tiistai 31. tammikuuta 2012

Christian Wolff: Reasonable thoughts on God, world, and human soul, furthermore, of all things in general - Pre-established harmony

Ever since Descartes suggested that the finite world consisted of two types of substances, material and spiritual, the question of possible interaction between the two had formed a dilemma. Descartes' own suggestion that pineal gland had something to do it was considered a failure. An easy solution would have been to get rid of one side of the equation altogether. But the rejection of spiritual substances or souls, that is, materialism of Hobbesian sort was considered antireligious. On the other hand, the opposite of materialism, which denies the existence of matter and which Wolff called idealism, attracted religious men like Berkeley, but was otherwise seen as rather farfetched.

Spinoza's solution was to deny that there is any true difference between soul and matter: both are merely one and the same thing from two aspects, thus, they do not interact, although changes in one reflect the changes in the other. But Spinoza's answer led to a pantheistic world view, where everything was a mere modification of original unity or God. A more theologically acceptable solution was occasionalism, according to which God had to give a helping hand, whenever an apparent interaction of any substances would occur. Problem was that occasionalism required constant wonders and so undermined scientific discussions.

Wolff follows Leibnizian solution of the problem, that is, he supposes that God had created the material world and the souls in such a manner that they appeared to work in harmony with one another. For Leibniz and Wolff, soul was closed off from any influences and all its states followed from its previous states. Still, soul could represent the world around it, because when the soul had been generated by the God, it represented the world perfectly and thereafer, because of the laws governing both matter and souls, the two will remain in perfect sync (one might object that two clocks that begin by showing the same time might not be synchronised after few days, but I will assume that God has ordained the laws in question so that the harmony remains).

Leibniz's theory is undoubtedly ingenious, but it somehow feels too elaborate. Furthermore, it still appears to verge on materialism. The body is not truly controlled by the soul, thus, whatever words are coming out of the mouth of the person sitting next to me, whatever actions she will perform – all this must be caused by some changes in her body in general and her brain in particular. I know that in myself there is something more – namely, my consciousness that exactly corresponds to the actions of my body – but in case of other persons I might as well assume that they are mere machines.

Leibniz and Wolff had, of course, a reason for adding independent souls to the equation. The material bodies can be destroyed through disassembly of their parts, but partless and simple soul cannot be disassembled. Thus, human consciousness should live on after the death of the body.

What is most unsatisfactory in this account of the immortality of the soul is that it apparently fails in its purpose. True, Wolff and Leibniz do conclude that the soul is immortal. But the connection between the soul and its body has been defined to be very tight: what soul perceives, what it imagines and what it thinks all correspond to some states in the body of the soul. Indeed, Wolff even goes so far as to admit that a fault in person's brain will lead to a fault in the corresponding perception of the soul. It would then seem reasonable that the capacities of the soul would be gravely diminished when its body completely ceased to exist.

Here Wolff relies on some outlandish speculations. He assumes it to be proven by a collague that the soul is generated at the very instance when its body is assembled. The capacities of the soul grow all the while when it is connected with the body (Wolff conveniently forgets cases of senility). Thus, Wolff concludes, as the state of the soul after death is a mystery to us, it is reasonable to suppose that it will continue developing and perfecting itself.

This is a good example about what I think the greatest fault in the whole chapter on rational psychology. Wolff already knows the answer he must get – soul must be immaterial, it must be immortal and its life after death must be happy and perfect. The grounds for these conclusions are then discovered afterwards, and no puzzle about the nature of the soul has ever actually existed.

So much then for soul: there's only God to discuss anymore.

sunnuntai 29. tammikuuta 2012

Christian Wolff: Reasonable thoughts on God, world, and human soul, furthermore, of all things in general - Soul as a force of representation

Last time we saw how Wolff denied the materiality and complexity of human soul. When we remember Wolff's twofold division of all things, we understand why he must assume soul to be a simple thing. Thus, all the characterisations of simple things fit also with souls: souls are essentially units of force and all the processes they undergo are based on this single force. The question is what sort of force a soul is.

Wolff's answer is that soul is a force for representing the world. Wolff's proof of his statement is rather circular. He can quite justifiably conclude that the soul has a capacity for representing the world, because it can sense the world and things in it. Yet, when Wolff then concludes that this force of representation is the essence of soul, because soul must have one force on which all the other characteristics are based, he ignores the possibility that the force of representation would be a mere modification of a more essential force of soul.

