James Mill, Analysis of the Phenomena of the Human Mind 2 - Yawns and hiccups

The latter part of the second volume of Mill’s book concerns the active or volitional part of the human mind. Mill notes that the cognitive and volitional sides of human mind share the same structure - for instance, volitional side also deals with sensations and ideas. The difference is, Mill suggests, that while sensations of the theoretical part are, in a sense, indifferent to the mind, the sensations of the volitional part are not, being either pleasant or such that the mind would want prolong, or painful or such that the mind would want to stop them. Mill makes it sound like the trivision of sensations would be hard and fast, while one might object that e.g. a sensation pleasant now might become indifferent and even painful, if it has to be endured too long.

Like indifferent sensations, pleasant and painful - or interesting - sensations can also be revived in ideas, Mill says, and such ideas of pleasant and painful sensations are called desires and aversions. This choice of nomenclature seems peculiar. Mill himself points out one possible point of contention: we also say that we desire things like cake, which are not sensations. In fact, Mill says, in all such cases we ultimately desire some sensation, e.g. the taste of the cake. Yet, there is a more important point of contention, because we can think of a pleasure we’ve had without desiring it. Mill offers the explanation that desires are actually only ideas of future pleasures. This explanation seems insufficient, because we could think of future pleasures and still not yet desire them. Indeed, it seems far more plausible to take desire as a primitive concept, especially as Mill’s explanation of pleasures already implicitly referred to it (pleasure is a sensation we would want or desire to continue).

In case of pleasant and painful sensations, Mill continues, we also make associations to their causes. In fact, thinking about such causes might affect us more than thinking of the pleasures and pains themselves. For instance, we might think of a past stomach ache with indifference, but still avoid the food that we think caused this sickness at the time. Mill appears to think that such affections are not just caused, but also defined merely by such associations, which seems again insufficient - surely they also contain the aspect of us wanting to gain or avoid something.

Mill notes that we often have stronger affections toward more remote causes of pleasures and pains. For instance, people often desire wealth, power and dignity more than, say, food. Mill has a quite convincing explanation for this peculiarity: remote causes, like money, allow us to gain more and a larger variety of pleasures than mere immediate causes.

An important subset of affection toward remote causes concerns other persons. In some cases, Mill notes, such affections are awakened by shared experiences and common interests. Then again, he adds, we also have a general compassion toward all humans, because the similarities with them make us associate their pleasures and pains with our own pleasures and pains. The more similarities we have toward some group of people, the more affection we have for them, for instance, in case of people from the same class (in a pre-Marxist fashion, Mill insists that only privileged classes could have such a class consciousness).

Mill touches also aesthetic affections, but unfortunately, not in any great detail. His main point is that we call sensations beautiful and sublime not because of themselves, but because of associations they convey in us. Thus, the humming of a beetle is found beautiful, not because of any intrinsic feature, but because it awakens in us the notion of summer. Because such associations may vary from one person to another, there is no universal criterion of beauty, Mill concludes: black seems ugly in a culture, where it is associated with death, beautiful in a culture, where it is associated with festivities. What is especially lacking in Mill’s account is the explanation what kind of associations are required for calling something beautiful or sublime.

When we have an idea of ourselves as the only possible cause for gaining some future pleasure or for averting some future pain (or some of their causes), we have a motive, Mill defines. Clearly, this definition works only if we assume, like him, that all thoughts of future pleasures involve desire. In any case, motives can work against one another, and indeed, Mill insists, only another motive can prevent us putting one into action. Different people are affected in different measures by same motives, and a particular affinity to some motive is called disposition. Mill notes that in common parlance we often confuse affections, motives and dispositions: thus, we may speak of lust when speaking of a positive affection toward sex (idea of sex as causing desirable sensations), of a motive for engaging in sexual relations (idea of ourselves as instigators of sex) or of a disposition to engage in sexual relations.

In a Humean manner, Mill considers cause and effect to be nothing more than a name for a regular association of certain events. Thus, he sees no problem in saying that sensations cause certain bodily actions - we can say that a pungent odour makes us sneeze, while a certain sensation in our stomach makes us hiccup. These examples might make Mill’s analysis of causation seem suspect, since it seems more likely that in such cases the sensation is not really the cause of the bodily movement , but merely shares with it a common cause (some bodily process).

In any case, because Mill thinks sensations can produce bodily movements, he sees no difficulty in ideas causing them also. In fact, he points out laughter caused by humour or weeping caused by sadness as examples of this kind of causation. Of course, Mill adds, such uncontrolled weeping is still not voluntary action. What is still required is the presence of a desire: when motives make us act, they are called will.

Mill does not then believe in any motiveless will. He insists also that will cannot awaken its own motives - this would be like baron Munchhausen lifting himself from his own hair. This rather plausible suggestion makes Mill go even so far as to suggest that it has no effect on the train of ideas, being just a process of translating ideas into action. Mill considers two possible objections. First is the notion that we often seem to will to recollect something. Mill’s answer is that actually we always only desire to do so. Similarly, to the second objection that we often will to attend to some sensations or ideas, Mill answers that attending means just that we find these sensations or ideas interesting. Mill’s answers seem just verbal confusions, since he admits that the very element that makes acts into acts of will (desire or interest) is involved also in these two cases. One might even rephrase the objections in a manner suggesting that there is a choice involved. Suppose we are attending to something complex, like a bicycle. The idea we have of it has different aspects, and we may then choose to attend to one of these aspects, say, one of the tires. Couldn’t we then say that we willed or wanted to attend to the tire?

Nikolai Lobachevsky: Geometrical researches on the theory of parallels (1840)

 

(1792-1856)

Euclid’s book on geometry has for ages been seen as an ideal of an axiomatic theory, in which everything is based on a solid basis of definitions and evidently certain axioms and proven through strict demonstrations, making the results presented appear indubitable. No wonder many works of philosophy tried to imitate Euclid’s style, to make their theories seem as indubitable and necessary, usually failing miserably to be as convincing as Euclid.

If you know your Euclid by heart, you know that he had not really achieved the ideal many want to see in his book. There are sometimes slight hidden assumptions in his proofs - and isn’t it a bit too empirical to carry around triangles and put them on top of one another (Euclid, I.4)?

The most glaring fault in Euclid’s work is, of course, the infamous parallel postulate. When compared with other postulates of Euclid, it appears complex and far from self-evident: “if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles”. The postulate can be made a bit clearer with some rewording and use of more modern phraseology - if line A cuts two other lines on the same plane, B and C, and the sum of interior angles on one side equals pi (or 180, if you are more into degrees), B and C eventually cut one another on that side and are therefore not parallel. Even with this rewording, it seems like a theorem we should prove, not a postulate to be just assumed.

Many professional geometers and even more geometry dilettantes were equally unimpressed by this postulate and tried to demonstrate it from other postulates. Their efforts led at most to finding other postulates that could replace Euclid’s. Most famous of them is the so-called Playfair’s axiom: given a line and a point, we can draw through the point, at the same plane as the line and the point, only one line that does not cut the first one. This does sound simpler, but still lacks the self-evidency of the other postulates.

Dissatisfaction with Euclid’s postulates and its alternatives continued, but no solution was forthcoming. All of this was changed by Lobachevsky’s seminal paper, Geometrische Untersuchungen zur Theorie der Parallellinien. Well, to be truthful, he had already written papers on the topic in his native language, Russian, in 1820s, but these did not circulate very widely (and in addition, I cannot read Russian).

Lobachevsky’s starting point is the Playfair’s axiom, but instead of just assuming it, he asks what would happen, if there were more than one line we could draw through the point - lines which would not cut the given line. He notes that even then we could find a single particularly interesting one among those non-cutting lines, namely, the limit between lines that do and those that do not, and suggests calling this the parallel line. Then, by tying Playfair’s axiom back to the original framing of Euclid’s postulate (C being the original line, B being parallel to it, A cutting them both and A and B meeting at the given point) and by making the assumption that A cuts C perpendicularly, he notes that in this peculiar setting B and A form an angle less than half the pi (or 90 degrees), thus contradicting Euclid’s postulate. The angle formed by A and B (and dependent on the distance of the given point from the line C), Lobachevsky calls the angle of parallelism.

