Crusius, Christian August: Road to certainty and reliability – Truth and logic

Crusius finally begins the proper study of logic, after the introductory chapters, from the theoretical part, studying powers and activities of understanding (Verstand) that make the knowledge of truth possible. By truth he refers to the correspondence of thoughts with their objects, or to put it more precisely, such a relation between an understanding that thinks and the object it thinks, so that if the former thinks that the something about the object is, is not, is possible or impossible, this something respectively is, is not, is possible or is impossible also independent of this thought. Crusius emphasises that in this definition one should not speak of the object being something independently of the understanding, since the definition should apply also in cases where the object handled is understanding itself.

Crusius notes that truth must be distinguished from both error and ignorance, where error means a lack of correspondence between thought and its object, while ignorance means a lack of any thought about a topic. In other words, we cannot speak of truth if there is no thought that has ideally exactly that which object has really. Crusius underlines that we are speaking here only of truth in its logical meaning, and in addition, there is also a notion of truth in moral or ethical sense, that is, truthfulness, which means correspondence of a state of mind with the intended meaning of external signs that are used for communicating this state of mind. Finally, Crusius also points out that sometimes we speak simply of truth, when we actually mean some true proposition.

Crusius notes that when an object is compared to an understanding, this understanding can be either a possible understanding or an actual understanding that has some knowledge of the object. In the former case, he clarifies, we are speaking of objective or metaphysical truth, which means thus truth or possibility of an object itself, insofar as it is regarded as something that could be known by any understanding, while the latter is then subjective or logical truth, which means truth in an actually existing understanding or such a relation between a representation and its object, where the representation and the object correspond and thus some truth is known. Furthermore, Crusius notes, all objective truth is subjective in relation to divine understanding.

In human understanding, Crusius continues, all subjective truth is generated by the impossibility to think opposite of what one is conscious of, where the impossibility can happen in all cases or only in the current conditions. He notes that our first thoughts are always sensations, while other thoughts are then abstracted from sensations, so that we become thus conscious of relations between our thoughts or propositions and can attend to them. Furthermore, Crusius says, when we attend to what we can and cannot think, we generate a very special kind of propositions or rules indicating awareness of deductive relations: if certain propositions are connected in certain manner through the ideas they contain, we are bound to take one as true, if we take the other as true. With such rules, we receive a capacity to make deductions with such rules. Now, Crusius argues, since we know the truth of every proposition from the falsity of its opposite, all knowledge of truth in human understanding happens through deduction, although we are usually not aware of these deductions, because they happen so easily.

On the basis of the previous considerations, Crusius states that subjective knowledge of truth in human understanding is dependent on the capacities of sensation, abstraction and deduction. According to him, these capacities are physical, hence, we can abstract physical laws from their use. In a similar vein, since these capacities are under the control of our free will, the laws of free will can also be abstracted from their use. Thus, Crusius concludes, the human understanding can find truths concerning the whole created world (both the physical bodies and the free will), if it just follows its own nature.

Conclusion that Crusius thinks he has proven is that human understanding works just fine by its own nature, even without any further education. Then again, he at once admits, errors are in this case possible, because our representations of the rules of deduction are obscure. Logic is thus required to make understanding more capable of knowing truth. In its abstract sense, Crusius explains, logic is a science that represents distinctly and exactly the effects and laws of understanding and thus shows its correct use. Logic has also, he adds, a concrete sense, according to which it is a capacity of a subject to know fundamentally the effects and the laws of understanding and its correct use.

Crusius considers the capacity of our understanding to work and thus to know truth without logical education and calls it natural logic, which means thus an inherent feeling of true and false that generates a capacity to evaluate grounds for and against something. A person with good understanding can thus recognise through this natural feeling, if some suggested laws and rules of understanding are untrue, which Crusius takes as a justification that incorrectness of suggested logical laws can be shown also a posteriori from experience, just like in arithmetics. Yet, he adds, there are more differences of opinion in logic than in arithmetics, since reflection on kinds of abstraction and on grounds of truth is more difficult than thinking about more concrete topics. This difficulty makes humans ignore the investigation of their understanding and thus rely too much on their natural logical capacity, which has a tendency to error. The wilful ignorance is furthered, according to Crusius, because treatises of logic seem to be so far removed from the use of understanding in practical life.

