Baumgarten: Metaphysics – Elements of the world

Just like with ontology, in cosmology Baumgarten appears to be rather close on Wolff's ideas, but a more careful study reveals important differences. One interesting point of distinction concerns the question what belongs in a world. With Wolff, it appears that souls do not exist within deterministic universe, but follow their own causal series. With Baumgarten, on the other hand, souls appear to be just as much part of the world as material objects. Thus, while for Wolff, egoism is a statement on what there exists in general (nothing but one soul), for Baumgarten it is a cosmological proposition (world consists of one soul or is simple).

Reason for Baumgarten's inclusion of souls in world might be his commitment to Leibnizian notion of monads. True, even Wolff had said that monads do correspond to what he called elements, but this admission was a bit halfhearted. Baumgarten, instead, is quite insistent on using the term monad. He even endorses the notion that these monads have some soul-like properties, by stating that materialists must deny monads, either in general or at least as parts of the world – because Baumgarten, like Wolff, believes that all complex substances consist of simple substances, which he identifies with monads, he can then simply deny materialism as contradictory.

While it is difficult to say what is the relation of elements and space in Wolff's philosophy – and even more difficult to say what is the relation of souls and space – Baumgarten states at once that monads are located at some point in space. They are still not mere points in space, because they also represent the world around them, some darkly, others clearly (idealism is then defined as the idea that all monads represent world clearly or are spirits).

Wolff was almost silent on how his elements combined into, first corpuscles, then visible material bodies – for instance, should we need an infinity of them? Baumgarten does not provide a full explanation either, but he at least has a more detailed story to tell. First of all, monads are spatially located, that is, they must be in some sense positioned in relation to one another. Now, this positionality was reduced in Baumgarten's philosophy to interactions – being near another thing meant just affecting it.

Now, Baumgarten held that monads in some sense affect one another. In fact, when one monad acts one another, this other monad must also react on the other monad. Such interlocking combinations of monads form them more stable connections. Their interaction forms their contact, and if no external reason makes them lose their contact, the monads stay together, forming a relatively stable material body.

Just like in Wolffian philosophy, with Baumgarten the activities of monads explain all phenomena on the level of bodies. Indeed, Baumgarten even says that because all monads are active and e.g. change constantly their relative positions (that is, start and cancel interactions with one another), bodies also must be in constant movement.

Although Baumgarten thus uses the language of monads interacting one another, it is still unclear how seriously this statement is to be taken. Does Baumgarten, like Wolff, admit interactions only with some primary elements, but deny it between spiritual and other monads? Or does he accept or deny all monadic interactions? These questions, along with the problematic of a perfection of the world, will be dealt next time.

Baumgarten: Metaphysics – World in general

A central part of Wolffian cosmology was the notion of a possible world – an alternative to the actual world. The notion appears also in Baumgarten's cosmology, but the nature of these worlds is necessarily quite different. In Wolff, it seems that these worlds are meant to be individual entities, although not actual – they are thoughts flying in God's mind, but infinitely detailed and thus completely determinate. With Baumgarten, on the other hand, there are no non-actual individuals, thus, merely possible worlds can be nothing but universals.

Indeed, what we are dealing with in Baumgarten's cosmology is more like a notion or concept of world – Baumgarten starts from the actual world and abstracts certain features that belong to the world. One could then add more features to these features of ”world in general” and these combinations might even be non-contradictory and therefore possible – yet, these combinations would still have an extension of at most one individual thing, that is, they would be predicates of actual world or no world at all.

World, for Baumgarten, is then such a series of actual finite entities, which is not a part of any other series. Without further ado, Baumgarten simply accepts that there is such a totality of actual finite entities, although nothing speaks against the possibility that we might have only a series of ever larger collections of finite entities.

World is not just a combination of finite entities, but an ordering of them, for Baumgarten. Indeed, there are several nexuses holding worldly entities together – causal chains and series of ends, for instance. It is then an important part of the very concept of a world that is must have some regularity and coherence – otherwise, it wouldn't even be unified. By this statement, Baumgarten denies that fables or faery tales could form any possible world.

Because world consists of finities, it cannot be completely good, but must contain some badness or imperfection. In particular, Baumgarten says, world cannot be completely necessary. Thus, Baumgarten can deny Spinoza's theory that world would be necessary. Then again, the existence of the world works also against an acosmicist interpretation of Spinoza – there is something else beyond God.

So much for the general notion of world, next time we shall see what Baumgarten has to say about the elements of the world.

Baumgarten: Metaphysics – Relational predicates

The rest of Baumgarten's ontology is perhaps not as original as the earlier sections, but it is at least interesting, because Baumgarten rearranges topics and includes in general relational predicates some issues that Wolff did not consider under relations. The first of these topics is identity and the related notions of diversity and similarity. Here we find Baumgarten, for instance, endorsing the Leibnizian principle of the identity of indiscirnibles: two different things cannot be completely similar.

Space and time or simultaneity and succession are also dealt by Baumgarten in the chapter on relations. Although Wolff had also endorsed the idea that space and time are nothing but relations, Baumgarten is making this notion even more explicit by this simple choice of how to present the topic.

Just like with Wolff, the central relational notion in Baumgarten's ontology is obviously causality. Cause is for Baumgarten, just like it was for Wolff, a more special modification of ground or reason. For Baumgarten, cause is specifically a ground for the existence of something. Just like Wolff before him, Baumgarten defines several notions important to causal considerations – some causes might coordinate with other causes in producing some effect, while others may be called more proximate, when compared with more immediate causes of something.

The most important type of cause for Baumgarten is probably the efficient cause, which has actively produced some reality or positive characteristics in something else (Baumgarten also invents the notion of deficient cause for those actions, which produce some negative characteristics). A number of other causal notions can then be defined in terms of whether they help an efficient cause to do something or whether they hinder it.

In addition to efficient cause, Baumgarten does also, just like Wolff before him, consider the other three Aristotelian causes: form, matter and final cause. This part of Baumgarten's ontology seems rather quaint, like a remnant of a past long gone.

The final relation Baumgarten considers is that between signs and what the signs express. Although Wolff did briefly consider this topic, Baumgarten somewhat expands Wolff's writing. For instance, he considers several sciences, in which one should either make up more signs (heuristics) or help us recognise past signs (mnemonics), and also tries to explain the genesis of human language.

So much for Baumgarten's ontology. Next time I'll look at his cosmology

Baumgarten: Metaphysics – Kinds of substances

The primary classification of things in metaphysical treatises has long been that of substances and accidences and Baumgarten's Metaphysics makes no exception. Substances are things that can exist without being attached to something else, while accidences have to exist in something else, namely, in substances. Furthermore, Baumgarten adds, accidences are not just something externally connected to a substance, but a substance must contain some reason why such accidences exist within it. In other words, substance is a force that in a sense causes its accidences – if completely, they are its essentials and attributes, if partially, they are its modes.

Now, substances with modes are variable or they have states, which can change into other states. Like all things in Baumgarten's system, these changes also require grounding in some forces. Changes effected by forces are then activities of substances having these forces. Such activities might be connected with changes in the active substance itself, but they might also link to changes in other things: these other things then have a passion. In latter case, the forces might act alone to produce a certain effect and then we speak of real actions and passions, or then the passive substance also has some activity at the same time as it has passions, and then we speak of ideal actions and passions. The division of real and ideal actions and passions is of importance in relation to Baumgarten's thoughts about causality.

Because all substances have forces, all of them have also activities – if nothing else, then at least activities towards themselves. Furthermore, activity does not define just the essence of substances, but also their mutual presence – substances are present to one another, Baumgarten says, when they happen to interact with one another.

Baumgarten divides substances, in quite a Wolffian manner, into complex and simple substances (Baumgarten does admit that we can also have complexes of accidences, but these are of secondary importance in comparison with complexes of substances). Not so Wolffian is Baumgarten's endorsement of Leibnizian term ”monad” as the name of the ultimate simple substances. Rounding up the division of substances is the division of simple substances into finite and infinite substances, in which infinite substance has all the positive properties in highest grade and thus exists necessarily and immutably – this is something we will return to in Baumgarten's theology – while finite substances change their states and have restrictions.

This concludes Baumgarten's account of the substances or primary entities of the world, and like with Wolff, we can already discern the outlines of the three concrete metaphysical disciples. But before moving away from ontology, we still have to discuss Baumgarten's account of basic relations of entities.

Baumgarten: Metaphysics – this or that

In Baumgarten's sketch of ontology we have progressed into the section on internal disjunctive predicates, that is, to the most general classification of all things. We have actually witnessed already one of these classifications, namely, the division of things into singular or universal, which with Baumgarten can be roughly identified with the division into actual and merely possible things.

