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.