Logic teaches the kinds of abstraction and methods of knowledge, thus, Crusius thinks, it is the only means to make cognition sharp. He even calls logic the soul of philosophy and scholarship, because it makes them correct and distinct. Because of logic, he underlines, knowledge is fruitful, and logic gives understanding the ability to know truth and evaluate judgements, hence, it strengthens our capacity to study. In effect, Crusius concludes, logic is the subjective foundational science, just like metaphysics is the objective foundational science.

Crusius identifies two weaknesses in natural logic, which the proper logic can fix. Firstly, he says, when we are dealing with complex topics, natural logic is not enough for distinguishing true from false and for arranging our studies in a suitable order. In other words, he explains further, when we use natural logic for dealing with a complex topic, we might find material for justifications or grounds, but we still cannot give them the proper form, that is, place them in such relations that would make them justifications of something. The result would then be, Crusius insists, that we may end up suggesting many grounds or justifications that in their current state do not justify anything. He thinks that this is especially true with probable proofs, where recognising true and false is more difficult. The conclusion of Crusius about the first weakness is that the natural logic is applicable only, on the one hand, in common tasks of human life, where object is characterised with sensuous properties, and on the other hand, in distinguishing moral good and bad, because our understanding of good and bad is supported by conscience and a feeling of guilt. The second weakness Crusius finds in natural logic is that the lack of proper logic often leads to errors and even outright scepticism.

Crusius goes on to divide the parts of logic. First of these parts is, according to him, the theoretical part that handles grounds that make the knowledge possible in the human understanding, and in addition, must also consider the powers of human understanding and its effects or concepts, propositions and deductions. The study of the powers of human understanding Crusius calls noology, necessary truths of which belong also to metaphysics. Crusius also emphasises that noology needs to investigate only what lies in the soul, together with the general features of the dependence of certain effects of understanding from the body. Then again, external conditions of sensations in bodies belong to the study of nature.

The other or practical part of logic, Crusius says, explains how the powers and effects of understanding should be used for the purpose of truth. It also deals with the illnesses of these powers, the experience as a modification of the power of sensation, use of concepts in divisions and definitions, use of propositions in judgements, and use of deductions in proving, recognition of seeming proofs and decision over colliding proofs. All the effects in unison, Crusius adds, are handled by the study of method and also in some special topics, such as interpretations, special kinds of probability and disputation.

Joachim Darjes: Introduction in inventing art or theoretical-practical logic (1743)

Darjes has been one of those philosophers who, while outwardly staying within the Wolffian school, have in truth distanced themselves from some key tenets of Wolff's system and taken their ideas to original directions. We have already seen Darjes suggest rather interesting innovations in his book on logic. If you know the field of German philosophy in the first half of 18th century, you won't be surprised to hear that his Latin book on same topic, Introductio in artem inveniendi seu logicam theoretico-practicam, is a much fuller treatment.

In a sense, most of the additions concern the necessary presuppositions of logic, that is, its metaphysical underpinnings. Like all the Wolffians thus far, Darjes considers certain key notions that we hold to be logical as ontological – for instance, the principle of contradiction is not a principle denying the affirmation and negation of the same proposition, but describes the ontological impossibility of incompatible things actualising at the same position. Darjes goes even further than other Wolffians, suggesting in a manner reminiscent of Russell that the subject-predicate -relation is not just a human convention, but reflects the order of reality itself.

Another interesting novelty in Darjesian ontology is that the basic ingredients of the reality are not so much individuals, but characteristics, of which individuals are then full combinations, to which no new characteristics can be added. Part of this ontological picture is the idea that some of these characteristics are atomic or not analysable to further characteristics. This picture resembles Wolffian idea of determinations, but seems ontologically stronger – Darjes takes characteristics to be things, if only partial ones.