Another important distinction for Baumgarten is the one between necessary and contingent matters, which is actually a somewhat dual classification in Baumgarten's philosophy. Firstly, there is the classification of necessary and contingent features of all things. Transcendental characteristics, which belong to all things whatsoever, are clearly necessary. In particular, all essences and attributes are necessary – this means only that the realm of possibilities is inevitably fixed and what is possible, must also be possible. Modes, on the other hand, are contingent, because one and the same thing can have different modes at different times.

This classification of features leads then to a similar classification in relation to things. Necessary things are such that have only necessary features, that is, which have only an essence and attributes, but no modes. Contingent things, on the other hands, have modes and are thus not necessary. We might also describe this differentiation in terms of mutability. Modes are such things that can change, that is, a thing might have this mode now, but something else later. In other words, modes are features that can vary, and things with such features can change them. Thus, contingent things are mutable. Necessary things, on the other hand, have no features that could change and are therefore immutable.

Another distinction having a close connection with the distinction of necessary and contingent is that between reality and negation. Actually, these terms form more like a scale, at the other end of which would be found complete negation, that is, a thing which cannot be described through any positive predicates. Baumgarten notes that such a thing would be actually nothingness, that is, such an entity doesn't actually exist, but all possible things are real or positive in some measure.

The scale of reality is then formed by noting how much negation is added to realities in a thing. At the other end of the scale, there is a completely positive thing with nothing negative in it, in other words, which is not limited by anything (this means obviously God). Other things, then, are sort of mixtures of positive and negative features.

Now, these negative features are either necessary to the thing having them or not. Necessary negations concern the essence or attributes of something – for instance, human beings have necessary negation of mortality. Baumgarten notes that the contingent negations or privations must then concern modes – for instance, if a certain person is blind, this is just a privation, because it doesn't belong to the essence of humanity to be blind. While all negations are bad things or evil, necessary negations are what Baumgarten calls metaphysical – they are inherent in the nature of things and thus something of which we cannot complain. Privations, on the other hand, are true defects, because they are defects that things ought not to have.

The idea of a scale going from absolute negation to absolute reality is no mere figure of speech for Baumgarten, because he truly thinks that one could quantify such intensive notions like reality and negation. This is part of Baumgarten's Wolffian heritage, in which mathematics is seen as a key point in all properly scientific research. Indeed, Baumgarten goes even farther than Wolff and with every metaphysical topic provides explanations what would be a unit of quantity for that notion and what meaning the ”greater-lesser” -relation would have with it. Thus, for instance, in a minimal ordering a minimal reality is grounded on another minimal reality and adding both units of reality and grounding relations will make for a more complex order (unfortunately, Baumgarten does not consider the question what to do in cases where the comparison of structures is not so easy – if order A has more units of reality than B, but C has more grounding relations than either, while still less realities than A, how should we compare quantities of A and C?).

Next time I'll continue with the division of substances.

Baumgarten: Metaphysics – Unity, order, truth and perfection

In the post-Kantian era of philosophy we are familiar with term ”transcendental” having something to do with the necessary presuppositions of knowledge and cognition. Yet, before Kant, transcendental described features that transcendend all differences between things, that is, that could be predicated of every existing thing or even of every possible thing. In a way, transcendental was just a synonym for ontological.

A list of such transcendental features or predicates was a traditional sight in works of metaphysics, although what to include in such a list might slightly differ from writer to writer. Still, if something could be found in all of them, it would be unity. Even Aristotle had maintained that ”being” and ”one” are almost synonymous, since all existent things are unities. Even Wolff had briefly followed the tradition and Baumgarten goes even so far as to dedicate a section of his metaphysics to the notion of unity.

Of course, one might have different notions of what being a unity means. Baumgarten approaches the term from the familiar notion of determinations – it is combinations of determinations that are somehow unified. More precisely, we might have either separable or inseparable sets of determinations, and unities are formed of inseparable sets. All essences, then, form such unities, because the essential properties of a thing cannot be separated without destroying the very thing. Because all possible things have an essence they are in this sense transcendental unities.

If unities concern things, order concerns conjunction of things, that is, many things grouped together. Conjunction itself might not be ordered, Baumgarten says, and this seems evident, since we don't usually say that hay stack is in order, although it does consist of many hays in conjunction. Order requires that something remains same in the things in the conjunction, and this same element can then be expressed in propositional form as a law.

A peculiar type of order lies in what Baumgarten calls transcendental truth, which is something altogether different from what we might call truth. For Baumgarten, transcendental truth is the ordering of some plurality into a unity. Truth in this sense requires then some principles according to which this plurality is unified. In other words, transcendental truth refers to a sort of stability holding things and their groupings together, while dreams should lack such truth, Now, since every possible things combines various properties according to general ontological principles, every thing must have transcendental truth, that is, it must be stable and not collapse into a heap of determinations.

While all orders do not combine things into unities, they might still in a sense connect things, for instance, by making them follow same laws and rules. Such a conjunction of many things is the essence of perfection, Baumgarten says, and whatever causes such a perfection is then good. While this might appear rather strange definition of goodness, we might justify it by noting that is quite aesthetic notion of goodness that is meant here. Just like in case of truth and unity, Baumgarten then defines transcendental perfection and goodness – since essence rules attributes of things, a thing is always in some measure perfect and good.

This concludes Baumgarten's tale of properties of all things whatsoever. Next, we shall see what he has to say about basic disjunctions or classifications of entities.

Baumgarten: Metaphysics – Definition of existence

One of the most perplexing parts of Wolff's ontology is his notion of determination – something that can be affirmed of a thing. Are these determinations subjective or objective? The definitions appear to support the former reading, but the way Wolff actually uses these determinations to define possible things seems to support the latter reading. Furthermore, it is unclear whether these determinations should be universals or abstract particulars, i.e. tropes. The most faithful reading would perhaps be to deny that determinations are either, since both universals and particulars are defined through the determinations. Still, they seem more like universals, since unlike with particulars, they could be joined with other determinations.

Whatever these determinations are, Baumgarten accepts the notion, although he defines it in a somewhat different manner. Something is determinate, Baumgarten says, when it has been posited as A or not-A. The term ”posited” might seem rather strange, and indeed it is so – it is not quite clear whether Baumgarten wants to say that something is affirmed as A or not-A or whether it merely is A or not-A or perhaps both. Still, what is posited in something determinate is then a determination. If the posited determination is positive, it is a reality, otherwise it is negation. Since it seems objectively quite hard to say, which predicates should be called positive and which negative, the division appears rather arbitrary – yet, it should not be just subjective, since Baumgarten clearly distinguishes cases, in which e.g. seemingly positive determinations are actually negative.

Baumgarten's manner of distinguishing various determinations appears familiar from Wolffian ontology. Determinations can belong to a thing either as the thing is in itself – then it a question of absolute or internal determinations – or then as the thing is with respect to other thing – then it is a question of relations or external determinations. The internal determinations of a thing are either ground for all other internal determinations – then they are essentials, sum of which forms an essence – while other internal determinations are affections. Affections are then either wholly grounded in essentials – then they are attributes – or not – then they are modes.

Now, Baumgarten notes that a possible thing must be something that can be regarded in itself or without any relations to other things – that is, a possibility must be something with at least a minimal identity, by which to regonise it. This is quite a remarkable suggestion that is not included, at least explicitly, in Wolff's ontology. The important consequence of this suggestion, on the other hand, is something that we find from Wolff. If something is possible, it must have some internal determinations, because without them we could not speak about anything, and since these determinations must be grounded on something, the possible thing must have an essence. In other words, all possible things should have an essence.

Clearly a thing with some essence could also be merely possible, since e.g. centaurs do have an essence without existing – this is something Wolff agrees upon. A natural question then is what makes something possible into something actual or existent. Wolff's answer is, briefly put, that it ultimately has something to do with God's decision to create just this particular world, but that it also lies beyond complete understanding of human beings. In this matter, Baumgarten deviates considerably from Wolffian example, although almost no one has recognised it.

Baumgarten almost equates the essence of a possible thing with its possibility. What about the rest of the internal determinations of a thing, especially its modes, which are not determined by mere essence? Simple, they are part of existence. More determinately, it is the sum of all the internal determinations that supposedly forms the existence of a thing. In other words, while all actual things clearly cannot have any more determinations and are in that sense complete, all possible things should also be in some measure incomplete or indeterminate.

Baumgarten's theory is remarkably curious, although even more curious is that Wolff has been considered to endorse this theory, at least implicitly. True, Wolff says that actual things are completely determinate, but he never affirms that all completely determinate things would be actual. In fact, Wolff identifies complete determination with another ontological notion, or individuality. As Wolff, for instance, accepts the existence of haecceitas, which might be described as an analogy of essence in individuals, it seems quite unreasonable to suppose that Wolff would have thought all individuals are actual.