Although Lobachevsky’s new geometry - later dubbed hyperbolic geometry, although he himself called it imaginary - has clearly different properties from Euclidean geometry, a significant portion of Lobachevsky’s paper is committed to show similarities to Euclidean geometry. The simplest similarity is that the new definition of parallel lines works similarly enough to the Euclidean notion, for instance, parallelism is a symmetrical and transitive relation.

A more intricate similarity Lobachevsky finds through notions of oricycle and orisphere. By oricycle Lobachevsky means such a curve in hyperbolic geometry, all perpendiculars or axes of which are parallel to each other. Furthermore, oricycle is also a sort of limit for circles - by enlarging the ray of the circle indefinitely, in hyperbolic geometry, the curve tends toward the oricycle. In a figurative way, we could say that an oricycle is an infinite circle. Interestingly, the same concept in Euclidean geometry means ordinary straight line.

The notion of oricycle taken into three dimensions forms, then, an orisphere. Technically, an orisphere can be formed from an oricycle by turning it around one of its axes. What is interesting is that oricycles on orisphere work like straight lines on a plane in Euclidean geometry, for instance, in a “triangle” formed of segments of three different oricycles, the sum of the angles equals pi.In effect, two-dimensional Euclidean geometry can be ingrained within three-dimensional hyperbolic geometry.

Although the aforementioned pseudotriangles in hyperbolic geometry do follow same rules as regular triangles in Euclidean geometry, regular triangles in hyperbolic geometry do not. Yet, Lobachevsky points out, when sides of the triangles in hyperbolic geometry decrease indefinitely, the more they start to resemble the triangles in Euclidean geometry, for instance, the sum of their angles approaches pi.An interesting consequence of this is that the bigger the triangles in question are, the more apparent the difference of the two geometries becomes. It becomes then an empirical problem to decide whether we live in a space with a Euclidean or a hyperbolic geometry - just make astronomical measurements of distances between stars and you might notice signs of non-Euclidean properties.

James Mill, Analysis of the Phenomena of the Human Mind 2

Second volume of Mill’s work on philosophy of mind clearly divides into two different parts, and I shall treat the latter part in a writing of its own. The first part continues the discussion Mill started in the first volume, that is, the analysis of common concepts pertaining to human cognition.

The first of these concepts are relational terms. You might remember from my previous post that Mill appeared to accept only monadic predication, which seems, of course, problematic for understanding relations. Mill’s solution is to suggest that relational terms like “parent-child” are actually names for a single phenomenon, consisting of two things. The different names just emphasise different aspects of this same totality. Connected to this notion is Mill’s idea that difference and opposition is necessary at least for such conscious entities as us - we do not really sense or think anything, if there is no change in our sensations and ideas. Together these ideas suggest surprisingly close tendencies with broadly Hegelian philosophers, who view the world as an necessarily interconnected system of oppositions.

Mill goes into great details classifying the various possible relations: difference and sameness of sensations, sensations as preceding one another, spatial relations of objects, temporal relations of objects, quantitative equality and inequality of objects, qualitative likeness or unlikeness of objects, same or different composition of ideas and ideas as preceding one another. A clear fault in Mill’s schema is the ignorance of relations with more than two relata. The closest Mill comes to discussing them comes with spatial relations, as he admits that even the idea of position of an object involves relations to all other objects. Still, even here Mill tries to simplify matters and concentrates on juxtaposition of two objects and such pairs like high and low or front and back.

If we inspect Mill's account of spatial relations in more detail, we find him, in a manner reminiscent of Fichte, reducing the genesis of our experience of space into muscular exertions, by which we move ourselves or things around us. In another sense, Mill’s notion of space reminds one of Leibniz, because just like him, Mill says that space is nothing but an abstraction from all the concrete positions and spatial relations between things. While Kant would object that surely space is prior to positions in it, he might approve Mill’s admission of a subjective element in our notion of space - we always associate a place with a further place, thus making our notion of space infinite.

A further peculiar element in Mill’s notion of space is that when we think of empty space, he insists, we think of something positioned in that space and then the absence of this something. This is a feature of Mill’s general theory of privative statements - he insists that thinking of absence of something, we think of both that thing and its absence (e.g., when thinking of darkness, we think of light and its absence). In case of space, this would mean that by empty space, we always mean space empty of something. Indeed, he confirms, because our experience of space is intrinsically related to the idea of something resisting our efforts, we cannot think of any space empty of everything.

Mills account of time is similar enough to his account of space that we do not have to deal with it in great detail - like space is for Mill just an abstraction of all positions, time is nothing more than just an abstraction from all successions. Reminiscent of Kantian tradition, Mill connects numbers also with successions. In other words, he points out that although numbers are used to count the greatness of synchronously existing objects, the act of counting happens through some successive operation.

Mill also investigates the notion of personal identity, especially over time, and reflection. His basic solution to this conundrum is to point out that personal identity is just a special case of any identity. Identity as such, say, of other persons, we come to know by seeing a person and remembering that we saw her earlier. Similarly, Mill says, we are always conscious of ourselves, remember being conscious of ourselves and hear testimonies of others concerning us at times, which we don’t remember.

Mill’s explanation seems flawed in many ways. Firstly, one might point out that he hasn’t ever really explained what it means of being conscious of oneself, because saying that consciousness in general is just a general name for sensations and ideas explains nothing about self-consciousness - what are we conscious about when we conscious of ourselves? Secondly, Mill’s explanation would at most tell what evidence we use to justify our assertions of self-, or indeed, any identity, but not what it means that something is identical with itself. Finally, while it is undoubtedly obvious that our assertions and experiences of self-identity are particular examples of assertions and experiences of identity, one might wonder, in the manner of Fichte, whether e.g. our experience of self-identity underlies our experience of all other identities (that is, whether we must be able to identify ourselves, before being able to identify anything else).

James Mill: Analysis of the Phenomena of the Human Mind 1 (1829)

In my previous post on James Mill, I noted that he emphasised the need for the study of the human mind as a precondition for planning education. Mill tackles this very topic in his two-volumed Analysis. First volume, which I will be studying now, deals roughly with the theoretical side of the human mind, while the consideration of the practical side is left for the second volume.

Mill’s viewpoint is clearly empiricist and he begins with an assumption of Humean undertones that everything in our experience is reducible to sensations (what Hume would call impressions), ideas, formed on basis of sensations, and groups and trains of ideas, generated from sensations and ideas through association. Starting from sensations, he enumerates the usual smell, hearing, taste and sight, divides sensations of touch into sensations of (moderate) temperatures, sensations of tactile contact, sensations of disorganisation, such as pain or itch, and sensations involving muscular exertion, and adds the sensations belonging to alimentary canal and possibly also to other intestines.

Mill’s portrayal of these various types vary from ordinary to perplexing, latter being exemplified by his insistence that the effects of opium are sensed in the alimentary canal and just strengthened by associated ideas. Indeed, one might argue that Mill should have added a separate class for clearly pleasurable sensations, such as is occasioned by stimulation of various substances and sex. In any case, Mill makes an important remark that when speaking of sensations, at least English has a deplorable lack of distinct words for a) sensation of one kind (say, a smell), b) whatever causes this sensation (also known as smell) and c) the organ for this type of sensation (yet again, smell).

Ideas, Mill continues, are then traces of sensations. While we have some say on what we sense e.g. by changing our position in relation to our environment, he affirms, we cannot control what ideas we will have or think about, because they are generated by sensations and other ideas through association. This association is governed, again in a Humean manner, by habit - if we are used to sensing various sensations or ideas together, either simultaneously or successively, we are bound to think one part of this group when another part is sensed or thought.