Another interesting, if only a passing addition to the preface of logic, is Darjes's account of truth. As you might recall, with Wolff, truth in the logical sense was assigned a place only in the applied logic, because truth required relating the content of pure logic – concepts, judgements and syllogisms – to what they are supposed to represent. In a sense, Darjesian reorganisation is quite natural. With Darjes, as with all Wolffians thus far, logic is based on psychology, because concepts, judgements and syllogisms exist within human soul. Surely the relation of these logical items to what they represent is not a mere afterthought, but a necessary part of the psychology of human thinking underlying logic.

I have already described the most important novelties in the Darjesian logic itself in my description of its German version. This does not mean that his Latin logic would have nothing of interest, beyond the preface. One peculiar feature of Darjesian Latin logic book is its emphasis on invention, clearly expressed in the title of the work. Darjes is anxious to present not just theorems, but also solutions to problems – for instance, Darjes does not just define clear concepts, but also explains how to make one's concepts clearer. This is not a complete novelty, since we just saw Bilfinger doing something similar in his own logic.

Although sections on rules for disputations, communication of truths and hermeneutics are an addition in Darjes's Latin logic, they are not that peculiar in the more extensive context of logic textbooks. More interesting is the second part of Darjesian logic, which he calls dialectics, in separation from the part containing analytics. In effect, what Darjes means by dialectics is a study of probability and a search for probable truths – it is like reading part of Aristotelian logic through Bayesian eyes. What is even more intriguing is Darjes's idea of applying probability to pondering testimonies or to evaluating different hermeneutical possibilities.

This is just a glimpse of Darjes's innovations. Next time I shall again return to Wolff's natural law.

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.

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.

Perfectly true order

I can be quite quick with Wolffian notions of order, truth and perfection, since I covered them already while discussing his German metaphysics. Something of a novelty is Wolff's definition of order, which he states to be a similarity in the modes of things either located nearby each other or following one another. Such an order is then an explanation for a certain thing with particular features being in the place it is – for instance, in a well-ordered library, the place of an individual book is explained by the classification system requiring that a book with certain topic is situated in a particular place. In the case of library, the order is contingent or based on the external factor that some librarian has arranged the books in a suitable manner. There is also a possibility that the order is based on nothing but the very essence of the things ordered: this is the case, for instance, in ordered sequences of numbers.

A well-ordered library?

The principle of ordering can be linguistically embodied in a rule or a set of rules, Wolff asserts. The different rules can then be organised into a hierarchy of rules, in which the different subrules are grouped under more general rules – think of an instructional booklet for keeping a library in good order. As anyone with some experience on libraries knows, often librarians have not been able to order all the books perfectly according to the instructions, for instance, due to physical limitations of the library building or insufficient time for organising books. Similarly, there can be defects in all sorts of orderings, which makes it plausible to speak of more and less perfect orders. A complete lack of order or confusion is also a possibility.

Truth in an ontological or transcendental sense of the word or reality, as we might call it, can then be recognised through its orderly nature. Dreams, Wolff continues, are characterised, on the contrary, by a lack of order of confusion. Wolff goes even so far as to suggest that dreams would be contradictory, which can at most mean that they contradict the rules governing true reality, or indeed, almost all sets of rules. Because all things should have some orderliness in them – at least they have an essence that determines their attributes and possible modes – all things are in some measure true, Wolff concludes.

Finally perfection, which Wolff identifies with the scholastic notion of transcendental goodness, is defined as consensus in variety or unity in multiplicity. Perfection must again have its ground, and this ground is the regularity or orderliness of its constituents. Lack of perfection can then be defined as imperfection or evil. This does not still mean that an exception in the orderliness of some structure would entail its complete imperfection. Indeed, the imperfection might be just apparent, because from a more extensive viewpoint the apparent imperfection might be governed by some rule.

