not even present himself as a pure Hegelian, but wanted to improve Hegel’s philosophy, while Göschel then suggests he wants to defend Hegel against this perceived attack.

Since we have dealt only with a part of Weisse’s suggested improvement, I will go through it in a summarised fashion. Firstly, he had said that he didn’t want to remove anything from Hegel’s logic, but thought it had to be supplemented in a fashion. Logic, Weisse had said, was a science of necessity, so all necessities should be handled in it. Thus, he continued, the final chapter of the logic had to still contain another trivision: logical method, as an undivided continuum of all the previous structures of logic, should be transformed into a differentiated space, which would then be transformed further, through connecting these differentiations into a new process or time.

Now, speaking as a Hegel-scholar, I see nothing to object in the process of developing space and time out of the logical method, as presented by Weisse, since this is in fact how Hegel himself does it. What is against Hegel’s intentions is only the grouping of space and time within logic, on the pretext that logic is somehow a science of necessities, compared with other parts of his philosophy, which should be sciences of freedom, according to Weisse. In other words, what Weisse is saying is that while logic describes what must be, the later parts of Hegel’s philosophy should describe only what exists, because of the free choice of God.

The problem is that Weisse’s notion of necessity is very different from the manner in which Hegel understands the word: of course, Weisse is really using the ordinary notion of necessity, so the confusion is understandable. For Hegel, necessity means in a sense the necessity of connections, in the sense that it is necessarily possible to move from what is described in an earlier part of his philosophy to what is described in a later part. Thus, for instance, once one has discovered the logical method, one can then divide the moments of the method and so form a sort of mental space of them. Of course, since such a necessarily existing possible connection need not still be used – we can freely choose whether to think space after the logical method – this necessity does not in any manner hinder our freedom. Then again, this duality of necessity and freedom occurs in all parts of Hegel’s philosophy and even in logic. What is novel in the further parts of Hegel’s philosophy, as opposed to his logic, is that one can then also find dedicated empirical counterparts for such logical models or concepts discovered through these connections – for example, the experienced, geometrical space.

What Weisse had considered as a necessary outcome of his emphasis on the difference of necessity and freedom is that the next part of Hegel’s philosophy – the philosophy of nature, should have begun with matter, which is something that does not necessarily exist, but is created by God. As something freely created, Weisse had added, matter is something of more worth than mere thinking, and in addition, something thinking can never completely penetrate. Of course, the truly Hegelian counterpoint would be to point out that all Hegel needs is to show that a model of space and time is necessarily connected to a model of matter – something moving within space and time – in the sense that we can, as it were, construct the latter model from the former. This connection of models is then in a sense reinforced by Hegel’s conviction that empirical space and time are nothing but ephemeral sets of relations that could not empirically exist without anything having those relations (that is, matter we can empirically observe). Furthermore, there would then be no question of not understanding what matter is, since the construction of its model just would be this required understanding.

From matter, Weisse had jumped straight to spirit, noting that like nature, spirit must also be something that is not describable by mere logical categories, but also something freely created by God. We probably need not repeat the basic fault in Weisse’s reading, but just in case let’s do it: jump from nature to spirit does not say that spirit would be somehow necessary, but only that a) given a model of nature (a realm of disparate entities), we can move to a model of spirit (a self-regulating process using these entities consciously for its own purposes) and b) empirically natural processes can in some measure be controlled by such a conscious self-regulating process.

Within Hegel’s philosophy of spirit, Weisse had ignored the so-called subjective spirit, mostly because he wanted to concentrate on both objective and absolute spirit, instead. Weisse had envisioned the realm of objective spirit to be divided into parts on language – which Hegel studied in the division on subjective spirit – on state – which Weisse apparently thought to contain almost all of what Hegel had studied in his philosophy of right – and finally, on world history – which for Hegel was only a final part of a study on state. From this short summary it is difficult to judge what Weisse really meant with this division, and the analogy he gives is not that much more helpful: language being like mechanism (perhaps because speaking persons are still independent of one another?), state like chemism (perhaps because persons unite into communities?), and finally, world history like teleology (perhaps because it is supposed to be a process with an end?).

Weisse’s theory of absolute spirit we are already very familiar with. He had begun with truth or science as life of spirit, then proceeded to beauty and art as spirit’s cognition of the external world and finally ended with divinity or religion as the most absolute phase of spirit. I have discussed this part of Weisse’s system (or more particularly, the second division of beauty) in more detail earlier, so I’ll overlook it here.