I suggested in a previous text that Wolff might be a precursor of German idealists, because he explicitly took activity to be the ontologically important characteristic of simple things and especially souls. But whereas German idealists like Fichte were willing to uphold concrete acting and the will behind it as the primary essence of human consciousness, Wolff decides to concentrate on the more dependent activity of representing.

True, Wolff does not consider representation to be a mere passive waiting for impressions of external things. Instead, representing is also an activity, somewhat like a painter who has to actively paint a likeness of her model. Yet, unlike action in the usual sense of the word, representation has to take its cue from the external things: it is not we who decide how the things should be shaped, but we shape ourselves to fit the things.

If Wolff’s suggestion is to be convincing, he will have to show how willing and desire can be explained through the activity of representation. Wolff’s simple solution is to state that representation of goodness equals willing or desire, that is, if we represent something as good, we at once are committed to making it happen: this commitment is will, if the representation is clear and distinct (i.e. well-defined), and sensuos desire, if the representation is obscure or even dark.

At first sight, Wolff’s suggestion appears rather farfetched. Suppose we have a lovesick boy who thinks that the object of his affection is the most desirable person in the whole wide world. Despite his devotion towards this person, the boy may still lack the initiative for suggesting a date, hence, the representation appears to still lack something contained by true active will. Still, we might consider the inactivity to be caused by an opposing fear of being ashamed: the activity that would in itself be instigated by the representation of the person as desirable would be nullified by a contrary representation. Thus, Wolff’s suggestion of representation as the essence of human consciousness has so far appeared reasonable: we shall see in the future, whether Fichte and others have more arguments against it.

One last thing that I shall discuss now is the question whether the soul really represents the world around it or whether it might fail to do so. Wolff seems to beg a question, when he bluntly says that because the force of representing world is the essence of the soul, it cannot fail to do this. Yet, Wolff appears to have a subtle point. If soul represents anything, then what we should call world is just that what is represented by the soul.

One should note that the soul might represent only a part of the world. Furthermore, the representation might still fail to be completely correct, or it might be a confused representation. The Wolffian world has only characteristics definable through the concepts of space and time. Yet, when the soul has a confused representation of such characteristics, it might sense colours, sounds etc., and if the confusion is strong, it might even have faulty sensations.

Still, the question remains whether the sensations and other states of soul might not be representations, but mere phantasma – then there would simply be no world to represent. The final nail against the idealist coffin is probably hit when Wolff discussed God and his relation to both the soul and the world. For now, he is satisfied to point out that idealism or the denial of the material world fails to follow the paradigm of finding a sufficient reason for everything. In Wolffian system change of sensations and perceptions is explained by corresponding changes in the world, but idealists cannot really explain satisfactorily why one perception is superseded by another.

So much for the soul and the world. Next time I shall discuss the relationship between the soul and the body.

perjantai 27. tammikuuta 2012

Christian Wolff: Reasonable thoughts on God, world, and human soul, furthermore, of all things in general - Can soul be material?

While in the chapter on empirical psychology Wolff merely observed the mental capacities of human beings, in the chapter on rational psychology he tries to determine the nature of the soul or the thing that has such capacities. Nowadays it is easy to think such an attempt as completely ridiculous: after all, Kant should have shown that rational psychology was based on mere sophistic reasoning. We shall have to speak of the Kantian criticism in the future. At this point we may just note the surprising fact that Wolffian theory of the soul begins with a reasoning of transcendental nature. That is, Wolff begins from the fact that human beings are conscious of themselves and investigates the presuppositions of this fact.

The beginning of Wolff's reasoning is innocent enough. We are conscious of something, Wolff says, when we can distinguish it from other things. For instance, I am conscious of a hand mirror, only if I am able to differentiate the mirror from e.g. hands holding it. Particularly, consciousness of oneself implies the capacity to distinguish between oneself and other things. In other words, consciousness is connected with a clarity of thoughts, which for Wolff meant a capacity to distinguish the object of thought from other objects.

Furthermore, in order to distinguish different objects from one another and to recognise them as different, one must be able to contrast them with one another and to consider them one after another, Wolff continues. In order to do this, the conscious being must have imagination and memory, that is, he must be able to think of things that are not present and to recognise them as having been present. Indeed, consciousness is generated, because we can think of a thought for a period of time, note that the time has changed, but the thought itself has remained.