Baumgarten, on the other hand, makes this bold move and declares all individuals to be existent, thus denying the possibility of merely possible individuals. One explanation might be that he has been led astray by the notion of positing in his definition of determinations. True, we human beings can posit some thing to be completely determinate, only if we can experience it and thus know that it exists. Yet, this does not mean that God with his infinite capacity of thinking – something which Baumgarten himself should believe in – could not think of a completely determinate individual, which still would not exist. It is then Baumgarten who has fallen for the old trick of confusing capacities of human understanding with the capacities of divine understanding – something, of which Kant was to later accuse his rationalist predecessors.

Baumgarten: Metaphysics (1739)

The worth of Baumgarten in developing aesthetics is generally recognised, but the case is somewhat different with his metaphysics. True, this part of his philosophy has also found its readers, especially as people have wanted to see, why Kant used it in his own lectures of metaphysics. Then again, one still finds articles, in which Baumgarten's metaphysics is seen as little more than a continuation of Wolff's metaphysics and all the innovations of former are just implications of the latter – a view which does no justice to either of the philosophers.

When one just glances the contents of Baumgarten's Metaphysica, one might think that the association with Wolff's metaphysics is justified, as we find the book divided into four parts: ontology, cosmology, psychology and theology. Of course, this is just an external classification and one could argue that even Kant and Hegel still retained it at least partially, without being Wolffians. To make a more reliable judgement on the relation of Wolff and Baumgarten, we must then go into the details of latter's metaphysics.

Let us begin with ontology. Again, on superficial level, Baumgarten has borrowed his division of topics from Wolff. Baumgarten takes ontology to be a science of most general predicates of things and then suggests that such predicates are either internal (i.e. monadic) predicates or relative, while internal predicates are either universal (true of everything) or disjunctive (combination of predicates, exactly one of which must be predicated of everything). Indeed, Wolff also described first several general features of things, then the most general genera of things and finally general types of relations. Yet, a subtle difference can be seen already in these divisions, since many of the topics described by Wolff in the first division belong to second division in Baumgarten's ontology, while with Wolff, the second division contained only the oppositions of simple/complex and finite/infinite.

An even more interesting difference lies in Baumgarten's discussion of Wolff's highest principles of ontology. It appears that for Baumgarten it is concepts that are far more important than principles, and e.g. principle of non-contradiction is investigated in a chapter dedicated to possibility. Even more distant from Wolff's methodology is the lack of justification of these principles. Wolff's strategy in both German metaphysics and Latin ontology was to make an inductive move from individual cases, in which contradictions were denied – from a single case involving our own existence (in German metaphysics) or from our general tendency to deny contradictions (in Latin ontology). Baumgarten straightaway defines combination of predicate with its contradictory as impossible and uses that definition as a justification to conclude that no possible subject cannot have contradictory predicates.

Of course, this might just be an expositional feature of Baumgarten's text. The terse style of the book belies that it is meant to be used as a text book, and it might well be that Baumgarten is just describing the general features of his ontology, instead of arguing for its validity. This might be suggested by the fact that Baumgarten makes at this stage a rare reference forward – the principles are justified by the conclusions we can draw from them.

In this rather terse beginning, Baumgarten makes a rather strange remark: ”A + –A = 0”. Later on Kant would speak against such statements, which appear to conflate purely formal contradictions with conflicts of opposed forces – and indeed, we have seen Hoffmann already make similar observations. Yet, it is perhaps not so much that Baumgarten would have conflated these two notions, but that he never had a notion of mere formal contradiction – this is something one could have seen already with Wolff, who thought that wooden metal was an example of contradiction, although logically speaking there's nothing contradictory in the notion. It might well be that we should take the equation of Baumgarten quite seriously – A and non-A are like two forces or tendencies inherent in all things and an attempt to actualise them both in the same subject can end up only with destruction of the subject.

It is important to take this ontological nature of Baumgarten's and Wolff's notion of contradiction seriously, because both philosophers used contradiction as a way to define nothingness or impossibility, and so in consequence the opposite, that is, the notion of something or possibility. In other words, the hidden ontological implication is that there are some primary forces and any combination of them is a possibility, just as long as these combinations are not mere nullities, that is, ontologically barren points of no force or activity.

This hidden view of primary forces is probably behind Baumgarten's next move, in which he, following Wolff's example, tries to prove principle of sufficient reason. Just like Wolff before him, Baumgarten defines reason or ratio of X in epistemic terms as something, through which one is able to know X. To possibly have such a reason or to possibly be such a reason are enough to make something rational, while irrational, that is, something that cannot be connected with any other possible state as having a reason or being a reason, is nothing more than an impossibility – the hidden presupposition is clearly that we cannot have any isolated fact or event, but all possible states are connected to other possible states.

With this hidden presupposition, it is easy for Baumgarten to show that the principle of sufficient reason is true. If these presuppositions are assumed, something not having something else as a reason could mean only that it has ”nothing” or a state of nullity as its reason, because mere being without no reason would be just incomprehensible. Yet, this alternative doesn't work either, since a state of nullity is in Baumgarten's ontology a synonym for impossibility – the only alternative left, then, is that this something has as its reason some non-null state or something else. Furthermore, similar reasoning works also for the other direction, that is, Baumgarten can conclude that all possible things are reason for something else.

So far, then, Baumgarten has mostly just augmented Wolff's presentation at some points and made its presuppositions even more glaring. Of course, while Wolff could always rely on experience, Baumgarten's terse method of presentation makes these presuppositions truly stand out. Next time, we shall see him moving away from Wolff's philosophy in an even more radical fashion.  

Christian Wolff: Universal practical philosophy 2 (1739)

If first book of Wolff's Philosophia Practica Universalis was all about establishing the primary principle of practical philosophy, the second book, published year later than the first one, is then about application of this principle to more concrete cases. One must still remember that concreteness is here only a relative notion, and we are far from solving any determinate ethical or political questions.

The basic rules for good human action Wolff has already stated in the first book. One should follow natural law, which means striving for one's perfection. Since perfecting oneself means finding reliable and consistent happiness, natural law also guides us to strive for our own happiness. And, since God has made the world order, in which people become happy in certain manner, living according to natural law means also living according to God's decrees.

A new element in the second book is the social side of human activity. We are not just completely indifferent about each other's actions, but for instance, agree with other's actions, try to persuade them to some things etc. All these various social relations make responsibility of the actions also shared – if I convince my neighbour to do something, it is partially my fault, if something bad happens through her actions.

An important feature of this social element of human action Wolff emphasises is emulation – we tend to imitate behaviour of other people. This is important especially for making people act better. That is, if we set up examples of good life, heroes and saints, people might tend to improve their own live by imitating the lives of such good examples.

Wolff's suggestion that moral improvement might happen through emulation is an important sign of his appreciation of the less than fully intellectual side of human activity. True, Wolff thinks that one should try to improve one's behaviour through moral reasoning. Yet, he also sees that this is generally not enough, but there must be something to rouse the sensuous side of human mind. Thus, Wolff suggests that symbolism and rituals could be used for quickly teaching people about moral truths.

Despite admitting the importance of such sensuous element for morality, Wolff is still pretty antisensualist, when it comes to determining the actual principles of action. Senses and imagination provide us only with confused knowledge, which still requires conceptual analysis and reasoning to become truly valid and certain. Thus, sensuality as a source of confusion must be inhibited, in order to make oneself truly perfect.

Now, sensual side of human being is in Wolff's eyes not just a servant of morality or a mere hindrance to properly good life – it is also a sign of a person's motivation for his actions. Here Wolff once again speaks about physignomy, and since this is a topic I've discussed earlier I shall now merely mention it.

So ends Wolff's treatise on practical philosophy in general, although these outlines will be filled with more detailed treatises on ethics and politics later. But in case of theoretical philosophy, new personalities were already taking Wolff's formerly dominating place.

Christian Wolff: Universal practical philosophy 1 (1738)

Wolff's Philosophia Practica Universalis deals with a part of his philosophical system that wasn't nominally studied in his German writings and which was first presented as part of philosophy by Wolff's disciples. That is, the topic is the general part of practical philosophy, common to both ethics and politics, while we have German books only of ethics and politics. That said, many of the topics dealt here were included in Wolff's German ethics. In any case, universal practical philosophy is meant to be a study of the most general rules guiding free actions through knowledge of volition, when it is determined to some actions or non-actions. The aim of this part of Wolffian philosophy is also to offer motives for doing certain things and means for achieving those ends. In general, it should give criteria for deciding when some action should be or should have been done – that is, a heuristic for discovering truths of moral and politics.