As for Göschel's critique of Weisse, he clearly knows the Hegelian liturgy, since he can at the right places state some key phrases loved by many followers of Hegel. Thus, when Weisse criticises Hegel of formalism, Göschel can at once point out that Hegel's philosophy is just the opposite of formalism, avoiding mere application of all external schemas. He connects this point at once with the idea that the universal beginning of Hegel’s philosophy particularises itself, thus becoming more determined with its development. Weisse’s supposed improvement, Göschel says, is on the contrary dualist, because it assumes something beyond logical method – content – which the method has to grapple with. All this liturgy has a proper Hegelian meaning – thinking is, for Hegel, an activity that can create content even when nothing else is given and can thus be used to model anything in the empirical world - but it is unclear how Göschel understood these words.

This unclarity becomes clear when we see how Göschel wants to solve the dilemma of necessity and freedom that led Weisse to improve the Hegelian philosophy. Göschel says explicitly that the thinking we follow throughout the Hegelian philosophy is not human, but divine thought – or at least it would be that, if this system could repeat exactly all the intricacies of the world around us. Thus, he says, the world around us is the creation of divine thought and therefore necessary, but there is much that seems contingent for us as mere humans. This is, of course, completely against the spirit of Hegelian philosophy, where the idea of necessary contingency is explicitly endorsed and no divine viewpoint outside the human viewpoint is accepted.

Göschel, on the other hand, is clearly committed to the Christian notion of God. Hence, while he recognises that Hegelian philosophy just begins, from nothing, he at once adds that beginning differs from beginner, thus, that it is God doing this beginning. This does not mean, he explains, that we should begin from God, since then we could never move away from God, which would drive us to pantheism. Similarly, he adds, we should not start from unconscious nature, consciousness or both together, since these beginnings would lead us, respectively, to realism, idealism and dualism.

A further example of Göschel’s tendencies is his choice of example for the supposed cyclical nature of Hegel’s philosophy, where the beginning and end should coincide. This example is the incarnated God that, Göschel says, is both the basis of true human cognition – because according to him, we would know nothing without Christ – but also the end of all human cognition. Thus, moving toward Christ, Göschel says, a person moves, on the one hand, to their beginning, but also to their end.

Göschel moves on to consider the specifics of Weisse’s reimagination of the Hegelian system. Beginning from Weisse’s derivation of method, space and time, Göschel notes quickly – and quite correctly – that actually these three are implicitly present much earlier in the development of Hegelian philosophy than Weisse thinks. Indeed, method is, of course, used through Hegel’s logic, and furthermore, abstract spaces and “times” or processes have appeared almost from the beginning of the logic (i.e. when Hegel starts by pointing out that thinking nothing begins a process – or becoming, as he calls it – which results in a construction of a space of qualities), and the later philosophy of nature really adds just the discovery of empirical counterparts for both of them.

Just like space and time, Göschel says, so is matter to be found already in Hegel’s logic, even if Weisse thought it was something unique to philosophy of nature. Indeed, the move from space and time to something that is spatial and temporal is similar to many moves in Hegel’s logic, where he moves from the thinking of e.g. existence to the thinking of something existent. As Göschel points out, we do a similar movement in our ordinary thought, when we introduce the notion of matter – we perceive something and then decide something or matter must be the basis of these perceptions. In fact, he continues, matter just is a hypothesis of thought and not something thought couldn’t understand. Göschel also suggests that while Weisse saw matter and even whole nature as inimical to thought, nature in its innermost essence really is at least an analogy to spirit – in other words, it is not just a passive receptacle, but an active striving toward self-organisation and even self-knowing. Therefore, it is just natural that matter will next give rise to motion.

Although Göschel at first appears to understand the introduction of matter in a manner faithful to Hegel, he then adds the un-Hegelian point that we should also investigate the genesis of matter or of nature in general, or in the more poetic terms he uses, how the water of thought solidifies into the ice of matter. Hegel really isn’t interested in the question of how things have temporally begun, especially in the case of nature – philosophy, for him, deals with what is present. Göschel, on the other hand, explicitly answers this question by saying that it must have been absolute spirit – in essence, God – that has created matter.

From matter, Göschel jumps straight to the end of Hegel’s philosophy of nature, that is, to living organisms, which are the most spiritlike forms nature can produce. In other words, while the realm of nature, Göschel says, differentiates and solidifies the moments of the fluid process of thought, its forms become more and more unified, in the sense that in the more complex forms and especially in organisms their parts are less and less independent of one another. Yet, even organisms are still no spirits. Göschel, following Hegel, suggests that we could thus call the whole nature sick in the sense that it always dissatisfies the demand of becoming spirit.