Although the account is rather simple, there are some questions that Mill leaves unanswered. For instance, Mill notes that in case of succession we are used to following the train of thoughts to the direction of the process involved: thus, a farmer is used to thinking of first planting the seed and then the seed sprouting. Problem is that we often think such processes in reverse and particularly do so, when looking for explanations, for instance, if we want to explain why plants grow, we think first of their growing and only then the idea of someone planting the seeds. Another problem is that Mill does not point out that there are associations, which appear to be a necessary product of the way we sense - for instance, a combination of colour with extension seems not just coincidental nor even one based on the nature of things sensed, but on a fact that we cannot sense coloured things, which are not extended.

Such groups and trains of ideas can, then, form a single idea out of many individual ideas, Mill says. Thus, since we are accustomed to sensing, say, a distinct rosy smell with a certain kind of sight, we tend to think of them as a single unit (a rose). Similarly, temporal trains of ideas should form complex ideas of processes.

The purpose of language, Mill suggests, is merely to communicate to others or to our future selves these various sensations and ideas, either individually or as complex trains of thought. Later on, he adds another purpose for the language, that is, making it possible to think of such otherwise difficult ideas like a polygon with hundred sides. This seems a very limited understanding of the purposes of language. Particularly, this appears not to note that sentences of a language are meant to indicate e.g. that something happens or happened, not just that we have sensed or thought something. Mill himself appears to be at least unconsciously aware of this, since he notes that all verbs carry with them the notion of existence. Yet, Mill uses “existence” here in a very strong sense, which makes him instantly think of this immediate connection as a detriment to language - if we speak of e.g. what chance is, Mill suggests, we immediately assume that chance is something existent, namely an individual object. It seems obvious that we need not go so far, in other words, when we say that chance is so and so, we truly affirm something about chance without assuming that chance is an individual existent.

The trains of thought we express in language indicate, Mill suggests, causal relations, relations of resemblance or different names for same things. The third option here is the most perplexing, since Mill includes in it such mathematical statements as one plus one equals two. One might accept this classification in such simple cases, but whenever the calculations become complex enough, it is doubtful that we have any concrete idea to name in both sides of the equation. For instance, can we really say we have a distinct idea of what 1000^1000 is meant to say? What this expression indicates is more like a certain task of calculation (multiply 1000 with itself 1000 times), and the sentence connecting this task to its result indicates a certain relation between numbers.

The remaining part of the first volume is dedicated to an analysis of certain central concepts of human cognition in terms of concepts introduced thus far. For instance, Mill suggests that consciousness means no feeling distinct from sensations and ideas, but is simply a general name for both of them: if I am conscious of something, I either sense or have an idea of it. Although one might agree with Mill that consciousness is nothing distinct from sensations and ideas, one might still ask in the manner of Leibniz whether consciousness - or better, conscious sensations and thoughts - could form a subspecies of all sensations and ideas. Indeed, we might assume that different sensations and ideas have various degrees of consciousness and by moving our attention to one aspect of a sensation or an idea we might become more aware of its components.

Of the concept of conception Mill notes that it simply refers to complex ideas. This is undoubtedly true description of how some thinkers have used the word or similar expressions in other language (say, Begriff in German). Yet, other thinkers seem to use concept and conception only in relation to linguistically expressed notions (thus, a mental image of a bicycle would not yet be a concept, whereas a linguistic expression “bicycle”, perhaps also with a definition of the expression, would certainly be). Related to this is the question whether conception is somehow active in comparison with mere sensation and “having an idea”. Mill suggests that the supposed activeness of conceiving is just a misdirection of the active form “I conceive” and that conceiving is as passive an event as dreaming or dying, which can also be expressed in an active form. While Mill’s point is well made, it could be that when philosophers have spoken of the activity of conception, they might have actually meant the relative independence of conceptions from external objects. After all, we can conceive things that do not exist, especially if conception is understood in a linguistic manner.

In case of imagination, Mill goes even farther in his redefinition of words and suggests that imagination is just a new term for having a train of ideas. This seems to go against all ways the word has been used. In an early modern discussion, imagination was closer to what we would nowadays call memory, meaning thinking of anything that isn’t currently present, even if we have perceived it earlier. Nowadays, we are mostly using imagination in the sense that Mill disparages as Dugald Stewart’s redefinition of the word: that is, imagination is a train of new thoughts. “It is implied in every wish of the child to fly”, Mill says, trying to be sarcastic, but we indeed speak of imaginative kids as having such inventive thoughts, often divorced from reality.

Especially confusing is Mill’s discussion of belief. He at first divides belief into three distinct classes: belief in events and real existences, belief in testimony and belief in the truth of propositions. Later he makes a reclassification, saying that belief in testimony is just a special case of a belief in events (those told by other people). Nowadays, many philosophers might want to classify all beliefs as concerning propositions, because the content of belief can be expressed as a proposition. On a closer look, Mill himself might agree, because he thinks that one part of beliefs in propositions, those concerning individual objects, are essentially beliefs in events and real existences (he would just have to make the assumption that all such beliefs can be expressed in propositions). This still leaves the problem that Mill’s account of propositions is too simple, allowing in principle only monadic predication - a problem we already saw in the case of his idea of mathematics.

An even bigger problem lies in Mill’s attempt to describe belief merely in terms of sensations, memories, associations and abstractions. For instance, he says that in the case of sensations and memories, belief means simply having them - if we sense something red or have a memory of it, we believe it. These cases already seem problematic. If Mill means just that having a sensation or having a memory is such an experience we can never doubt, we might accept that this is true, but this is, for the most part, not a very characteristic way to speak of belief (one might even say that only philosophers say things like “I believe I have a sensation of redness”, whereas usually people use the concept of belief only in cases where there is at least a possibility of things not being so). If, on the other hand, Mill would want to use the notion of belief here in a more substantial manner - say, as a belief that there is something that causes this sensation of redness or that there was something that I now remember as red - then we immediately see that belief is definitely not identical with sensation or memory. True, sensation and memory might well be evidence and occasion for such a belief, but there might still be doubt e.g. whether what we remember really was red and not blue.

Mill’s mistake is even clearer in his supposed examples of belief. If we spin around very fast and stop, we get the feeling of the earth spinning beneath us. Mill suggests that we also believe that earth is really spinning, which seems far-fetched. Even more, Mill makes a quick throwaway line that fearing something implies also believing in it - hence, he says, anyone who is afraid of ghosts must believe in them. A quick consideration makes Mill’s statement seem unfounded, even if he thought it so self-evident to need no justification. Picture a person hearing a strange noise in her house during the night. She might be afraid that there is a burglar in her house, but she might still be uncertain whether there is any burglar and thus not really believe in the existence of this burglar.

Indeed, Mill appears to make no distinction between modalities of actuality and possibility, belief being intimately related to the former - we might consider e.g. a sensation or memory, without being sure of its object being real. In the more complex cases, he says that habitual associations just are beliefs - if we tend to think of the sun rising after it has set, we believe that it will rise again after setting. Again, this regular or habitual association might be a ground for believing something, but there are cases where we might still have doubts, whether e.g. the sun will rise everyday for the whole infinity of time.

This is not to say Mill’s book is completely without merits. His account of abstraction is particularly interesting. Mill’s basic point is the difference between what calls notation and connotation. A word like “red” notes a certain property of individual objects, but it also connotes something, namely, those very objects that can be called red. In more modern terms, we might say Mill is here talking about the difference of intension and extension. Abstraction, then, means that we ignore the connotation of the word and think only of its notation: we think of redness without any reference to red things. Mill’s point is that abstractions are then nothing truly existent, but always dependent on the ignored connotation - there is no Platonic redness floating around without red objects.

Günther, Anthon: Preschool to speculative theology of positive Christianity. Second part: Theory of incarnation (1829)

 The first part of Anthon Günther’s work began with the theoretical problem of describing the nature of God and his relation with nature and finite spirits. Günther opposed modern pantheism, which tried to put God on the same level with finite entities. He insisted that divine self-consciousness is on a completely different level from human self-consciousness, where the former involved God positing its own substance as an object (Logos) different from God as subject and noticing the identity of itself as object and itself as subject as a third entity (divine Spirit), while human self-consciousness could note its own dependence on this interconnected trinity of entities. At the end of the first part, Günther hinted that we could still learn more about divinity through our conscience, which he suggested was a direct pronunciation of divine existence to humans.