An important question is obviously what to count as free action. The basic definition Wolff suggests is that free actions are not based on natural necessities, but on the liberty of soul. Wolff is here not trying to define or explicate human freedom – this should be the task of metaphysics – but merely takes the notion of freedom for granted. Basic distinction is that while sensuous appetites and aversions are natural, everything based on rational decision should be free. Although the distinction seems quite rigid, even in case of sensuous impulses there is some measure of freedom involved – we can e.g. freely move away from the vicinity of things causing certain sensuous appetites. Even such things as ignorance won't make actions unfree, if we just have had capacity to overcome this ignorance.

An important feature of free actions is that they can be evaluated, that is, they are good, bad or indifferent. For Wolff, the criterion of goodness and badness is dependent on the notion of perfection – actions promoting our perfection are good, while actions promoting our imperfection are bad. Wolff thinks also that these evaluations are natural in the sense that they are based on the essence of humanity – humans form a certain genus of entities, thus, they should act in a certain manner. The essence of humanity thus form the content of a natural law, which can thus be distinguished from all positive laws, authority of which is based on mere arbitrary decisions of human beings and their communities. Natural law works as a sort of general framework, on which all positive laws are based in the sense that the validity of the positive laws is instantly cancelled if they happen to contradict natural law.

Because the natural law is based on the essence of human beings, knowing natural law should be just a case of knowing what humans are like. Thus, natural law should in principle be possible to know by anyone. This was especially important conclusion in view of the topical question, whether atheists could be moral persons. Wolff concludes that they can be, at least partially. Natural law does have parts concerning God – human beings must work toward the glory of God. Yet, a significant part of natural law should be independent of such demands and thus be something that even an atheist could follow.

What then is a relation of God to natural law? God, as the creator of the whole world, has also decided that entities with the human essence exist. Thus, God might be called the instigator of natural law. In one sense, this doesn't really say much. True, following natural law will inevitably lead to happy and even blessed life, while transgressing natural law will in the long run lead to mere misery and torture. Yet, this is not so much because of God's particular punishments, but because making oneself perfect will also make one happy, while life geared toward one's imperfection will inevitably work against one's happiness. Although these rewards and punishments of good and bad actions are hence merely natural, nothing speaks against the possibility that God might decide to reward or punish people in a more personalised fashion according to the merits and demerits of their actions.

Following natural law leads thus to natural and perhaps even to special divine rewards. This still does not mean, Wolff says, that these rewards are the only motive for following natural law. Indeed, a virtuous person – that is, someone who has habituated herself to act according to natural law – will do good things just because he loves doing them, no matter whether she would get any tangible rewards for them. Similarly, a truly vicious person would be so engrossed with her perverted ends that she would not discontinue her wicked ways, even if she knew about the punishments awaiting her bad life.

Although Wolff thus accepts the power of habituation in forming one's moral outlook, the general tendency of his practical philosophy is rather intellectualistic. Thus, it is no wonder that according to Wolff, conscience is a form of judgement, instead of feeling. In other words, if one's conscience gives bad advice, this is not so much due to insufficient training or inner depravity of conscience, but more on a lack of good judgement. This does not mean that conflicts of conscience would not lead to any effect that we could feel – on the contrary, if we find out that our judgement has lead us astray, pangs of conscience will follow.

This first part of Wolff's general practical philosophy contains only quite theoretical principles that will be applied to more practical questions in the second book. The final topic Wolff manages to cover in this book is the question of responsibility. Generally speaking, Wolff thinks it is only free actions we can be responsible for. This does not mean that e.g. habits or deeds made in ignorance cannot be blamed or commended – habits can be followed with clear awareness, and ignorance might be something that we could have avoided. Although Wolff does not provide a general explanation what actions to blame and what to commend, he does mention what might be called second-level habits that are to be blamed or commended. Thus, diligence in following natural law is to be commended, while negligence of it is to be blamed.

Hoffmann: Study of reason – Opening up probabilities

Hoffmann's idea of demonstrating truth of something is based on the notion of closing off possibilities – when we can show that alternative accounts are against some principle of reason, we can be sure that the remaining account is the true one. In some cases, we cannot do this either for a proposition or for its contradictory. In that case, we can just conclude that both propositions are possible.

This possibility in question is logical, and as one might have guessed, Hoffmann thinks it is just one type of possibility. A more formal notion is verbal possibility, which just means that the words used in a proposition refer to some ideas. On the other hand, a more substantial notion is metaphysical possibility, by which Hoffmann means lack of contradictions, while even more substantial is physical possibility, which means capacity to physically actualise content of some proposition.

Getting back to logical possibilities, they are lacking in the sense that they come with no way to justify them. Indeed, this lack of justification makes it natural for us to reject them and thus they can be called internally improbable. As one can clearly see, if proposition and its opposite are both considered just possible, both of them are internally improbable. A more interesting notion of improbability is relative improbability, which is improbability arising from comparison of proposition with its contradictory. Probability is then defined as a counterpart to relative improbability: if we consider proposition to be more likely to affirm than its opposite, although both are possible, the proposition is probable.

Just like demonstration must be based according to Hoffmann to some principles, so must argumentation through probabilities. The basic idea behind argumentation of probabilities is that a proposition always implies or involves a number of conditions that the world must satisfy. Some of these conditions could be accepted without any ado, but others require more justification. The more a proposition involves conditions that require justification, the less probable it is.

One interesting question is whether Hoffmann meant us to read these characterisations of probability objectively or subjectively. The answer is that he actually had both possibilities in mind. Probabilities might be just subjective, if our incapacity to justify the seemingly improbable propositions is just based on our lack of experience or on general limitations of human cognition. If we can show that neither is the case, we can conclude that the probabilities are objective.

It might appear that Hoffmann's principle of probability is difficult to apply in concrete cases. Yet, just like in case of demonstration, the highest principle implies a number of more particular principles that are easier to use. Thus, we know that the less possibilities an event has for occurring, the less probable it is. This means, among other things, that a single possibility is more probable than a combination of many independent single possibilities and that a more indeterminate possibility is more probable than a more determinate possibility.

Hoffmann is satisfied with mere general rules, but notes that there are many kinds of probability, each having their distinct rules. As one could guess in case of Hoffmann, the probability could be about causal or existential propositions. Causal probability can be physical, that is, concern reasoning either from causes to effects or from effects to causes. On the other hand, it may also be political probability, which concerns reasoning from the means a person uses to the ends he strives to attain, or moral-practical probability, which concerns reasoning from given ends to means required for those ends.

Two kinds of existential probability concern things past (historical probability of what has happened) and things in future (whether something will happen in these conditions). In addition, Hoffman points out a third class relating to signs. These signs might be some concrete things, for instance, when a diplomat tries to determine what a representative of foreign nation means by his expression. Yet, in most cases the signs are words. One is either trying to determine the meaning of words in general, in critique, or then the meaning of words in a particular text, in hermeneutics.

The importance of emphasising these different types of probability lies in the distinct presumptions made in each field. Presumption, Hoffman defines, is a proposition taken as probable in some particular field of knowledge. The presumptions are valuable, because due to their probability they can be used as premisses in probable reasoning. Particularly, if some proposition is in conflict with such a presumption, its contradictory will be more probable. Hoffmann enumerates a number of possible forms of presumptions: we might, for instance, think something is probable, because its absence is rarity or because there is no cause to suggest otherwise – or even that this presumption is accepted by reliable authorities.

Hoffmann goes to some lengths to describe how probabilities could be quantified. In general he delineates two alternative possibilities, arithmetical and geometrical. In arithmetical quantification of probability one chooses some arbitrary unit of probability and compares other probabilities to it, while in geometric quantification of probability they are compared to the totality of completely certain proposition.

***

This is as far as I will go with Hoffmann's Vernunftlehre, although he still does have couple of interesting things to say about the forms of method (analytical, synthetical and analytic-synthetical) and their various subtypes (for instance, mathematical synthetical method differs in Hoffmann's eyes very much from other types of synthetical method, because it alone cannot be used to justify existence assumptions). Instead, I am going to make a comprehensive estimate of Hoffmann's life work.

Because most of Hoffmann's shorter writings had been written against Leibniz, Wolff and Wolffian school and even his masterpiece, Vernunftlehre, contained many explicit and implicit criticisms of their positions, it seems especially interesting to consider what are the actual differences between Wolff's and Hoffmann's positions. Clearly, Wolff and Hoffmann disagreed especially in metaphysical questions – e.g. Hoffmann thought Leibnizian idea of pre-established harmony to be ridiculous, while Wolff suggested it was the best possible hypothesis about body-soul interaction. But what is especially interesting is the question whether Hoffmann's logical works are any different from Wolff's logic.