Since Weisse ignored the first part of Hegel’s philosophy of spirit – the so-called subjective spirit – Göschel does not say much about it, but he does reprimand Weisse for not taking it seriously. Subjective spirit should be the first step away from nature and still partially linked with nature, and because this necessary first step is missing, Göschel insists, Weisse’s account of objective spirit appears to lack objectivity, which it then has to find beyond thought. It is for this reason, Göschel suggests, that Weisse considers human community or state to be mere means to an end – the world history. On the other hand, Göschel, following Hegel, thinks that world history is just the highest shape of the human community – the court of the whole world.

More sympathetically Göschel relates to Weisse’s idea that language is part of the objective spirit, while Hegel had restricted it to the subjective spirit. In fact, Göschel thinks that logic already as pure thought is some type of language, as the etymology suggests (logos meaning word). Subjective spirit, then, is the place where language is generated, Göschel continues, but objective spirit does have its own language, and the deepest shape of language can be found in absolute spirit, and more particularly, in art.

It is no wonder that Göschel finds Weisse’s account of absolute spirit very wanting, since it is based on the very idea that philosophy and thought is not enough and that there’s something more to be found beyond it. Göschel himself, on the other hand, suggests another way to amend the end of Hegel’s philosophy. In a rather formalistic manner – and in a manner followed by many Hegel-interpreters after him – Göschel takes a bit too seriously the trivisions of Hegelian philosophy and tries to correct Hegel by suggesting a better trivision, thinking he has thus made considerable progress. Thus, while logic is for Göschel the natural first point of the system, the second point should not be the philosophy of nature, but the whole philosophy of creation, dealing with nature (passive beginning), soul (separation of something active from nature) and human spirit (free activity). The third point, then, would be theology, as the study of God. Although he does not explicate this idea more closely, it clearly appears opposed to basic ideas of Hegel’s philosophy – God is not just something completely removed from creation and especially from human life, but merely one form of human existence.

Thomas Carlyle: Sartor resartus (1831)

(1795–1881)

At first glance, Carlyle’s Sartor resartus is a parody of philosophical treatises, especially those from Germans of late 18th and early 19th century. This is suggested by the name of the imagined thinker, Teufelsdröckh (something like “Devil’s dirt”), and his supposed hometown, Weissnichtwo (“Know not where”). Add to this that Teufelsdröckh is meant to be a professor in Allerley (“all sorts of things”) and that his main work – the theme of Sartor resartus – studies philosophy of clothes, and the reader is bound to expect that Carlyle is not taking any of this seriously.

Yet, when Carlyle finally gets to the fictional work itself, an air of depth and seriousness appears. He does make mockery of a scholarly tendency to get bogged down in insignificant details in his description of the historical-descriptive part of the work, where Teufelsdröckh, among other things, spends a whole chapter on the topic of aprons. But the tone of the work changes, when Carlyle turns to the second, philosophical-speculative part of Clothes-philosophy.

Clearly influenced by Kantian thinkers, Teufelsdröckh begins by rejecting the absoluteness of time and space and comes to a conclusion reminiscent of Fichte – there’s nothing as real to be discovered in the world as me. Yet, he immediately continues, it is not as obvious what this me is. His first suggestion is to note that underneath all the clothing, we humans are nothing more than naked animals. Still, Teufelsdröckh at once adds, humans are also spiritual beings, and this especially through their clothes: a judge radiates a certain authority just because of certain clothing. Indeed, without clothes, civilisation as we know it would be quite impossible: for instance, where to carry one’s purse, if not in one’s pockets?

Clothing, Teufelsdröckh says, is something through which a spirit converses with other spirits. In a mystical fashion, he suggests looking through all these raiments of clothing, into the innermost essence of human beings. Here is revealed a mythical conclusion that the whole material universe can be seen as clothing for eternal.

Carlyle interjects at this point a fragmentary biography of Teufelsdröckh, supposedly composed from a collection of his random notes. This biography has its share of fantastical elements – Teufelsdröckh being supposedly a foundling with a possible noble heritage, raised by a pair of commoners as their own. Still, for the most part, the beginning of the story is a quite realistic, if somewhat parodied tale of a German would-be-scholar trying to make a living by finding a patronage for himself.