One might reasonably ask whether Wolff is smuggling some normative notions into his ontology with these definitions. Indeed, he appears to suggest by associating the notion of orderliness with words like truth and perfection that order is somehow preferable to a lack of order. Why should we assume that reality is well-ordered, instead of being at least somewhat chaotic? And why should we deem regularity as something perfect and worthy to strive for?

The most plausible defense of Wolff is to assume that the definitions as introduced in ontology should as yet carry no normative weight. Instead, the names hint at future arguments in future parts of philosophy, where the notions are shown to coincide with how we usually understand these words. Thus, we might see e.g. in theology that God has created an orderly world and in ethics that regularity is something we should strive for.

So much for these notions, and indeed, so much for general characteristics of all things. Next time we shall look at some complexities of space-time.

Truth to be told

With syllogisms ends the theoretical part of Wolff's Latin logic: we are not anymore just looking at the various shapes human cognition can take, but actually think how to use these various shapes. The practical part of logic begins then by investigating truth, thus giving logic its purpose: it is true judgements that we want to find, or at least truthlike or probable propositions.

The investigation of truth began at least with Aristotle's De Interpretatione, where a judgement was said to be true, if what was said of the subject or topic of the judgement did hold of the topic: it is somewhat uncertain whether this is what nowadays is called a correspondence view or deflationary view of truth. This, of course, was just a definition of truth, which is not useful in telling when a judgement is true: this is work for the criterion of truth. Criterion was a particular interest of hellenistic thinkers, especially Stoics, who suggested that certain appearances were reliable basis for forming judgements, and their critics, Academicians and Sceptics, who noted that Stoics did not have a reliable criterion for recognizing these appearances.

Wolff makes this distinction between definition and criterion of truth in terms of nominal and real definitions: even if we can explain what truth is, we still cannot reliably find truths. His nominal definition is at first sight rather Aristotelian: proposition is true if and only if its predicate applies to its subject. Yet, one might foresee some difficulties: proposition should be linguistic entity, consisting of words, is truth then nothing but a formal relation between words?

This question is closely related to the supposed overreliance of Wolffian metaphysics on logic, evidenced by his wish to base ontological law of sufficient reason on logical law of contradiction. We have seen that this overreliance has been just a misunderstanding, because Wolff viewed even the law of contradiction in an ontological sense, as describing the fight of incompatible possibilities over actuality.

Indeed, the relation of the two disciplines is rather opposite, as Wolff thinks logic to be an offshoot of metaphysics, particularly ontology and psychology. Words are not just abstract marks with a peculiar syntax, but produced by conscious beings and refer to possible thoughts of those conscious beings – this is the link to psychology. Furthermore, these thoughts are not just mental images, but represent independent things – this is the link to ontology. Wolff can then add another nominal definition of truth: judgement (or proposition expressing it) is true, if and only if it coincides with the thing it represents.

Now, it is clear that this nominal definition cannot by itself tell whether a proposition or judgement is true. Wolff's suggestion for the real definition or criterion is at first sight rather perplexing: if predicate is determined by subject, the proposition or judgement is true. At first sight one might fail to see how Wolff's definition makes sense. Consider an unconditional universal judgement, like ”humans are rational”. Here, Wolff continues, the subject or humanity as such determines a set of predicates that apply to this subject and one of these predicates happens to be rationality. The problem appears to be whether this definition is then too strong, as it seems to talk more of a conceptual, essential or necessary truth: even if all actual humans would be rational, it might be that humanity would still not imply rationality, because there could be irrational humans. The problem is solved, if we consider universal judgements as ranging over all possible worlds – or else, if we suppose they have an implicit condition that we consider only the actual world and its inhabitants.