The arguments thus far have been essentially about characterising what it means to be a conscious personality: e.g. a person needs to have a memory, in order that she would have a sense of continuity of self. I cannot see why Kant or his followers would have any reason to argue with these considerations. In fact, much of the Kantian and post-Kantian German philosophy consists of such theorising on the nature of human consciousness, although in a somewhat deeper level.

What Kant and his followers would probably find unacceptable is the next move where Wolff tries to prove the immateriality of soul or the thing that is conscious. Wolff starts by noting that all material processes must be explicable through mere mechanical movement of material objects. Thus, if soul would be material, thinking would also be such a mechanical process. Now, human beings can be conscious of their own thinking, that is, they can note that the starting and the end point of thinking are different and still parts of a continuous process of one thing. Here Wolff simply states that such representation of continuity is impossible with mere matter: material objects as complexes can at best represent only other complexes, but they cannot represent a unified process of thought.

Wolff's blunt statement that matter as a mechanism cannot represent thought processes is quite unsatisfactory, especially as we nowadays don't think that matter consists merely of lego-like blocks that interact only through mechanical contact. Wolff does try to amend his reasoning by noting that material object can represent things – for instance, we can make a clay model of a building – but it cannot represent the original as separate from the representation. I have a feeling that Wolff has here confused first- and third-person perspectives. Surely an external observer cannot see e.g. brain as a representation of the process of thought,but this does not mean that the brain could not represent this to itself, if it just were conscious.

The situation appears even worse, when we consider that by denying the complexity of the soul Wolff has to accept the possibility of a simple thing representing complexities, which appears at least as difficult as a complex representing a unity. Indeed, how could a single partless entity represent a complex of many entities correctly? The only possibility appears to be that the complex is characterised through passage of time: at one point soul represents one part of the complex, at another point other parts and at final point the combination of the two previous phases. Indeed, we might well believe that human consciousness does work in this manner: e.g. when looking at a boat moving at the sea, we concentrate first on its rear end and then on the other end and only after that note that both parts go together.

The problem with this solution is that it once again threatens the supposed unity of consciousness. Suppose that I am thinking of myself. This act of thinking then represents some state of my mind, say, a memory of yesterday. But this act as simple can only represent one thing, thus, it cannot represent itself. We could then begin a new act of thinking that had the original act as its object. This procedure could be iterated indefinitely and so a problem is revealed: no matter how far we'd go, there would always be left at least one act of thought that had not been combined with other acts, that is, the very act of thinking all the other thoughts. This problematic was something that intrigued some of the later German philosophers, although Wolff appears to not have noticed it.

Wolff's argument for the immateriality of the soul was then unconvincing. Next time we shall see whether he can at least characterise this supposed immaterial entity.

keskiviikko 11. tammikuuta 2012

Christian Wolff: Reasonable thoughts on God, world, and human soul, furthermore, of all things in general - Infinitesimal elements

Because the world is a complex object, it must ultimately consist of simple substances: we have already seen this statement in the chapter on ontology, although the argument supposedly justifying it was faulty. Just like the world was already characterised by its complexity, these ultimate elements of the world are characterised by their simplicity. They cannot, for instance, have any spatial magnitude and thus differ from Democritean atoms. Yet, they must still be placed within some place – or more likely, remembering the Wolffian notion of space, their relations should constitute space.

Wolffian elements should then be infinitesimally small, just like mathematical points. Then again, they cannot be mere points. Wolff uses as a justification anothe principle he learned from Leibniz – the so-called identity of indiscernibles. This principle is based on the higher principle of sufficient reason. All things must have a reason, thus, there must be a reason why one thing is in one place and another in another place. Because the Wolffian space is relational, he thinks that the reason cannot lie in the space itself – space cannot exist without things and their relations. If now the two separate things are supposed to be completely similar, there cannot be any characteristic causing one to occupy a different place from the other – in other words, they must occupy the same place, and indeed, be identical.

Whatever one thinks of Wolff's attempt to justify the principle, it is clearly against taking mathematical points as true existents: point cannot be distinguished from another point through nothing else, but its position. Wolffian elements resemble then more Leibnizian monads, with the exception that Wolff does not take seriously Leibniz's idea of perception as the essential characteristic of all monads. True, he does pay lip service to the idea, but only in the restricted sense that all the elements reflect the whole world by being in harmony with it, in other words, by being in harmony with one another: the state of one simple thing matches the state of other simple things, e.g.. when one thing is in a state of activity, another is correspondingly in a state of passivity.