It is easier to begin with similarities and on basis of the common elements to find the specific differences characterising Wolff's and Hoffmann's notion of logic. First of all, it is clear that both Wolff and Hoffmann understand logic not just as a description of a formal structure of thinking, but as a methodology of scientific research. But the two philosophers differ in their beliefs concerning the unity of this methodology. Wolff strives to give a unified methodology of sciences, and in cases where he admits the existence of many methodologies (e.g. historical and philosophical methods, or demonstration of truth and argumentation for probability), he is keen to suggest that one of them is ideal. Hoffmann, on the other hand, is more aware of the differences between disciplines and their methodologies – mathematical reasoning differs from physical and moral reasoning.

Wolff is not a hard-headed rationalist trying to spin everything out of empty definitions, which is often the caricature applied for him, but instead, he used a more mixed methodology, in which empirically discovered premisses play an important role. Hoffmann's methodology is similar, when it comes to empirical matters, but his acceptance of a variety of methodologies allows far more tools of securing knowledge – all reasoning cannot be reduced to syllogisms, Hoffmann insists.

Both Wolff and Hoffmann also accepted that all human methodologies have their proper limits and that especially divine affairs lie beyond the ken of human understanding. Yet, the reasons for their acceptance were somewhat different. For Wolff, it is more of a quantitative question – human understanding just cannot regard all the infinite facets of the actual world, let alone all the possible worlds or the infinite mind of God. In Hoffmann's eyes, there are more essential reasons, why human mind cannot understand some things – it has to follow the agreement of its ideas and shun from conflicts between ideas, but it might well be that these are merely laws of human thinking, which might lead even to contradictions if taken to extremes. This brings us to the greatest difference.

What is missing in Wolff's methodological works is a deep consideration of the very capacity to know – he just assumes the psychological make-up of human mind and proceeds to state what are the best ways to gather knowledge for such a mind. It is characteristic that Wolff relegates the question of truth to the applied part of logic. With Hoffmann, on the other hand, this question takes the center stage. He is quite aware that justifying our capacity to know the truth is quite difficult and requires a completely different methodology from other sciences – if we would dare, we could call him a transcendental philosopher before Kant.

Hoffmann: Study of reason – Solving antinomies

In the last post, we saw Hoffmann deal with various types of deduction or proof and the emphasis was on the question what type of formal properties make for an acceptable demonstration. He is still well aware that formal validity is not enough for a good demonstration. The premisses must obviously be true, but this is something that must be justified through further proofs and demonstrations and does not therefore suggest any new line of investigation.

There is still something other than mere truth in the premisses that is important for the goodness of demonstrations, Hoffmann says: premisses must be suitable for use in demonstrating these conclusions. What Hoffmann is against here becomes evident through a simple example: petitio principii. In cases where the chain of reasoning is somehow circular, the premisses might well be true and the form of reasoning quite valid, but some of the premisses still are improper as justifications of these particular conclusions.

Another, more important element in this propriateness is that premisses must be at least as substantial as conclusions. In other words, one cannot use mere nominal definitions as justification of conclusions stating the existence of something. Hoffmann is once again pointing to Cartesian proof of God's existence, which confuses the necessity of linking thought of existence with thought of God and the actual necessary existence of God.

The notion of propriateness in reasoning is also of importance for Hoffmann, when he is considering conflicts in demonstrations. Lewis White Beck, the grand old scholar of pre-Kantian German philosophy, congratulates Hoffmann as introducing to German philosophical culture the notion that we must sometimes evaluate between demonstrations of seemingly equal validity, which appear to have contrary conclusions – to Beck, this is one way in which Hoffmann laid ground for Kant. Unfortunately, Beck is exaggerating, since even Wolff's logical works contained chapters dedicated to this very topic. Still, Hoffmann is at least unusually thorough in this matter.

Hoffmann notes that often these seeming conflicts, especially in metaphysical matters, can be solved by noting that one demonstration is based on mere ideal premisses – that is, it doesn't describe reality, but only the manner in which we link our ideas. The trick is then to know which of the demonstrations fits the bill better. A sure sign is when one demonstration is based on the second or third basic rule of deduction (the necessary linking or separating of ideas according to our understanding), while the conflicting demonstration is based on mere principle of non-contradiction. In such cases one must believe the latter demonstration, because first rule of deduction trumps the second and the third. Thus, although we cannot understand how God could exist everywhere at once, if denying this would land us in contradiction, we would have to accept the omnipresence of God.

In case of apparent conflicts in physical matters, it has often happened that one demonstration supposes that only a single force works in the situation, while the other demonstration supposes that only another, quite opposed force works in the situation. The apparent conflict of demonstrations is then explained by this opposition of forces, and to truly determine which force wins the contest, one must check which force is the strongest.

A special case consists of moral conflicts, in which different laws and maxims are used in deciding the goodness of certain actions. Here the crux of the matter is to balance and measure the various laws and maxims that might motivate us to act in certain manner.

So much for demonstrations, next time I shall investigate what Hoffmann has to say about probabilities.

Hoffmann: Study of reason – The species of deductions

Hoffmann admits that deductions or proofs are the core of logic: while concepts and propositions might be the result we strive for in logic, deductions are the primary logical means, by which these results are gained. Thus, it is no wonder that he spends dozens of pages for a division of types of deduction – especially as he thinks that the usual method of dividing deductions is quite faulty.

Hoffmann's main criticism of the traditional Aristotelian logic is its overt reliance on syllogistic. True, we might be able to transform all deductions in syllogisms, but this loses the peculiarity of different deductions and loses sight of the different conditions in which different types of deduction apply.

The simplest form of deduction is purely verbal: it changes something contingent in a proposition, without affecting the relations between ideas. Such a change might affect only a mode of cogitation, such as when we start from a proposition ”work is means for earning money” and conclude ”earning money is the purpose of working”. Similar verbal changes occur when some irrelevant abstractions are removed or added, such as when we from proposition ”burning biomass is a way to produce energy” conclude ”if we burn biomass, we produce energy”. Such verbal deductions might appear rather useless, but Hoffmann notes that they are often important ingredients in more difficult deductions.

Slightly more complex are deductions involving opposition in the sense that they deduce from a link between ideas X and Y a link between the non-existence of Y and the non-existence of X. This might seem like a verbal deduction, but the involvement of opposition, instead of an affinity of ideas, gives this type of deduction a distinct look. Hoffmann also delineates various types of this sort of deduction, which include disjunctive deduction (”Soul is either mortal or immortal, it is not mortal, thus, it is immortal”), deduction of immediate opposition involving predicate (”All created things are finite, therefore, none of them are infinite”), deduction of immediate opposition involving copula (”It is true that snow is white, therefore, it is false that snow is black”) and deduction of immediate opposition involving subject (”movement is change of place, thus, rest is non-change of place”).

Another quite simple type of proposition not following syllogistic formula is conversion, which can be simple or not involve change of quantity (”Some cats are grey animals, thus, some grey animals are cats”) or accidental or involve change of quantity (”All cats are animals, hence, some animals are cats”). Together with a suitable deduction of opposition, conversion can be used to form contrapositions.

Taking look at three types of deductions delineated thus far – verbal deduction, opposition and conversion – we note that two of them share a commonality. While deduction of opposition works through some clash of ideas – these ideas cannot be connected together – both verbal deductions and conversions work through ideas sharing some common element, that is, through subordination. In case of verbal deductions and conversions this common element is something peculiar – meaning of words in case of one, and relation between certain propositions in case of other. In addition, one might also make deductions, which are based on nothing else but bare subordination – if A is somehow linked to B and B is somehow linked to C, then A is also somehow linked to C. This fourth type of deduction is once again not syllogistic, Hoffmann says, because the link in question need not be that between species and genus.

It goes without saying that although all deductions are not syllogisms, Hoffmann allows still that all syllogisms are deductions. Syllogisms are also deductions based on subordination or common elements between ideas, but here the subordination is of a particular type – because A is a logical part of B and B is a logical part of C, then A is a logical part of C, where A being a logical part of B means that A is species or individual under genus B.

Syllogism is then a deduction based on the notion of logical parthood. There are also other deduction types based on part/whole -relations in general. In some of these, one deduces from a feature of part or parts to a feature of whole. One can, firstly, deduce that something characterising all parts characterises also the whole (if all parts of human body are made of flesh, then the whole human body is made of flesh), secondly, that something characterising no part does not characterise the whole (if no part of animal is unhealthy, then the whole animal is not unhealthy), and thirdly, that something characterising a part characterises also the whole (if hand of a person is injured, then we could say that the whole person is injured). Hoffmann notes that all these deductions work only in some special contexts – for instance, although individual units don't have any number, collection of units does have.