The second part of the book engages this very topic of human conscience. The setting of the first part - a theology student exchanging letters with his uncle, a mouthpiece of Günther - continues in the second part, by nephew presenting to his uncle the problem of evil. Nephew notes that because modern pantheism denies freedom of human will, it has to accept that evil is just a necessary aspect of human consciousness, which could be overcome only by returning humans to the unconscious existence of animals. In effect, nephew insists, this would mean either that the devil is equally strong as God or that God himself is also the source of evil.

To make his point, nephew picks out two recent philosophers who had discussed the question of evil. First of these is I. H. Fichte, whom we met in the first part of the book and who was the son of the more famous philosopher, J. G. Fichte. Fichte’s ideas on evil begin from the Kantian notion that humans have an innate and inexplicable predisposition toward evil, which hinders the freedom of our will. Fichte tries to explicate this notion further by suggesting that the universality of evil requires that we must assume an inexplicable, supernatural, destructive principle as the source of all evil - that is, Fichte endorses dualism. Furthermore, Fichte assumes that humans have had to decide between the creative principle or God and the destructive principle, temporal existence in separation from God being the result of a wrong choice. Nephew points out that the idea of a pre-temporal choice releases temporal human consciousness of all responsibility for their life choices. In addition, he notes that this idea of temporality as a result of corruption is in contradiction with another theory of Fichte’s, namely, that of God revealing himself through human spirits.

As his second example, nephew chooses Bernard Heinrich Blasche, better known as a pedagogue. In his more philosophical works, Blasche endorses a panentheist position, where God is the point of unity of the world, finite entities being just necessary self-particularisation and differentiation of this unity. Evil means for Blasche simply separation from original unity, being thus a mere intrinsic development of a possibility inherent in God himself. In effect, nephew concludes, Blasche simply identifies God with the devil.

Uncle agrees with nephew that the two philosophers fail to explain the true origin of evil. He sees Fichte as ultimately being committed to pantheism, because of his notion that individuals are just revelation of God, which means that they can never truly be separate from God and therefore cannot be evil. Blasche, on the other hand, ultimately follows the trend set by Schelling, whereby freedom is swallowed by necessity. In an interesting side remark, uncle notes that his contemporaries do the very same thing, when they explain bad decisions of individuals by differences of temperament and bodily influences.

With the options of the eternal dualism and the interpretation of evil as a modification of good ruled out, it is up to the nephew to come up with a third option. The only solution left, he thinks, is that evil arises from the level of finite entities, being thus something that is not a necessary part of existence. For instance, he concludes, in the original state, as intended by God, humans were not evil, but they became evil, when they opposed divine will and made their own interest into their highest law. Yet, this solution begs the question: how could a human, made perfect by God, fall into evil?

Nephew tries to find the answer from the works of a noted theologian, August Tholuck. Tholuck had insisted, firstly, that God couldn’t have given human a predisposition toward evil. Yet, Tholuck had noted, humans had an ability for evil in the sense that being evil wasn’t in contradiction with the essence of humanity, but only with the end appointed by God to humans. No true reason could persuade a perfect human to turn evil, Tholuck admitted, but they could be instigated to a blind, reasonless act, if deceived by deceptive reasons. Tholuck’s conclusion had been that the allure of the devil had been persuasive enough.

Uncle is not convinced of Tholuck’s account. He notes that it hinges on a formal notion of possibility, which outlines only what is thinkable. A more substantial notion of possibility is linked to actuality in the substantial sense, which the uncle defines as just another name for the system of causal relations. Possibility and necessity, he suggests, are then just different ways to reflect on this nexus of causality: we speak of necessity, when causal relations are certain and uniform, and of possibility or contingency, when the relations are uncertain. Furthermore, nature is especially characterised by necessity and spirits by possibility, because latter have a freedom to manipulate causal chains that the former do not, and indeed, uncle insists, with spirits disposition cannot really be distinguished from possibility or ability.

Because ability and disposition to evil cannot be separated, uncle notes, the seeming contradiction still remains - why would God allow humans to choose evil? The reason, uncle remarks, cannot be that finite creatures as such could not exist without this possibility, because natural things as necessary cannot be evil. Uncle thus denies the Augustinian idea that evil derives ultimately from finite entities being created out of nothing and thus having intrinsic lack in their essence - he notes that Augustine mistakenly treated nothing if it was something substantial. Augustine’s mistake led then to the same error pervading also Tholuck’s theory, uncle says - both philosophers thought that evil was caused by acting blindly and without reason, although it is quite the opposite, that is, evil and sinful action causes blindness.

Uncle returns then to the original state of human beings. God, he begins, created other beings, firstly, because he wanted to reveal himself to other beings, and secondly, because he lovingly desired that other beings would share in his blessedness. The original human being, uncle describes, had a spirit created immediately by God and a body fashioned by organic forces created by God. This original human being knew God as the source of its existence, itself as a subject of this knowledge of God and nature as something in close connection with itself. Now, uncle continues, God revealed also to human being the end fashioned to it and commanded the human to form itself according to that end by taking part in the blessedness of God. In a sense, then, the original human being, as imagined by the uncle, was not yet perfect, but could perfect itself through its own action, making human then a sort of image of God as the creator. The original human being became evil, uncle explains, because it chose to not subjugate to divine will. By so doing, it did not cancel its own existence and certainly not the divine existence, but merely contradicted the divine command to remain in connection with God.

Nephew accepts at once uncle’s account and adds quickly that other, non-embodied spirits or angels must have also faced a similar choice - essence of the sin of the devil is the same as the sin of humans, that is, choosing oneself over God. The consequence of this sinful choice, he notes, is that the sinful creature cannot anymore be called the image of God, that is, it is not in connection with divine substance - by trying to become positive in itself, a creature distanced itself from God, just like two positive poles of magnets repel one another. In case of humans, nephew explains, this distancing means especially the loss of God-given ability of human spirit to control its animal body effectively. In effect, then, nephew suggests, sin of spirit of trying to rule by its own force leads to flesh rebelling against the spirit. Concrete effects of this rebellion, he points out, are the eventual succumbing of human bodies to forces of nature in death and the necessity of humans to reproduce sexually. But it is not just nature that opposes the sinful human being, but also divine will, nephew adds, and the human hears this opposition as a voice of its own conscience declaring guilt for the sin.

Uncle is ready to add a few important details to the nephew’s account. Firstly, he points out that the sin of fallen angels differs from human sin, because the former do not have bodies and therefore do not reproduce and have further generations of angels or a history in the proper sense of the word. Thus, uncle deduces, disembodied spirits could not really experience any salvation, but they are eternally condemned to an existence without God. How can such eternal damnation be justified? Uncle’s answer is that this is simply what the fallen angels have wanted and always will want - their choice was to live without God, who out of his love lets the fallen spirits live without God. Indeed, he continues, this is the very purpose of the existence of free creatures - to let them decide whether they want to live in the light of God or to shroud themselves in a shadowy existence of a sinner.

Furthermore, uncle shows another sense, in which the image of God has been destroyed in the sinful humanity. What is given to a human being when he becomes an image of God is not the full divinity, which a finite creature could not obtain. Instead, it has to be something that could be shared by humans and God, namely, self-consciousness. Now, even sinful humans are conscious of themselves in a sense, but their self-consciousness is not as clear as when they understand their relation to God. Instead, sinful humans can confuse themselves with God or nature or confuse God with nature. In other words, various forms of non-Christian ideologies, like pantheism, are another consequence of human sin.

Finally, uncle points out that guilt is not in a proper sense of the word a consequence of the sin. Sin, he explains, is a relative concept, in which someone changes his relation toward God. Now, a necessary counterpart or the other side of this sinful action is a reciprocal action of God severing his connection to the sinner. Feeling of guilt, uncle says, is then the necessary form in which sinful persons experience their own sinful action. Difference is that the sinful action cancels itself immediately - by severing its ties to God, sinner also destroys the abilities, by which it could again make sinful choices. On the contrary, the feeling of guilt lingers on as a thought of God, which is now as good as dead for the sinner.