We have already seen in a previous text (http://thegermanidealism.blogspot.com/2011/11/units-of-force.html ) what actually individuates Wolffian elements: they are all units of force or activity, each developing independently of all others. What Wolff adds in this chapter is the explanation how bodies are generated out of the elements. Just like states of all the elements are harmonious in general and this general harmony constitutes the world, the states of particular elements might have a stronger harmony and thus form a complex unity or body.

Wolff goes to great lengths in explaining what characteristics all these bodies have: for instance, bodies consist of an essence (the structure of having been assembled in a certain manner from elements), matter (their activity of resisting externally induced movement) and moving force (their activity of moving themselves and mediately also other bodies). This analysis is not very original, but in essentials lidted from Leibniz's physical writings, and not philosophically fruitful, so I shall ignore it.

What interests me more is the relationship of the elements and the bodies. The existence of bodies is dependent on the existence of simple elements: a faulty assumption, perhaps, but one which Wolff endorsed. The divisibility of bodies has then a limit, because the elements cannot be divided anymore. This limit Wolff places outside possible experience, when he once again confirms that elements as simple things cannot be seen. This time he even has a proper argument: elements cannot be affected by movement, hence, light will not interact with them and they are therefore invisible to us.

On the other hand, bodies as spatial must be divisible into further spatial things, that is, further bodies. Wolff appears then to accept both infinite divisibility of bodies and the existence of a limit for that divisibility: indeed, his arguments for both are almost exactly those Kant will use in his second antinomy. Kant's antinomies are based on the assumption that the two arguments are both convincing and that both of their results cannot hold at the same time: Kant can then note that this apparent paradox is avoided by adpoting his own transcendental idealism. We have already seen at least one argument in the second antinomy is far from convincing. If we can also find out a convincing reason how Wolff could accept the two arguments without falling into contradiction, Kant's ”negative argument” for transcendental idealism would fall apart.

The simple solution for the seeming contradiction is that the indivisible elements are not extended, but point-like entities: thus, they are dimensionless and cannot be divided anymore. Analogically, mathematical figures can be divided into further and further figures, but no division leads into anything smaller than indivisible points. In other words, elements are the result of a practically impossible infinite division of bodies: thus, after every finite division we are in a point where the antithesis of Kantian antinomy works, although there is a final limit which no finite division can reach and in which the thesis holds.

This is enough of Wolffian cosmology. Next time we are back with studying human soul in rational psychology.

sunnuntai 8. tammikuuta 2012

Christian Wolff: Reasonable thoughts on God, world, and human soul, furthermore, of all things in general - World as a clockwork

You might think that after a chapter on empirical psychology Wolff would turn into rational psychology, that is, that he would explain what has been observed of human consciousness. Yet, a chapter on cosmology or the study of world intervenes with the pretext that knowing the essence of human soul requires knowing the essence of the world.

The basic structure of the world Wolff discovers through observation: world is a series of variable things that exist side by side one another (i.e. in space) and one after another (i.e. in time) and generally are connected to one another in the sense that anyone of the things contains a reason why the others near it in space and time are situated as they are. World is then a complex thing, that is, a thing consisting of things that are parts of the world.

The notion of a complex thing is familiar already from Wolffian ontology, and indeed, most of what Wolff finds characteristic of the world is a simple application of previous ontological results. Thus, world as a complex is defined by being a certain combination of its parts, like a structure built out of Lego blocks. Yet, the temporality of the world ensures that it is not a mere static structure, but processual, and indeed, its later states are based on nothing else but its previous states. The world is then like a machine – and Wolff specifically compares it to a clockwork, where the position of the hand is determined by its earlier positions and by the movement of the machinery.

World is then for Wolff deterministic and all events in the world are certain, if the previous events are known. Yet, this does not mean that the events would be necessary: they could have happened otherwise. Analogically, there is not just one possible way to make a clock, but the parts could have been assembled differently. True, we don't see any alternative worlds lying around, like we do see clocks of various sorts, but we can read alternative world histories in works of fiction. Wolff is here applying the idea of possible worlds, which he has probably picked from Leibniz.

The assumption of possible worlds creates doubles of the modalities of necessity and possibility. Firstly, we could speak of absolute possibility and necessity, that is, of what is possible or necessary in all possible worlds. Secondly, we could speak of possibility and necessity within one possible world: what is possible in this sense is something that has happened, happens or will happen in this particular world. What is specifically impossible in one possible world are the events of all the other possible worlds. The possible worlds contradict then one another: only one of them can be actual, no matter what David Lewis says.