Understandably, Hoffmann also thinks there are deductions moving from wholes to parts. An important specimen involves causal notions – what made a whole makes also the parts. Here the whole must really be caused by this something in a proper fashion – parents can be said to have generated their child, but because they haven't actually generated the whole child, we cannot say that they would have created her soul. Another possibility is to deduce from the notion of species as a whole that some of its features are at least possible features of the genus (if birds do actually fly, then animals in general might be capable of flight) or to conclude from something affecting the whole that a part is also affected (if the whole house is painted red, then also the roof is so painted).

We are now in a position to give a more detailed division of deduction types. All the types of deduction thus far discovered have been based on either opposition or subordination. Those based on subordination had several subtypes, one of them being the general type, based on nothing more than mere subordination or existence of some link between ideas. More particular types of deductions based on subordination included verbal deduction, based on the nominal meaning of words, and several types based on some sort of part/whole -relation. This leaves only the conversion uncounted, and it could be described as being based on the logical relations between subjects and predicates. This description suggests another type of deduction, based on some further, non-logical relation – for instance, if we know that Philip is a father, we know he must have a child.

Of the three groups of particular deductions of subordination (verbal deductions, deductions based on logical or non-logical relations and deductions based on logical or non-logical part/whole -relations), the third group contains still some further subtypes. We have seen logical part/whole -relations used in syllogisms, while deductions from parts to whole and vice versa used what Hoffmann calls non-integral part/whole-relations, in which parts can be separated from the whole and other parts. This still leaves the possibility of deductions involving integral part/whole-relations, in effect, magnitudes. One type of such deductions involves comparisons – if we know that Caesar achieved same results with less soldiers being killed than with Alexander, then we can conclude Caesar was a better general than Alexander. In such deductions we use the known order of the magnitudes of certain qualities as a standard for deciding the order of the magnitudes of other qualities – furthermore, we require some justification or reason connecting the standard to the case to be decided.

While in comparative deduction we do not know the exact quantities, in mathematical deductions we do. Mathematical deductions come in many varieties, simple deductions relying on some easy calculation (if a person makes one sin in an hour and is awake seventeen hours in a day, he will make 365 x 17 sins in a year), but more complex depend on intricate relations between various quantities. Most interesting type of mathematical deductions are those, in which some quantities (three sides of triangle) determine some other quantities in a stronger sense (such as the sum of the three angles): Hoffmann calls them mathematical deductions a priori. In these cases, it is not just a matter of quantities in some relation, but quantities having causal effects - therefore, these deductions belong to a completely different type.

All the deductions thus far have mostly been what Hoffmann calls existential, that is, they depend on static features and relations of things or ideas. The only exception was the group of mathematical deductions a priori, which Hoffmann counts as a form of causal deductions, which are based on necessary links leading from causes to effects. Hoffman delineates a number of subtypes of causal deductions: simple causal deductions, which move through one causal link from cause to effect, complex affirmative causal deductions, which use a combination of causal links to get from a distant cause to its effect, negative causal deductions, which show the impossibility of getting to some effect from a cause, imperfect causal deductions, which move from effects to causes or by analogy from similarity of causes to similarity of effects, and causal deductions of opposition, which determine the effects of opposed causes. An important point to emphasise is Hoffmann's insistence that causal deductions have different conditions of application than mere existential deduction. For instance, one cannot just assume a general existential proposition, like law of inertia, to explain some effects, if one is not clear on the actual causal mechanism leading to these effects – or then at least this is not deduction, but a weaker type of argumentation.

A special kind of causal deduction, which Hoffmann raises to a status of independent type, is formed of practical deductions, which either attempt to show that some action is means for a purpose or then argue that some element of the supposed means prevents the fulfillment of the purpose. What makes practical deductions separate from other causal deductions is a normative element – in practical deductions we are often interested to show also that some means are good or even best for achieving some goal.

This concludes Hoffmann's discussion of types of deduction. To summarise, his division of types of deduction is as follows:

1. Existential deductions

A) Deductions of opposition

B) Deductions of subordination

AA) General deductions of subordination

BB) Particular deductions of subordination

a) Verbal deductions

b) Deductions based on relations

i) Conversions

ii) Relative deductions

c) Deductions based on part/whole -relationships

i) Syllogisms

ii) Deductions based on non-integral part/whole -relationships

aa) Deductions from parts to wholes

bb) Deductions from wholes to parts

iii) Deductions based on integral part/whole -relationships

aa) Comparative deductions

bb) Mathematical deductions

2. Causal deductions

A) Causal deductions as such

B) Practical deductions

What is interesting in this division is Hoffmann's attempt to make the traditional theory of syllogisms less formal and make logic into a general scientific methodology, through which also peculiarities of causal reasoning could be handled. We shall see more of Hoffmann's attempts to give more methodological substance to logic in later posts.

Hoffmann: Study of reason – Divisions and judgements

Logical division, Hoffmann says, shares some similarities with definition, since, in a sense, both are divisions – in definition, we divide a concept (say, humanity) to more abstract concept (rationality and animality). A third form of division is then mathematical division of quantities into smaller quantities. The peculiar sort of division we now investigate, on the other hand, is a division of genus into its species. Its importance lies in providing premisses for disjunctive deductions – if we know all the species of a genus, we know that a member of the genus must belong to some species.

Compared to his account of definition, Hoffmann's discourse on divisions is rather straightforward. Just like in case of definition, Hoffmann distinguishes between nominal and real division – in nominal division, the different classes have merely a common name, but in case of real division, they truly belong to same genus. A real division presupposes then, obviously, idea of genus as a whole and idea of species as separate from one another. Furthermore, division also requires a ground for distinguishing the species from another and also some element that is common to all the species – this latter element should then be something essential to genus, or otherwise there might be a species that wouldn't have this element. Species should also fill the genus in the sense that no other species can belong to the same genus. Finally, changing from one species to another should affect thing in question in some essential manner – thus, if a piece of iron from London changes into a piece of iron from France, nothing of consequence happens to iron and therefore iron from London and iron from Paris do not form a true division.

After division, Hoffmann turns his attention to judgements, and we can be equally quick with them also. Hoffmann counts various manners in which a judgement can be imperfect. There are external reasons, such as when the proposition is more restricted than it could be, that is, when we say ”for some x”, when we could as well say ”for all x” – in such a case, improving the proposition would require a change in the subject. There might also be internal reasons, such as ambiguity – improving such a proposition does not change the subject or predicate, but merely modifies the connection between them.

Hoffmann describes in more detail methods for improving ambiguous propositions. In many cases, all it takes is to clarify the concepts or ideas that form the judgement, which is something Hoffmann has already explained in theoretical part of his work. There is also the possibility that the ambiguity derives more from the manner of connection between ideas in judgement. Hoffmann especially mentions comparative judgements, such as ”A has more quality X than B”, where X is a quality that can appear in many shapes – for instance, because intelligence is something that can appear in many shapes, ”A is more intelligent than B” might mean e.g. that A does crossword puzzles better than B, makes calculations more reliably than B etc. In such cases, Hoffmann notes, we should state clearly in what manner A exceeds B.

So much for divisions and judgements, next time we shall see what Hoffmann has to say about deductions in his practical division of logic.

Hoffmann: Study of reason – Defining definition

One important result of the theoretical part of Hoffmann's logic was to understand the importance of the clarity of our ideas, but also to note the ambiguity of what clarity means – it is quite a different matter to have sensational clarity than analytical clarity. Now, Hoffmann notes that it is either quite easy to make our ideas sensationally clear – if we have forgotten what an apple looks like, we just have to go out and see an apple – or then it is quite impossible – we cannot sense things like courage, for instance. The case of analytical clarity is more intricate, and definitions, or combinations of abstractions resulting from analysis, are the primary tool for gaining it.

Hoffmann's definition of definition starts from an actual explanation of how definitions are formed – first, we analyse our ideas, then we combine the analysed abstractions in order to see how our original ideas consist of certain features or to find completely new ideas. He declares that this is far more satisfying way to define definitions than just describing them as revealing the essence of things – such a definition does not yet tell how we can discover the structure of any essence. Only slightly better is to characterise definition as a combination of genus and differentia, which actually says merely that all things share properties with other things, but also differ from them. Its main fault lies in suggesting that all definitions must have such a structure, although one might also define an idea as a common element in several genera (just like humans can be defined as belonging to both genus of animals and to genus of rational entities).