The biography takes again a more fabulous turn, after Teufelsdröckh experiences a failed romance and starts to travel, apparently meeting world historic individuals, like Napoleon. Yet, Carlyle leaves these external details mostly untold and concentrates on the spiritual development of Teufelsdröckh, who begins from a state of scepticism and desperation (everlasting no), but finds inner strength to resist the fear of a world without meaning. Then, after renouncing himself, Teufelsdröckh discovers the divine or the everlasting yea in the world and has now a purpose for which to produce things.

Returning to the Clothes Philosophy, Carlyle shows Teufelsdröckh praising the simple, self-made leather clothing of Quaker George Fox as the most important point in modern history. In comparison, the official church seems to Teufelsdröckh full of sham priests, whose clothes have become shallow masks with no spirit within. This does not mean that Teufelsdröckh would disregard all religious symbolism in favour of simple adornments. Quite the contrary, he praises symbols in general, which at the same time stay silent or conceal and speak or reveal things, and especially religious symbols, in which the artist behind the symbol has also become a prophet. These religious symbols just need to have behind them the divine or infinite, which uses the symbols as signifying some deep truths.

Two kinds of persons Teufelsdröckh is said to honour: an honest worker, toiling for their daily bread, and a spiritual worker, toiling for the Bread of Life. Best it is, he says, when both are combined in the form of a peasant saint. Although this admission might seem like a praise of a worker, it has its darker side: Teufelsdröckh does not take seriously the Malthusian idea that workers could starve to death if overpopulation continues. Instead, he is more worried that in the current time, when even priests are mere empty cloaks, workers will not be able to find their spiritual bread. The result of this non-existence of religion, Teufelsdröckh says, is that everyone will turn against everyone else, caring for nothing but their own independence, poor perishing from hunger and overwork, and rich perishing from satiety and idleness.

Teufelsdröckh is still optimistic. Even if the dying society is empty like disregarded clothes, at least clothes will carry the memory of the person who used to wear them. He also hopes that the society will at some point be reborn like phoenix, although it is now burning itself up. Indeed, he even suggests that like a snake is already growing itself a new skin, when it discards its old one, something new is already building up in our society - radicals of today already carry the seeds for the rebuilders of tomorrow.

From the current politics, Teufelsdröckh returns to the metaphysical, or as Carlyle says, transcendental level. Teufelsdröckh begins by comparing the notions of miraculous and lawlike. At first noting that science has progressed away from finding divine in miracles and searching it in the regularity of the cosmos and its laws, he continues by insisting that science has still only penetrated a small portion of the infinity of nature. Furthermore, he suggests, if nature is nothing but clothing for the divine - or to take another simile, a book written by God - why should it be just a cookbook full of recipes (i.e. laws of nature) and nothing more significant? Instead of regularities, Teufelsdröckh again wants us to return to appreciating the miraculous in our study of nature. Isn’t a miracle still a miracle, if it appears regularly? And isn't a miracle still a miracle, even if it is caused by internal workings of our mind (e.g. when we appear to see devils and witches)?

Teufelsdröckh goes even so far in his disdain of regularities that he, taking a cue from Kant, denies the validity of space and time, when it comes to metaphysics. Space and time may have to be taken for granted in our every-day life, but when it comes to the divine and even to the capacities of the mind, he insists, space and time are of no relevance: indeed, we can instantly think of things far from us or past or future. While living in this spatio-temporal world, he concludes, we are like ghosts appearing in a physical form, and after our seeming death, we return to the eternal from which we arrived.

Carlyle ends his summarisation of Teufelsdröckh with the consideration of two classes peculiarly engaged with clothes: dandies and tailors. Dandies, he defines, are people whose lives are dedicated to clothing and who thus, in a sense, have an inborn understanding of the philosophy of clothes: a poet making a work of art of themselves. In fact, dandies form, Teufelsdröch suggests, a religious cult with their own dogmas of what to wear and especially what not to wear: a new form of the old superstition of self-worship. As a contrast to dandies, Teufelsdröckh points out the so-called poor-slaves or drudges, whom he somewhat ironically describes as resembling monastic orders in having taken an oath of poverty. If the dandies worshipped themselves, he adds, the drudges worship earth, since all they think is where to get the next round of potatoes. In fact, these two so-called sects are nothing but the two classes of rich and poor, whom Teufelsdröckh earlier envisioned as tearing down the civilisation in their quarrel with one another.