As any philosophy student should know, the idea of possible worlds was important for Leibniz as a component in the justification of the perfection of the actual world: God knew all the possible worlds and as a wise and good person chose the best possible world to be actualised. We are still at a chapter on cosmology and God will be investigated only later on. Still, Wolff prepares the issue by characterising the notion of the perfection of a world.

Wolff begins by noting that all complex things and thus all worlds have some sort of regularity and are therefore valuable: remember that in the chapter on ontology Wolff had defined perfection through regularity. Yet, worlds are not all of same value, Wolff adds: some are more regular than others. By regularity Wolff does not mean a mere uniformity, which by itself would not mean perfection. Instead, diversity is also an essential component in perfection. In other words, the value of the world is to be decided by the question what sort of laws it has: a good world follows a number of laws, all of which form a rational hierarchy. Note that Wolff does not intend that we could deduce what these laws could be. Instead, one finds the particular laws through abstraction from the actual phenomena and more general laws through abstraction from more general laws. In this manner Wolff justifies the general law that nature makes no leaps.

The possible worlds are nowadays treated as a legitimate way to explain e.g. modal properties of sentences. Yet, Wolff's manner of suggesting a scheme for the perfection of the world is rather unbelievable, because there are a number of possible scales for measuring the perfection of anything. The problem can be better grasped through the analogy of clockworks.

There are rather different types of clocks and watches, although the main principle and purpose is the same for all of them. Now, while one clock might beat the others by being more realiable and always on time – say, some atomic clock – another clock might be cheaper, although not as precise as a time keeper. Then again, a fancy pocket watch might not be cheap nor reliable, at least if its owner forgets to wind it, but it still is ecological, requiring no batteries, and probably the most sylish of the three examples. It would be rather difficult – if not downright impossible – to say which of the three clocks is the most perfect: all of them are good in some respect and bad in other respects.

It appears reasonable to suppose that the perfection of possible worlds would be similarly and most likely even more multidimensional: that is, there would be no single criteria for deciding the perfection of the world, but several. Hence, although one world might perfect according to one criterion, another world could well be perfect according to another criterion. How should one then choose between them?

True, the Leibnizian-Wolffian God might have some clever mathematical formula that would take into account all the different aspects of perfection and hence be a perfect criteria for deciding between several possible worlds. The problem with this solution is that one should still demonstrate that this clever formula could not give the same value to two different possible worlds: otherwise, the possibility of two equally good worlds would still remain. We shall see later if Wolff has any argument to support this claim.

So much for macrocosm, next time we shall visit the opposite context or the microcosm.

sunnuntai 1. tammikuuta 2012

Christian Wolff: Reasonable thoughts on God, world, and human soul, furthermore, of all things in general - The animal that couldn't decide

Nominalist philosopher Jean Buridan is nowadays best remembered from the infamous ass that was placed at equal distance from food and drink and starved to death, because it couldn't decide which it should choose first. In effect, the story of the ass involves a question on how the capacity of deciding and willing works: if the ass has a capacity to make a spontaneous and completely arbitrary choice, it can avoid the trouble quite easily. The dilemma of Buridan's ass has a long history, but now we are interested in Wolff's manner of solving it.

Wolff defines willing (Willen) as an inclination towards something that is taken as good. Somewhat confusingly he defines unwilling (nicht Willen) as the inclination to avoid something that is taken as bad: I shall ignore this complication and treat Wolffian unwilling as a mere modification of willing. What is important is that Wolffian willing always requires a preceding notion of what is good and bad: this notion is a motive (Bewegungs-Gründe) for the act of willing.

Wolff seems then step right into the trap of Buridan's ass: if one cannot act without any reason, then one cannot just choose one form of sustenance over another. Yet, here the Leibnizian notion of inobservable effects on human soul becomes important. Wolff can assume in earnest that the case of Buridan's ass can never truly happen, because there will always be some small detail that will subconsciously make us inclined us to choose one possibility over the other.

Wolffian notion of subconsious motives implies that the process of human willing can never be completely transparent to the subject of willing. In other words, although a person would have a clear idea of what was good for her (such as not smoking cigarettes), an affect could still tempt her to act against her better interests. This is the idea of the enslavement of human will to the affects that was a common subject at the time of Wolff.