The account so far has shown how a human being in their original state could have sinned. The next problem is why humans now appear to be born already in a sinful state. Traditional answer was the notion of an original, hereditary sin, which was a middle position between traducianism - the idea that spirits of humans were born out of the spirits of their parents - and the Origenean theory that human spirits had existed before the birth of their bodies and had been condemned to an earthly life because of a choice in that earlier, pretemporal state. The official catholic position was that human spirits were generated by God, at the same time as their bodies were generated, thus making the two other positions untenable. The mediating position indicated that original sin of the first was somehow transmitted to their descendants, even if the spirits of these descendants were made directly by God. Question is how this transmission was possible.

Nephew considers first the solution offered by Philipp Marheineke, a theologian of Hegelian school. Marheineke suggested that all humans shared the original sin, because they all were part of the human genus. This general sin, instigated by first humans, had to still become our personal sin through our individual choice, Marheineke said, because without personal choice we could not be responsible for the sin. Marheineke also suggested that this choice was somehow inevitable, so that no individual was in the end exempt from guilt. Nephew notes that Marheineke’s solution is no real solution: if the choice of evil is necessary for humans, then they are not really responsible for the original sin and are like mere animals.

Nephew’s answer to Marheineke is that original, hereditary sin must be something essentialy different from personal sin based on our bad choices. Furthermore, he differentiates between a complete personality of an actual individual, created by free choices, and spirit as a complex of unactualised potentialities. Nephew points out that even before becoming a full personality, individual spirit is active, for instance, in differentiation of various psychological capacities. These prepersonal activities of spirit, nephew concludes, are still unfree or instinctual and could be said to be affected by the original sin, if they were hindered by separation from God.

Nephew’s answer still leaves open the question why God continues to create human spirits that remain in separation from God. His solution lies in the dual nature of humans. Beyond spirits, he says, humans also have bodies, which happen to be naturally generated and connected to divinely created spirits. This means, nephew insists, that humans form no mere abstract class, but a genus or family, where the first person represents the whole of humanity. Because new humans belong to such an organic whole, their spirits must be affected by the corruption of the first humans. In effect, this means that the new humans are also divorced from God, coming into contact only with the voice of conscience declaring human guilt. Even more, nephew insists, the activities of new humans are tainted by a tendency to pridefully choose oneself over God and a fixation with nature and its delights.

Nephew admits that God could still create spirits linked to divinity, but these would form a completely new species, unrelated to the descendants of the first human. He also admits that God could simply destroy the family of humans, but won’t do it, because of a possibility to eventually save some of the lost humans.

Uncle still presents some clarifications to the hereditary nature of original sin. His main point lies in the notion that humanity is connected by a sort of Platonic idea (although he calls it Kantian). This idea is not just an abstract concept, he explains, but a true organic unity, through which we humans can feel a connection with one another. In effect, it is also a blueprint for generating humans, which was perverted by the sin of the original humans and thus resulted in the creation of perverted humans.

Uncle also explains that the sinful disposition of the humans does not lie in their spirits as such, which still have the ability to choose God. Instead, the perversity or sinfulness lies in their being disconnected from God and at the same time connected with an animal body. The animal body as such knows nothing about God, because it feels only appearances and lives only for sustaining itself through its descendants. Spirit, on the other hand, starts to revolve around itself, when not sustained by divine light. Because the human spirit is organically connected with the body, it is also tempted by its sensuous concerns. Still, uncle notes, there is something helping spirit to gain control over the body and turn again toward God, namely the voice of conscience.

The next letter of the nephew concerns the various ways humans could relate to the call of conscience. The relation to conscience is, in fact, the way in which the nephew classifies various religions. He wants, thus, to present an alternative to various philosophies of religion of German idealists, where religions were usually put in a developmental order. As an example, nephew gives an account of Johann Erdmann’s philosophy of the history of religion, which seems like a slight modification of the Hegelian philosophy of religion. Nephew’s judgement is clear: human beings have an innate tendency for such abstract conceptualisations that have little to no basis in empirical facts.

True principle of classifying religions, nephew insists, is whether followers of that religion have obeyed the call of conscience or not. The latter, he surmises, is the essence of paganism. By turning away from the call of the God, pagans cloud their understanding of the proper relation of humans to God and nature. Firstly, they might think humans as essentially similar to nature, falling to some sort of pantheism. The nephew supposes two possible extreme forms of pantheism, with various mediating positions between them. First type of pantheism supposes that spirits are emanations from the absolute and nature is then a yet further emanation from spirit. Although nephew does not identify this idealistic pantheism with any particular religion or philosophy, it bears a striking resemblance to Neoplatonism. The second, realistic form of pantheism reverses the roles of nature and spirit, suggesting that human spirit is just a development of its natural side. Nephew finds traces of this idea in Greek polytheism, in the sense that Greeks believed some humans could eventually evolve from mere natural state into real divinities.

A contrast to the pantheistic religions, nephew continues, is provided by dualisms, where the struggle between spirit and nature is explained through the existence of two equally powerful principles. He suggests that dualism has two extreme forms, corresponding to two forms of pantheism. Just like realistic pantheism speaks for the self-development of humans, an ethical dualism, exemplified by Persian religion, states that humans should become heroes fighting for the good principle. On the other hand, just like idealistic pantheism speaks instead of action, more of an occasional mystical retreat into the original unity, theoretical dualism, which nephew identifies with Buddhism, supposes that humans spirits will eternally be mere playthings of dualistic forces, reincarnating from a better fate to worse and back.

Even paganism wasn’t completely mired in error, nephew admits and points out various indication of theism in Hindu writings. Even more important to him are hints of a coming saviour in various pagan religions. Yet, nephew says, the proper answer to the call of conscience - obeying God - was shown by Jewish people. Because of the proper answer, nephew explains, they received a second revelation of God, not as a commanding lord, but as a loving father. When the rest of humankind was falling more and more toward error, the chosen people could keep the idea of loving father alive.

In addition to the new revelation, nephew adds, the original revelation of a commanding lord had to be kept alive also, which happened by God declaring in audible voice the divine law. Thus, God very literally ruled the chosen people, while pagan societies were based on mere human will. Nephew also notes another contrast: while paganism spread all over globe, the force of Judaism was not in extension, but in intension, making it understandable, why there could be only one chosen people. Despite being a positive contrast to paganism, nephew reminds the reader that Judaism had its weak points also.Jews confused symbols, like animal sacrifice, with their true ethical meaning. Eventually, this led to Jewish cult becoming a mechanical following of rites and rituals, while the prophecies quickly became mere signs of an awaited upcoming political upheaval.

When the juxtaposition of paganism and Judaism had developed to its extreme, nephew continues, a saviour had to arrive. The task of this saviour or Christ, nephew says, was to build anew the original relation between humans and God. This second Adam had to be, then, directly unified with God or one of the moments of the trinity. In fact, nephew adds, he had to be the moment that is involved in God becoming an object both to himself and to others, that is, the second person or Logos. Because Christ should save humanity, he should also have a body belonging to the human family. Finally, Christ should face a similar choice like the first humans did, that is, he had to renounce sin both externally, by living in poverty, and internally, by freely obeying the plan of God.

What puzzles nephew is the relation of the human and divine side of Christ. The official catholic dogma was another mediating position between extremes, one of which held that the divine nature swallowed immediately and completely the humanity of Christ, while the other extreme held that the human Jesus was only in his adult life attached to Logos during his baptism. The mediating position stated that Christ united two different natures (humanity and divinity) within a single unified person. Nephew thinks that this unification of persons makes the human side of Christ too subservient, since Christ then has no human self-consciousness distinct from the divine self-consciousness.