The very last fragment Carlyle has selected to introduce from Teufelsdröckh’s work – before announcing that Teufelsdröckh has vanished from the face of the earth – is reminiscent of the earlier fragment about George Fox as a producer of his own leather outfits. Here Teufelsdröckh consequently praises tailors as sub-creators. Indeed, he suggests, aren’t all creative people in some sense tailors of their own kind?

János Bolyai: The science absolute of space: independent of the truth or falsity of Euclid's axiom XI (which can never be decided a priori) (1832)

 

(1802–1860)

A good example of a remarkable coincidence of two persons having almost the same idea roughly simultaneously is the discovery of non-Euclidean geometries, and more precisely, the so-called hyperbolic geometry. We have already seen how Russian mathematician Lobachevsky approached the idea of not assuming Euclid’s parallel axiom, and we are now about to see the Hungarian János Bolyai do it in his own manner.

One might say that the interest in the parallel axiom ran in the Bolyai family, since János’s father, Farkas Bolyai had for a long time tried to deduce the axiom. Indeed, he had warned his son that the parallel axiom was something younger Bolyai should keep away from, since one could waste a lifetime thinking about it. To older Bolyai’s surprise, younger Bolyai sent his father a short paper dealing with the issue, which older Bolyai published as an appendix to his own textbook on mathematics.

The topic of Bolyai junior’s article is primarily the absolute geometry, that is, a geometry where neither Euclid’s parallel axiom nor its denial is assumed. Thus, just like Lobachevsky, Bolyai is interested firstly in the similarities between the Euclidean and the hyperbolic geometry. Again like Lobachevsky, Bolyai defines as a parallel line to a given line X as that precise line, which is a sort of limit of all the lines drawn through the same point y and not cutting the given line X, in the sense that any line falling from that point y more toward the given line X will cut this given line.

Bolyai also shows, like Lobachevsky before him, that parallelism, defined in this manner, is a transitive relation. Bolyai goes even further and shows that with the parallel lines, the congruence of line segments is also a transitive relation. He then notes that given a line segment AM, one can consider a collection of all such points B that if a line segment BN is parallel to AM, it is also congruent to it. Bolyai doesn’t really give any other name to this collection, but F. In addition to F, Bolyai considers the intersection of F with any plane containing AM, which he calls L, while AM he calls the axis of L. He also notes that F can be described by revolving L around AM. Because parallelism and congruence of line segments is transitive, every line segment BN starting from a point B in L and parallel and congruent to AM is also an axis of L.

In Euclidean geometry, Bolyai notes, this L is simply a line perpendicular to AM - and F, similarly, a plane perpendicular to AM. In hyperbolic geometry, on the other hand, L is not a straight line, but a curved line, and similarly F is a curved surface. Indeed, they are what Lobachevsky called respectively oricycle and orisphere. Like Lobachevsky, Bolyai notes that oricycles in an orisphere work like straight lines in a Euclidean plane.

Now, Bolyai pictures an axis AM move through its oricycle L, always staying at same angle to L. He saw that the other points of the axis AM described further oricycles, that is, taken C from AM would describe an oricycle, for which AC would be the axis. Furthermore, taking corresponding parts of two such oricycles, the relation X of their lengths is always a constant, which depends not on the length of the parts, but only of the distance x of the points on AM. Bolyai also notes that these oricycles are always congruent, although part of one appears to be multiple of the corresponding part of the other.

Bolyai further notes that whether one supposes Euclidean or hyperbolic geometry to hold, spherical trigonometry – that is, study of triangles, as it were, on the surface of a sphere – always follows the same rules. Then again, he adds, with the ordinary geometry the case is quite reversed. In Euclidean geometry, given the length of at least one side of a triangle and at least two other elements of the same triangle (whether angles or sides) are known, the other elements can be solved. In hyperbolic geometry, on the other hand, one has to also refer to some length x, of which the corresponding relation X is known, to make similar calculations. Bolyai suggests using length i, defined by having as the corresponding relation e - the basis of natural logarithms. This length i would then work as a sort of natural unit of length in the hyperbolic geometry.

The intriguing question is then, which of the two, Euclidean or hyperbolic geometry, is the one describing the world we live in. Bolyai notes that we cannot really determine this without any empirical facts to guide us, since neither of the two geometries has any intrinsic flaw in it. This statement goes against the common idea of Bolyai’s contemporaries that Euclidean geometry is somehow inherently intrinsic. As if to just spite such thinkers, Bolyai ends his short article by showing how one can construct in hyperbolic geometry a square equal in area to a circle – something that is impossible in Euclidean geometry.