The problem of Buridan's ass is often connected with the question whether humans have a free will. In my opinion, the supposed connection is spurious: Buridan's ass could circumvent its dilemma through a simple flip of a coin or some quantum mechanical randomiser forcing the ass to act, but such a mechanism is not really free will. Now, Wolff appears to agree with me: if willing always requires a motive, a purely arbitrary choice is still not willing.

One might criticise Wolff for making human free will deterministic: if one would know all the motives of a person, one would know what she would choose in a particular situation. Yet, I find, firstly, that this possibility is just something that is commonly accepted: if one knows my likes and dislikes, one can immediately say that I will always choose a keylime pie over a chocolate cake, and in general, if a person's character is known, her actions can be predicted in some measure. The question of predictability of human willing cannot decide the question of the freedom of the will: chaotic phenomena like weather are practically unpredictable and quantum mechanical phenomena are unpredictable even in principle, but they cannot be called free actions.

Furthermore, the whole setup of knowing all the motives of a person is rather unbelievable, especially as the person interacts all the time with her environment and might gain new, previously unknown motives. For instance, if I heard two persons betting over whether I will eat keylime pie or chocolate cake, I might choose the cake just for the sake of upsetting the gentlemen. Thus, the existence of motives for all human actions does not even rule out the unpredictability of these actions.

Wolff himself notes that the deterministic theory of human mind confuses the analogy between motives and causes. Both are types of reasons or grounds, but they are still essentially different. For instance, scales require some cause to move them out of the state of equilibrium, but they cannot be motivated to do something as humans are.

Wolff himself places the freedom of human will in the capacity of self-determination. This does not mean that a human being could arbitrarily choose what it wills, because Wolff thinks such a notion would lead to a vicious circle. Instead, Wolff emphasises the fact that a free action is caused by the human being itself, according to its own notion of what it would be good to do in the current situation. Hence, Wolff can present a sort of evaluation of actions: the more a person knows about what is truly good for him, the more freedom his actions show. On the other hand, freedom cannot be forced on anyone, because a forced freedom would be just externally determined self-determination – a contradiction in terms.

With this text, the chapter on empirical psychology in Wolff's German metaphysics is closed. Well, Wolff does remark that the processes of human soul appear to be related to processes in our body, but this unification of soul and body will be dealt in more detail, when we come to rational psychology.

In the next post I shall begin the study of Wolffian cosmology, but I would still like to make some comments on empirical psychology in general and especially its Wolffian version. Later German philosophers were not really enthusiastic about this discipline. Hegel's criticism is still rather mild: empirical psychology is just disorganised observation of whatever capacities we happen to find within ourselves and does not reveal the nature of consciousness, of which all these capacities are mere modifications. Hegel's description is rather accurate, especially in case of Wolff, who has merely moved from one faculty of soul to another, still, a bit unfair: the nature of the soul Wolff intends to reveal in another chapter, dealing with rational psychology. Analogically, one should not disregard natural history just because it does not offer any general theory of nature, but mere empirical observations on individual natural phenomena.

Kant's objections against empirical psychology in his Metaphysical foundations of natural science are more severe: science of psychology based on empirical observation is an impossibility, because a) all true science, such as physics, must use mathematics, b) all mathematics requires constructing concepts in a priori intuition, c) the a priori intuition corresponding to the object of psychology or soul is time and d) time as one-dimensional cannot be used for constructions.

Kant's argument is rather convoluted, especially as we are still far from Kant's main works and concepts like ”a priori intuition” and ”construction” in their Kantian sense are to be defined only much later in my blog. Yet, we may for now note one important link in the argument: psychological notions cannot be quantified. Indeed, if by science is meant something like physics, science aims largely to discover relations between various quantities.

Now, Wolff appears actually to uphold the ideal of mathematized science, as befits a mathematician. In fact, he points out that many human faculties come in grades, that is, have a quantity that is analogical to numbers and sizes. For instance, a person can have a better or worse memory and one might even improve one's memory or enlarge its grade.

Of course, the existence of quantities of mental faculties does not still mean that these quantities could be measured, which is a condition for truly quantifying phenomena. Yet, in case of some mental faculties this seems rather easy. For example, we could well measure the grade of our memory e.g. by measuring how many words I could remember after a certain time of practice: the relation between the time and the number of the words might then be used as describing the grade of one's memory.