The lack of human self-consciousness is especially vital in relation to the question of salvation, nephew clarifies. How can we call Christ a representative of humanity, if he experiences everything like God would, for instance, knows everything that is about to happen to him? And is his choice of pure life really something worthy of applaud, since the choice is made by a divine person? Despite his doubts about the means of salvation, nephew does not want to follow Duns Scotus, who said that God had just arbitrarily decided to let Christ be crucified and then accept this as a salvation for humanity. Instead, nephew insists God must have had a reason for choosing the particular method of salvation he did.

It is again up to the uncle to explain what the nephew had not understood. His main point is that Church Fathers and scholastics were interested in their account about the objective side of the entity called Christ - is this combination of divine and human sides a unified individual entity? This is evidenced by the Greek of the original, hypostasis, that was translated as person by the Latin church - it is not so much a personality, but an individual existence, compared to general nature or substance, that the word refers to. Subjective experience, uncle insists, became a philosophical topic only after Descartes, so it is not a wonder, if the phenomenology of the experience of Christ was not a problem older philosophers or theologians considered.

Thus, uncle finds it acceptable to assume that the human personality of Jesus exists as well as the consciousness of divine Logos in Christ. He notes that multilayered personality is not a rare thing, because even the divine trinity has a unified abstract personality built on top of three more concrete personalities. Other examples uncle mentions are a consciousness of the natural genus, built on top of experiences of individual animals, and human personality, which consists of an animal and spiritual consciousness. Thus, although Jesus was joined with Logos to form a single, unified entity or Christ, Jesus the human need not have the divine perspective of things, even if he was always aware of sharing his thoughts with Logos. At times Logos controlled Christ, but at other times it left the control to Jesus, who then was just as human and ignorant of the true essence of everything as we all are.

Nephew still wants to tackle the question of how the suffering of an innocent person like Christ can help the sinful humans. His point of reference is the theory of de Maistre, who suggests that guilt has something to do with our animal life, embodied especially in blood, so that it has to be paid in blood, no matter whose blood it is. The nephew has several things to criticise in this account. How can our unfree animal side be held accountable for the sin, which has been instigated by our spiritual side? And how can someone else’s blood pay for one’s own sin?

The true explanation, nephew says, is the essence of a human being as a synthesis of animal body and spirit. Just like persons of trinity, our animal and spiritual sides are so closely interconnected that even guilt of the spirit touches the animal body. Now, while spirits as such are independent individuals, animals form an organic whole - a genus - which also makes the inheritance of guilt possible for humans. Indeed, a sin of the representative of the whole genus - the first living person - can make the whole of humanity guilty in the eyes of God. Because humans have a dual nature, their genus can have two representatives - while Adam represented the animal side of humanity, Christ represents its spiritual side. And, nephew concludes, just like Adam’s sin can be inherited by the whole genus, so can Christ’s salvation work be inherited by all humans. Of course, he adds, it requires some effort from the part of the individual human to imitate Christ and become worthy of his salvation.

Salvation is not yet over with the sacrifice of Christ, uncle notes, because Christ merely removed human guilt, but did not yet reconnect humans with God. The work of reconnection, he explains, is left for that moment of divine trinity, which unifies the earlier ones, that is, the Spirit or the sense of community between Father and Logos. The work of the divine Spirit, uncle continues, parallels the work of Christ. Christ was, firstly, a priest who sacrificed himself for the whole of humanity - his followers experience this sacrifice again and again in sacraments, like Eucharist. Additionally, Christ was a prophet who taught the truth of God to his disciples - his followers continue telling this truth to further and further persons. Finally, Christ was a king who set out a hierarchy among his disciples .- the community of his followers are ruled by law and justice.

What uncle is describing is obviously the Christian church, in which humans try to imitate divine salvation through their faith and charity and gain for this service the sacraments, in which the divine Spirit reconnects them with God. This church is to divine Spirit in a sense what Jesus was to Logos, with the exception that church and Spirit do not form a unified entity. As a good Catholic, uncle and Günther with him, places most importance to priests, who represent the human side of salvation. Priests form a distinct class in the Church, just like Jesus was special among humans, but they are not direct descendants of him, just like Jesus was not born from copulation. In fact, it is the class that matters in priests, so the moral worth of the priest does not affect the worth of their position. In fact, uncle concludes, priests are just servants created by the community for the purpose of objectifying the life of love.

What then should we think about Günther’s grand theory? Express catholicism is not a common sight among philosophers nowadays, so many of his basic suppositions seem suspect and quite outlandish. Furthermore, Günther’s attempts at modernising the old faith appear to not have convinced his catholic contemporaries. Even more, his means for this modernisation - theories of consciousness in idealist theories - have been opposed and even supplanted by other trends, making it look quite quaint in the eyes of all except scholars of this period of German thought. Günther's book reads then like a curious relic, which in another possible chain of events might have led to a large scale rethinking of the Catholic faith.

Évariste Galois: Demonstration of a theorem about periodic continued fractions (1828)

(1811 - 1832)

Mathematics is a field where wunderkinds are a real possibility. It is a field with abstract enough objects that can be grasped even with very little experience, even if dealing with them and their interrelations might require some innate or acquired skills.

A good example of such mathematical wunderkind is Galois, who had managed to make significant strides in algebra before his death, when he was just a few months over twenty year old. Indeed, his first paper, ”Démonstration d'un théorème sur les fractions continues périodiques”, was published just a few years before his death, making his life as a mathematician remarkably short.

The paper itself contains just one beautiful theorem, with a proof simple enough to understand, once you just see how Galois does it. First, some terminological explanations are in order. The topic of the article is continued fractions. To understand what this means, one can start from a sum of a whole number and a fraction of the form a + 1/b. Then let us suppose that the denominator of the fraction is not just another whole number, but another sum of a whole number and a fraction: the whole is then something like a + 1/(b+1/c). We can clearly continue doing the same again, adding fractions within fractions. Like in many other cases we have witnessed, we can think of this development continuing indefinitely into ever smaller and smaller fractions and progressing closer and closer toward some definite number.

Now, the simplest kind of a continued fraction to deal with is such where the numbers a, b, c… follow some clear rule. A specifically simple case is such, where after a while, the numbers a, b, c…continue again from some previous number of the series, repeating after that the same series of numbers over and over again. In such a case, the continued fraction is called periodic.

Before Galois, mathematician Lagrange had showed that periodic continued fractions had a special relationship with quadratic equation, Ax2 + Bx + C = 0. The root of such an equation - that is, a number, which makes the equation correct when put instead of x - can be expressed as a periodic continued fraction, and conversely, periodic continued fraction is a root of such an equation.

Galois continued Lagrange’s work and demonstrated another relation, involving especially immediately periodic continued fractions. If the number where the repetition begins is same as the first number a - that is, if there is no additional sequence of numbers at the beginning of the series - the continued fraction is in the terminology used by Galois called immediately periodic.

Let’s say we have an immediately periodic continued fraction, where the repetition of the numbers begins after the fourth, d. Then the fraction is of the form a + 1/(b + 1/(c + 1/(d + 1/(a + … If you look very carefully, you can see that the denominator following the first d repeats the whole series representing the fraction. In other words, if we designate the fraction with x, then we can say that x = a + 1/(b + 1/(c + 1/(d + 1/x))).

Now, it is a simple task requiring simple operations to dig out the x on the right side of the equation. I’ll just give the first few steps to explain what I mean: a - x = - 1/(b + 1/(c + 1/(d + 1/x))); 1/(a - x) = - (b + 1/(c + 1/(d + 1/x))); b + 1/(a - x) = - 1/(c + 1/(d + 1/x)) and so on. The end result of this manipulation of the equation is this: -1/(d + 1/(c + 1/(b + 1/(a - 1/x))) = x. In the place of the inner x, we can again start writing the series from the beginning: -1/(d + 1/(c + 1/(b + 1/(a + 1/d…

In other words, Galois has found by this simple method a new periodic continued fraction. This new fraction also works as a root of the same quadratic equation as the original periodic continued fraction. In addition, the numbers of the new fraction move in opposite direction from the original one. Furthermore, if we assume that all the numbers a, b, c and d are positive, the original fraction expresses a positive number larger than 1, while the new fraction is a negative number smaller than - 1.