Equally erroneous, Hoffmann thinks, are the usual ways of differentiating between nominal and real definitions. Nominal definitions cannot be mere explanations of words compared to real definitions as explanations of things, since in explaining how a word is used, one is also explaining what sort of thing one is speaking of. Furthermore, nominal definitions are not defined by consisting of mere sensuous ideas, since we can well have nominal definitions of e.g. character traits. Most importantly, Hoffmann denies the validity of equating real definitions with generative definitions, since one and the same thing might be generated in many ways, and one and the same method of generation might produce many different kinds of things.

Instead, Hoffmann thinks that the division between nominal and real definition lies in difference between possibility and actuality. Nominal definitions are such that define mere ideas, and all they need is general coherence. Real definitions, on the other hand, should refer to things beyond mere ideas, and thus, when announcing a real definition, one should take care that the definition defines something that truly exists.

Rest of Hoffmann's tale of definitions concentrates then on real definitions. The most important division of them consists of what Hoffmann calls first concepts. The idea behind this notion is somewhat complex. Hoffmann thinks that all real definitions should be justified through something. One possibility is to justify them through other concepts and their real definitions, but obviously this route cannot go on indefinitely. Thus, at some point we must come to concepts, definitions of which have to be justified through things themselves, and these then are the first concepts.

Such concepts might describe individual properties of things, but also combinations of such properties or essences, which might be essences of either naturally or artificially produced things and which might be either necessary combinations (like three angles with three sides) or contingent (like heaviness with gold). In general, first concepts divide into five classes. There are relative essences, consisting of mere ideal relations, mathematical essences, consisting of mere quantitative properties, existential essences, consisting of existentially connected properties, physical essences, consisting of causes and effects, and moral essences, consisting of means and purposes.

All these essences have different ways to be defined, Hoffmann remarks. Relations can be defined only through the properties of what is related, while mathematical essences can be defined either through their method of generation or through their sensuous properties. Definitions of physical essences depend on whether the things in question are natural or artificial: natural physical things might be defined by their method of generation, their various sensuous properties and causal powers and their relations to other things, while artificial physical things are defined by their structure and their purpose. While moral essences in general should be defined just in case of purposes and means, especially in case of rights and obligations one must also consider conditions in which those rights and obligations can be actualized.

Finally, existential essences can be defined through various means. Firstly, they can be defined through sensuous changes affected by them – for instance, substance is something that subsists by itself, that is, that we can see to exist in various places, not bounded to another thing. Secondly, they can be defined through their inexisting parts or abstractions – for instance, a real thing can be defined through its abstracted properties of a) being thinkable and b) existing outside thinking. Finally, they can be defined by explaining their method of abstraction – for instance, extension is that which is left of a spatial thing, when we abstract from its forces and from the substrate behind them.

Hoffmann also considers whether one needs some further essences, notably in metaphysics or logic. In case of metaphysics, Hoffmann can just note that all essences handled in it, fall into some already dealt cases. Same holds in logic, where e.g. a concept of subject is relational and concept of deduction is causal.

First concepts serve as a beginning of definition, and Hoffmann characterises all further forms of real definition also through their purpose in cognition. He also notices that some definitions might actually have various purposes and thus fall into more than one kind. Furthermore, he mentions fascinatingly that some definitions, what he calls ignoble, serve no purpose at all – unfortunately, he provides no example of such an intriguing class.

The two true classes of real definition, which are not first concepts, are characteristic definitions, which help to distinguish things, and causal definitions, which help to explain sensuous properties of a thing. The two classes overlap one another, as Hoffmann already implied. Starting from causal definitions, it is not so much the existence, but properties of things that are explained by them – the definition begins from the essence of a thing and thus can be used a premiss to explain why the thing has this or that property. This is a very wide understanding of causality and could be applied also e.g. to mathematical things.

Characteristic definition, then, might actually be also a causal definition – by showing the essence of a thing, we also make it possible to distinguish it from other things. This sort of characteristic definition Hoffmann calls a priori, but he also accepts a posteriori characteristic definitions, which are clearly non-causal – in these definitions, we distinguish a thing through some conditions we find it in.

This concludes Hoffmann's theory of definitions. Next, he will handle divisions.

Hoffmann: Study of reason – Learning from experience

While the first part of Hoffmann's grand work studied theoretical underpinnings of knowing truth, second part should deal with the difficult task of finding truth in practice. This involves going through questions already dealt in the first book, but from a different perspective. For instance, in the first book we learned to classify ideas according to various criteria, such as their sources and their relations to one another. In the second book, Hoffmann wants to merely how to achieve ideas that can be used for acheiving truth.

Now, an important precondition for achieving truth is to have ideas at all – no ideas, no knowing truth. Furthermore, the primary and in a sense first source of ideas is sensation or experience, which also connects ideas with things. Thus, a precondition for knowing truth, Hoffmann says, is to have reliable experiences of things and especially avoid any possible mistakes in experience, reasons for which Hoffmann goes on to enumerate – we might think we have experienced something, which we haven't actually experienced, our experience of something might be lacking in details etc.

Of these reasons, the most important is the first – some things really are beyond the ken of our experience and cannot thus be justified through experience. We have already seen that the truth of experience itself is something that cannot be experienced, but must be justified through some further arguments. Similarly, we cannot really justify through mere experience that what we experience has just the properties we experience it to have. Thus, a Leibnizian, who denied that external things had any influence on our soul, could not say that the world existed in the manner that our sensations appeared to suggest – and not even that there was any world outside ourselves to speak of.

Furthermore, there are plenty of other things that we cannot directly sense, like future events and infinite collections of things, which prevent us from basing universal propositions on mere experience. In addition, because we cannot observe things that haven't really happened, but might have happened, we cannot draw contrafactual conclusions from mere experiences – e.g. we cannot say on the basis of mere experience that someone would have dies, if she would not have taken a medicine.

A further important question for Hoffmann was to decide what sensations and experiences to choose as basis of further investigation, since clearly one could not consider everything one sensed. Here Hoffmann emphasises the role of experimentation. One should not just go on perceiving things randomly, but e.g. make a preliminary hypothesis and see whether it fits what we perceive. Furthermore, in case of complicated questions one should divide the problem into several subproblems, in order to make it easier to find the important observations. This is not to say, Hoffmann admits, that controlled experiments are the only worthy way to experience and that mere observation is of no consequence. On the contrary, it might well be that such observations reveal some unexpected facts that could not have been discovered through tightly controlled experiments.

Such is Hoffmann's short investigation of the intricacies of experience. Next in the progress of methodology, Hoffmann considers definitions.

Hoffmann:Study of reason – The search for truth

While Wolffian school had relegated the question of truth to the practical or applied side of logic, Hoffmann understood its value and insisted placing it in theoretical side. Corresponding with this exalted place, Hoffmann's actual investigation of truth is surprisingly thorough, even if it ultimately fails as a reliable evidence for truth.

First of all, Hoffmann delineates the topic by noting that we are not speaking of moral truth, which means correspondence of a speech or writing with author's intentions. Instead, it is truth as the correspondence of one's actual thoughts with actual things that Hoffmann has in mind. Furthermore, this subjective truth is dependent on still further notion of objective truth or correspondence of possible thoughts with actual things – this objective truth, Hoffmann says, is reducible to the notion of reality or actuality.

Hoffmann notes the paradoxical nature of ascertaining the possibility of objective truth. Such ascertainment can only happen through some general proof, but it is just these human tools of proof that are in question in this investigation. Human ability of deduction or inference must then be applied to itself in order to show its own validity, which makes the whole endeavour rather circular. Hoffmann notes that this is just inevitable and even distinguishing feature of all basic principles – proofs for them must be of completely different sort than proofs of common propositions.

The first and foremost task is to investigate the formal principles by which human beings prove things – that is, what we would call rules of inference. We already know that we feel forced to accept these rules, but this does not mean that the rules would work also with actual things. It is the explicit task of the three highest principles to provide this required link of ideas with things, while other principles might just connect ideas with one another.

Beginning with the highest principle of non-contradiction, Hoffmann notes that the only way to justify it is to show how impossible it would be to think against it. Suppose we consider the proposition ”something both is and isn't”. This proposition must be accepted as either true or false, both true or false, neither true or false or epistemically uncertain. The last possibility can be ignored, since uncertainty concerns only the status of a thinker and not the proposition itself.

We are then left with four options, of which we would like to show the falsity to be the most convincing. We cannot really state that the proposition would be both true and false, since we cannot understand what that means. If we accepted that it is neither true or false then the proposition wouldn't even be a proposition, which must always be either one – and we would have nothing to think about at all. The final possibility would be that the proposition is true, but accepting something as merely true already presupposes that we can use the (epistemic) principle of non-contradiction of propositions, which in turn is based on the (ontological) principle of non-contradiction of entities.