Günther, Anthon: Preschool to speculative theology of positive Christianity. First part: Theory of creation (1828)

 

1783 -1863

A controversy surrounding pantheism (or atheism and Spinozism, as it was first called) has been a mainstay of German philosophy since at least the time of Christian Wolff, and ever new generations of philosophers have faced the condemnation of having breached the lines of orthodox Christianity. In Anton Günther’s Vorschule zur speculativen Theologie des positiven Christenthums it is the generation of Schelling and Hegel that faces now the same accusation.

Günther’s aim is to defend Christianity and to show how the new philosophies fail to understand its basic tenets. At the same time as Günther is criticising them, he is also clearly influenced by some of the ideas of the other German philosophers, in ways that resemble Coleridge’s new reading of the idea of trinity.

Günther’s book is structured as an exchange of letters between a theology student and his uncle, who is afraid that the nephew has fallen to pantheist thinking. The evidence for this suspicion lies in certain theses reminiscent of ideas common to many of the idealist thinkers of the time. In these theses, philosophy is regarded as a single entity, developing throughout history through various relatively true philosophical systems. Furthermore, philosophy is here regarded as having essentially the same mission as religion, and in addition, as bridging two different phases of religion: an undeveloped awareness of divine in feeling would have been supplanted by Greek realistic and polytheistic philosophy and Greek philosophy would have been superseded by Christian idealistic philosophy, which would finally lead to an age of reasoned consciousness of God, where philosophy would not be needed anymore and wise humanity would rule over all nature and create a new heaven.

Nephew then defends himself that despite his conviction that philosophy will lead to a new understanding of God, he does not think that this would necessarily imply supplanting Christianity with pantheism. Indeed, he insists that theism is an equally valid way to do philosophy.

Nephew outlines his position in more detail by dividing all possible philosophical systems into two kinds: critical philosophy begins with the faculty of cognition and takes care of not overstepping its limits, while transcendent philosophy does precisely what critical warns against and starts from what is absolute. He specifies this rather Kantian division by noting that transcendent philosophy describes the relation between absolute and relative being in terms of substance and its accidental modifications. Critical philosophy, on the other hand, tries to - again in Kantian terms - leave room for faith in matters pertaining to things outside cognition.

The student makes an even more intricate division of philosophical systems, although only in a footnote. Uncle is not that impressed with it, noting that all philosophical systems are in a sense critical, because they all must begin with some facts of consciousness, and at the same time also transcendent, because absolute or God is always one of these facts of consciousness.

His own understanding of philosophy is built around several oppositions. One of them is the primary opposition between absolute and relative being, by which uncle means, effectively, God and the world. Another opposition lies within the relative being, that is, opposition of nature and spirit. A third opposition cuts across the second opposition: in both nature and spirit we can differentiate between accidental or phenomenal appearances and their substance or noumenal ground. Furthermore, he finds yet another opposition between the phenomena multiplicity and the noumenal unity: both natural and spiritual appearances can be reduced to two opposed forces. One of these forces is always passive - in case of nature, contraction, in case of spirit, receptivity - while the other is active - respectively, expansion and spontaneity.

All of these opposed concepts are familiar from Kantian and post-Kantian discussions. Uncle - the probable voice of Günther himself - notes that they are also among the facts of consciousness, from which philosophy should begin. For instance, uncle notes that in our self-consciousness we are conscious of ourselves as spirit, but also of something distinct from us and spirit, that is, nature. By studying both spiritual and natural phenomena, uncle suggests, we can find the basic forces behind them. Uncle points out that this already leads us from accidental variability to more stable and substantial level; even more apparent this substance behind phenomena is to us in our experience of ourselves as a stable unity behind individual experiences. Finally, we are aware of ourselves being conditioned, which then requires the assumption of something that can exist just by itself.

Basic question of philosophy, uncle suggests, has always been to explain how these various components of experience are related to one another, and different systems have a different answer. Some of them concentrate on the relation between nature and spirit, like naturalism, which take substance of spirit be just an effect and a product of substance of nature, spiritualism, where the roles are reversed and the substance of nature emanates from the substance of spirit, hylozoism, where the two are identified, and dualism, where the two substances differ, but interact. Some philosophical systems try to settle the relation of natural and spiritual appearances, like sensualism, which takes all spiritual phenomena to be caused by natural phenomena and therefore raises the status of senses, or intellectualism, which takes the opposite stand and states that the world of experience must be a product of our representations.

The more important question in Günther’s schema concerns the question about the relationship between absolute and relative worlds, and it is here especially where the character of uncle finds evidence for his pantheism accusations. Some systems regard nature and spirit as mere accidents of divine substance: following tradition, uncle calls this acosmic pantheism, because this system denies the existence of any world distinct from God. In a sense opposed to this is what the uncle calls cosmic pantheism, where God is just the goal to be actualised through world history, which is then a process of God’s self-revelation. Further forms of pantheism the uncle mentions hold God or absolute to be spatiality (monadistic pantheism, where all becoming is mere illusion), temporality (compared to previous, all stability is here illusion), substantially identical with nature (pantheistic naturalism, where nature is revelation of divinity) or substantially identical with human spirit (here human spirit is just a limited mode of God and nature this limitation, and God is revealed through the system of finite spirits). With all of this evidence before him, uncle concludes that pantheism is a necessary result, when philosophy attempts to describe the relation of God to nature and spirit.

Nephew objects that there is still some room for a non-pantheist philosophy, where God is described as a creator of the world, creation being an external relation between God and nature. He does concede that creation cannot be handled theoretically, because it is based on God’s unconditioned, free causality, which cannot be conceptualised. Creation is still justified on practical grounds, because it is the only possible basis of ethical freedom.

The basic idea of creation, nephew says, presupposes that there is a world distinct from God and God distinct from the world. World can, he admits, be said to be in God, but only in the sense that God thinks even possible worlds. In addition to this, world still needs to receive existence, which is based on a free act of God. At the same time, nephew says, God reveals himself as the most perfect entity through the world to other, less perfect entities outside him, who are capable of knowing and loving God and so taking part in his blessedness. These less perfect entities or spirits God has created as his likeness, but not as equal to him.

Nephew also makes a Kantian distinction between the sense world and the intelligible world. The sense world is only the manner in which the intelligible world appears to finite spirits, thus, God has no real relation to the sense world. Because spatiality is the property of the sense world, God is not in any spatial relation to the real world. Still, nephew insists, God is outside the world in the sense that he is not finite.

Uncle notes that nephew’s model of creation resembles the system presented in Vorschule der Theologie (note the similarity with the name of this book), written by I. H. Fichte, son of the more famous J. G. Fichte. In Fichte’s system, as presented by Günther, absolute realises itself by giving independent existence to a difference implicit in it and forming a sort of body to itself through its self-division. Absolute retains and knows its unity in and through its division and is thus a self-conscious God only because of creation. The divisions are in the fashion of Leibnizian monadology themselves relative absolutes or self-contained universes and therefore also self-conscious personalities.

The concept of relative absolute reminds the nephew of another recent philosophical work, by Georg Friedrich Daumer. Daumer’s starting point, nephew tells, is an idea found in Schelling’s essay on freedom that God himself had a basis or ground in an ultimate, featureless indifference, on top of which divine self-consciousness was built. For Daumer, nephew says, God is always self-conscious and this indifference is more like something divinity rips out of itself - the relative absolute - and makes into a basis of finite world. In effect, this Daumerian relative absolute is a blind generating force that searches for its own self-consciousness and eventual reconciliation with God.

Nephew uses the Daumerian idea to solve a fault he finds in Fichte’s system, where there appears to be no place for nature outside self-conscious subjects. Nephew notes that most post-Kantian philosophers have taken nature as a dynamic whole and thus something real. If Fichte were right, nature would then also form a self-conscious subject and would be on the same level as human spirits, which the nephew cannot accept. His own idea was to take nature as a mere shadow of true reality, but now Daumer has given him a new idea - if nature is just this blind relative absolute, humanity is still on a higher level, because it does not just strive, but can also reach back to God. The only worry nephew now has is that it seems to restrict God’s omnipotence, if he can never create something truly different from himself, but only modifications of divinity - when God creates, he should not be just positing his own essence.

It is time for the uncle to lead the student away from the quagmire he has got himself into. The first target of uncle’s criticism is nephew’s Kantianism, evident especially in latter’s insistence that spatial sense world was nothing real and that God had nothing to do with it. Günther goes into more detail with Kant’s idea of space and time as a priori forms of experience in an appendix, where he balances Kantianism with Aristotle’s objective notion of space and time and both with Augustine’s manner of grounding space and time to God. In the main book, uncle merely notes that while it was right to say that worldly and therefore spatial relations do not concern God, it is wrong to insist that no relation holds between God and the spatial world. He also adds that Kant’s attempt to make room for faith actually managed to just set faith aside somewhere where it could be forgotten.

Uncle also notes that Fichte’s system is essentially another form of pantheism, because - as the nephew had feared - in it God just multiplies itself or posits other absolutes similar to itself. He also notes, making fun of the idea mentioned in the beginning about apparently different philosophies being just phases in the development of one philosophy, that pantheism, as exemplified by Fichte’s system, and Kant-inspired criticism, as exemplified by nephew’s system, are more like eternal rivals, neither of which can be seen as development of the other. Ultimately, the decision between the two systems boils down to the question whether facts of self-consciousness should weigh more than demands of reason. Human self-consciousness is inevitably bound to a consciousness of something else limiting us - nature - and thus to an inevitable dualism between finite or relative and infinite or absolute being. Then again, our reason strives to reduce everything into a unified whole and to envision the relative world as a revelation of absolute. Although not yet spelling it out, uncle hints of a possibility of a third option more satisfying than either criticism or pantheism.

Uncle also makes short shrift of Daumer’s position. At first, he quickly dismisses Schelling’s essay of freedom, which influences Daumer, by noting that Schelling introduces without any justification dualism within absolute, thus, making it into relative being. Daumer himself, uncle continues, makes again the pantheistic assumption that God can only posit something similar to itself (relative absolute) and that God needs the world for its own self-consciousness.

We then get an interlude with nephew’s letter, where he notes the similarity of his time with the time of Neoplatonists and Church Fathers. He suggests that just like Neoplatonism was a syncretist hodgepodge of various mystery religions and mythologies covered with magical superstition, modern idealism is also a similar confusion of oriental pantheism with mysticism of intellectual intuition. Furthermore, nephew insists that whereas Church Fathers appropriated from Neoplatonism all that was worthwhile (especially the notion of supersensuous world above the world of senses) and added solid historical background in the form of Bible, the task now ahead is to take what is useful in modern pantheistic idealism and give it again a solid grounding in Christianity.

Uncle takes up this challenge by picking as the important result of modern idealism the analysis of self-consciousness. Consciousness as such unites two distinct moments: what is represented and what represents. Self-consciousness is a form of consciousness, in which representing subject makes itself its own object. Immediately subject can know only its activities or interactions with some objects, while it can know its substance or essence only through the mediation of these activities: in the words of a common analogy, eye can see or be aware of itself only through the seeing of other things.

God, the uncle continues, should also have self-consciousness, although it is one of a peculiar kind, because it is absolute. Still, even God must have something as its object, before being capable of self-consciousness. Unlike human consciousness, God can simply posit its own essence as its own object. At the same time, it must posit a common substance for God as subject and God as object. In a manner very reminiscent of Coleridge uncle states that this threefold structure of divine self-consciousness is what Christianity has called trinity. In other words, God necessarily emanates three persons from himself in order to know itself.

Self-revelation of absolute, which reason required for completing its demands, happens then already at the level where only God exists, because God posits its own essence as a new object. Question is why God would still create something other beyond himself and his persons. Uncle concludes that God’s goal must have been to reveal himself to someone else who is not God.

Within the created realm, uncle continues, nature and spirit share similarities, but on a more substantial level they differ and oppose one another. Thus, both nature and spirit are based on a pair of opposed forces and their underlying unity, but with nature these two forces are necessarily related (action and reaction), while with spirit spontaneity need not correspond with the receptive side of human mind, and thus, spirit can freely rise above what it senses. Spirit and nature cannot then be reduced to one another and also not to any indifferent substance underlying them. Their opposition is also not based on their combination, which is just as finite and relative as both of them, namely, humanity as a combination of spirit and body. Their existence, uncle concludes, can then be based only on something third above them, which has created them.

God is then something completely different from both nature and spirit, uncle says, and completely incommensurable with them. In a sense, God is even opposed to finite creatures. God has a unified essence and substance, which appears in three essential forms. World, on the other hand, contains three different kinds of substances (nature, spirit and their combination or humanity), but they all share the same form of revealing their substance through a dualism of basic forces. Still, uncle points out, both the world as a whole and individual created beings can be regarded as God’s images - individual creatures are relative absolutes, since they have life principles that work as a foundation of a sum of appearances, while the world as a whole is a trinity of substances.

Nephew’s final letter starts by recounting traditional properties of God, such as his omnipotence, omniscience and love, all of which are essential reasons why God created the world and how he could do it. He notes that some philosophers deem such properties too anthropomorphic, while only accepting spirit as God's characterisation. Nephew points out that it would be actually better to distinguish spirit as a finite entity from God as absolute - although God is not necessary, like nature, he is also not free in the sense of finite spirit.

He then turns to the question, whether human reason can by itself know that God exists. He notes that philosophers have had two positions on the topic. First position insists that reason has in its own self-consciousness also an immediate mystical awareness of divinity. Nephew cannot accept this position, because it is an obvious fallback to the pantheist position, where humans and God are identified. The second position, on the other hand, accepts that we have only mediate knowledge of God, but suggests that this is possible only if God comes and directly interacts with us. Nephew is skeptical, whether knowledge requires such a direct interaction with its object - we can deduce the existence of absolute even from the awareness of ourselves as conditioned entities.

A related problem concerns the role of faith in getting to know absolute. The prominent opinion, as the nephew points out, was that faith had at least something to do with it. One party, endorsing the idea of reason having a immediate connection to God, identified this immediate connection with faith and insisted that only this immediate cognition or faith was required, while understanding as mediate cognition was dependent on immediate cognition and could only be of use in the multiplicity of the sense world. Understanding and its traditional proofs of God’s existence could still enliven faith in us, even if they really couldn’t prove anything. The opposing party insisted that understanding has something to do with cognition of divine: faith was created in us by God’s interaction with us and understanding was required for refining it into cognition through traditional proofs of God’s existence. Nephew points out that both parties have tried to find an immediate connection with God, one through its own self-consciousness, other through God’s interaction with us. Yet, both must admit that understanding and its mediate, conceptual thinking is required for knowing God, since immediately we can know only our own states, but not what produces them.

In the concluding letter of the book, uncle congratulates the nephew for endorsing two controversial ideas. First of these is the idea that God is properly speaking not a spirit. True, God has similarities to spirits: both are non-material and have self-consciousness. Still, they both have widely different essences, just like animals and humans do not share their essence, although both have the capacities to sense and imagine.

The second controversial position is that we can know God even without direct connection to him. The opponents of this idea insist that only similarities between the knower and the known make knowing possible. Uncle points out that this would make it impossible for us to ever know things of nature, which have a different essence from us. He points out the possible objection that humans can know nature through their bodily side, but rejects it instantly by noting that it ignores the unity of human self-consciousness - it is not the eye that sees, but the self-conscious human using the eye.

Uncle notes that the principle of similars knowing similars has a true kernel: we must know something similar to ourselves, that is, we must be conscious of ourselves, before we can know anything else. Still, this does not mean that we have to turn in something else in order to know its existence. Furthermore, the knowledge of God provided by our knowing the conditionedness of ourselves is only theoretical knowledge of absolute. If we truly want to know God as God or his personality, uncle concludes, we must know him also through hearing him speak to us through our conscience.