We might be skeptical about Hoffmann's desire to base epistemic principle of non-contradiction on ontological principle of non-contradiction, but it was quite common in his days. Hoffmann's proof is then a sort of trilemma: either there is nothing to think about, when we discuss of ontological contradictions, or then ontological contradictions just are beyond our capacities to think – or then we must just accept the principle of non-contradiction.

One might say that this is a rather good proof that the principle of non-contradiction is natural rule for us, since we cannot even imagine what it would even be like, if world did not follow it, but that it does not really justify that the principle also holds with real things. Hoffmann accedes this point and asks us then to think about such a thing that would both be and not be – since we cannot do it, we cannot even say anything about it and it would thus lie completely outside the realm of meaningful discussion, in which notion like truth can only be applied.

Hoffmann's apparent attempt has been to prove the validity of the principle of non-contradiction, but what he has been capable of proving is more like incapacity to speak of the truth of contradictions and the existence of contradictory things, except by denying them – quite good result in itself, since it makes evident that when discussing truth, one can just assume that no contradictions exist. The only remaining worry is that some other type of intelligence might find contradictions quite acceptable and would be capable of speaking about them, thus making it possible to connect the existence of contradictions with the idea of truth. Hoffmann's only remark is that while it is verbally possible to accept the existence of such thinkers, from the viewpoint of out notion of truth such thinkers would be speaking mere absurdities. In other words, such thinking would be quite alien to our way of thinking and our notion of truth and we would be quite justified to deny that their thinking has anything to do with truth.

While we must thus accept the principle of non-contradiction, as valid among all things we have the ability to think of, in case of the two other highest principles we must accept some restrictions. In a sense, we might be able to use the very same method as we used in justifying the highest principle. Suppose, for instance, that we must think about two features, A and B, always as combined together, but that in actual fact A and B would not be combined in some thing, but it would be A without any B – say, while we must think that force is always connected to some substance, there would be a force that would not be connected to a substance. The problem in thinking about such a possibility would be that we would have to think about a contradiction – we would be naturally forced to think about the necessary connection of force and substance, which makes us incapable of even holding the notion that forces could exist without substances. Again, this proof merely pushes the possibility of things, which would cancel the validity of the second principle, outside the realm of meaningful discussion. Furthermore, Hoffmann holds, the second principle works only when the two properties are both positive, that is, when we are referring to two ideas we must always think together. If, on the other hand, the other idea is only negative, that is, actually a mere lack of an idea, the necessity to think of an idea together with a lack of another idea might just be a result of our limited conceiving ability – Hoffmann is here probably thinking of our incapacity to think of properties of God in a positive manner.

The justification of the third basic principle of proof follows a similar pattern as the justification of the second principle. Hoffmann asks us to consider two ideas we find repugnant to connect and then asks us to try and think that the two would be actually connected – the result is that there is actually no subject to talk about, since the two ideas cancel one another. Just like with the other principles, the justification removes all discussion of such combination of incompatibles beyond field of meaningful discussion about truth. And just like with second principle, Hoffmann notes that the third principle can be used only in restricted manner – we might be seduced by our inability to sense or perceive a connection of two properties to think that they would be incombinable even in realms surpassing mere senses. The restrictions on the two latter principles also make metaphysics often into a mere probable discipline, Hoffmann concludes – we cannot be completely certain whether some seemingly incompatible combination of properties cannot truly be actualised.

Assuming Hoffmann's justification of the three highest principles of inference have been accepted as bridging the gulf between ideas and things, we can then accept the rest of the principles justified through these three principles. Often these sub-principles, such as Hoffmann's version of the principle of sufficient reason, rely on some necessary connection or incompatibility of ideas, which can then be accepted as a proper pattern of inference in realm of things also through the use of second or third main principle – thus, because we must always think changes of a thing either as caused by external agents or as happening through spontaneous action of the thing, in a meaningful discussion of truth this connection should be thought to hold also between all things.

One can do little with mere inference patterns or one needs some material propositions as premisses of one's inferences. A simple set of these is provided again by the highest principles – through the second and the third principle we can accept as immediately true axioms all propositions combining things we necessarily connect and separating what we necessarily separate. Yet, this is not enough, Hoffmann admits, and we must also defend the general reliability of our experience, and more precisely, of sensations, on which experience is based.

Hoffmann's defence of sensations is divided into three parts. Firstly, we must know that we can distinguish sensations from other similar mental events, such as imaginations. Hoffmann's justification for this seems overtly simple: we can identify sensations as being produced by external objects. In other words, in sensing the human consciousness is passive, that is, it is incapable of saying what to sense – in comparison, imaginations might be produced by free choice. Problem is that we often still appear to be able to confuse sensations with various other mental occurrences. Hoffmann himself admits as much and delineates four cases where confusions might happen: when we are sick, when we are dreaming, when our sensations are obscure and when we are mixing implicit inferences with our sensations (in the last case Hoffmann is referring to the famous case of a square tower that looks round from a distance).

The first two cases Hoffmann dismisses quickly just by saying that we are well able to recognise sickness and dreams – since he is not explaining his point, it is difficult to say whether he means that an external observer could do it or whether he thinks there truly are some clear marks, by which a sick or dreaming person could recognise one's condition. The case of obscure sensations Hoffmann can clear up pretty quickly by noticing that obscure sensations do not produce as much confidence and can therefore be discarded because of the doubt they produce.

The final case is perhaps the most intriguing. Hoffmann notices that in affirming something as round, we are actually saying that it has no angles. Yet, we cannot straightaway sense lack of anything – we can merely not be able to sense something. This lack of sensation might then be caused by various things – there might not be anything to sense, but the thing to be sensed might also be far away etc. When we then move from a sensation of tower containing no angles to a proposition that the tower has no angles, we are not just perceiving, but using this perception as a ground for an unjustified inference – the unreliability of the proposition is then no proof against the reliability of sensations. Hoffmann also notes that all causal propositions must be based on similar inferences, because we cannot literally see one thing causing something else – an important acknowledgement of a Humean statement.

Supposing then we accept that Hoffmann has some evidence fo supposing that we do reasonably well distinguish sensations from imaginations, we come to the second question: is there actually any object behind a sensation? This is the place where Hoffmann can criticize the two other leading theories of body-soul-interaction: Leibnizian pre-established harmony and occasionalism. Hoffmann attacks Leibniz' theory, because according to it we could actually never distinguish sensations from imaginations, since both are actually produced by the soul itself. Here Hoffmann apparently doesn't notice that sensations might be so obscure that we never really notice they have actually been produced by ourselves. Yet, Hoffmann has a separate argument against that point: if the difference between sensation and imagination is only that one is more obscure than the other, then this difference is only one of degree and one could easily overcome it through careful clarification. We are here approaching the Kantian idea that sensation with its passivity is completely different in nature from more active events of mental life and thus in need of a clear demarcation from latter.

Occasionalism doesn't pose as much a challenge to Hoffmann. Supposing God would make us experience sensations – something he could well do, Hoffmann admits – we would have to imagine that he wants to deceive us into believing that things exist. Yet, this appears to contradict God's good will, so there is no reason to believe that these things would not exist.

The final question concerning sensation is then whether sensation reveals accurately what features an object has. Here Hoffmann has an easy answer. What do we mean by saying that e.g. proposition ”grass is green” is true? Surely it can only mean that when we observe certain object, called grass, this object produces in us the sensation of green. Generally, with such propositions based on immediate sensations, truth means merely the accordance of the proposition with other sensations (actual or possible). All we need to see, then, is that sensations are reliably consistent in the sense that what we once perceive as green is in similar conditions still green.

Now, all of the arguments thus far have aimed at defending the possibility of objective truth, that is, at showing that in an ideal case a person following these rules of inference and having sensations could make reliable conclusions. Problem is whether we can still prove the possibility of subjective truth, that is, can we show that we are actually in a position where e.g. we can reliably follow our intuitions about connections between ideas. Hoffmann's answer is that certainty lies in the inner sensation, in other words, in our capacity to be aware of our own ideas as states of our mind. If we have vivid enough sensations of our idea, we can be convinced that our mental capacities are working fine and that we can rely on them in constructing truth claims.

Problem of Cartesian demon is still lurking. What if some powerful being would have made us think that we are reliably perceiving something, even though we are not? Hoffmann's peculiar answer is that according to his beliefs such a being could only be God, and if God wants us to believe something, then we know that belief is good for us, even if it is not literally truth. The answer belies Hoffmann's pietistic background, but also has an interesting pragmatist twist: if it works, why bother fixing it.

This concludes the theoretical part of Hoffmann's work. Yet, we are still only halfway through his massive book, since we still have all of the practical side to investigate. I shall begin with the question of using experience correctly.