The example above accounts for how the criterion is about to be used for universal propositions and judgements. Because affirmative and negative propositions come always in pairs and one of them cannot be true, while other is, negative propositions don't add anything new to the equation. Same is true of particular propositions, because if some rabbits are white, this just means that all rabbits under some unspecified conditions compatible with being a rabbit are, that is, there are some properties such that from the concept of a rabbit with these properties the concept of whiteness can be deduced (and this combination of characteristics is not contradictory). If for some particular proposition or judgement ”some Ps are Qs” no such conditions exist (that is, for no M, such that ”Px and Mx” is possible, does "Px and Mx" essentially imply ”Qx”), then, because Q itself would otherwise be one such M, Q and P cannot have any common elements or no P is a Q.

The case is rather different with singular propositions/judgements, which cannot just be reduced to previous questions. The subject in question would be an actual existent individual, which in Wolffian philosophy can exist only within one possible world, actual or non-actual. The quest for truth of a singular judgement, e.g. ”Peter writes a book” would need to determine whether writing a book is something that is currently happening with the complete concept of Peter, which in the case of an individual boils down to seeing whether we could perceive Peter writing something at the moment.

Wolff goes on to note that this notion of truth is such that it is retained throughout deductions, that is, if premisses are true, then conclusion must also be true. As the starting points of a demonstration should be as true as anything can be, demonstration appears to be relevant from an epistemological viewpoint. Indeed, Wolff goes as far as to say that demonstration is the only thing one requires for separating truth from falsities – bold statement and apparently rationalistic, but one must remember that Wolff does admit empirically verified premisses in demonstration.

Wolff makes rather curious connections between truth, possibility (non-contradictoriness) and conceivability (capacity to form a concept of something):he says that affirmative judgement corresponds with a possible concept (negative judgement with an impossible concept) and that one can conceive only true propositions. The first connection is actually rather simple to understand. True affirmative proposition, like ”gold is yellow” describes a possible complex concept of yellow gold. Indeed, in the case of such a universal proposition, the concept is possible in all circumstances, or the combination of the two concepts is necessary, if we just have a distinct enough concept of gold. Then again, a true particular affirmative judgement, like ”some gold is pressed into coins” describes a combination possible in some circumstances. True negative universal proposition ”gold is not black” says that it is not possible to think of black gold (even if we could think of a black goldlike substance), while true negative particular proposition ”some gold is not pressed into coins” tells that this combination is not possible in some circumstances.

Conceivability thesis then just follows from the definition that those propositions are conceivable that one can form a notion of. In case of trying to conceive yellow gold, the statement seems plausible, but what about the proposition ”all gold is pressed into coins”, which is clearly false, although one can think of gold pressed into coins? Wolff's point appears to be that one cannot think of gold in itself, without any further properties, as pressed into coins: gold coins is gold under some circumstances and not generic gold.

Conceivability forms a sort of transition from the objective notion of truth to more subjective notion of certainty. No proposition is certain or uncertain in itself, but only in relation to some particular person: if I know whether a proposition is true or false, I am certain of it, but if not, I am uncertain of its truth. A certainty can be gained a posteriori through observation or a priori through demonstration, which can be either direct or indirect: we shall speak more of these notions, when we discuss Wolffian methodology.

A notion closely related to certainty is probability, which Wolff defines in terms of requisita ad veritatem, which could be translated here as truth conditions: in effect, Wolff is discussing of those things on which to base affirmation of certain judgement. Thus, for a definition like ”triangle is a figure with three sides” the truth conditions are the various characteristic marks contained in the concept of triangle: definition must be based on these characteristic marks and account for all of them. Any other universal categorical judgement, on the other hand, has the definition of subject as its truth condition. Thus, the truth of Pythagorean theorem should be decided on the basis of the definition of triangles. Then again, in case of a hypothetical judgement, we also have to take the preconditions or the antecedent of the judgement into consideration. If we then follow Wolff's suggestion that particular judgements are hypothetical judgements with indeterminate conditions (for some unknown conditions and all X of certain species, if X fulfills these conditions, then X has a certain property), the truth of a particular judgement ”some bananas are rotten” would boil down to i) definition of a banana and ii) the possible existence of some conditions under which bananas would be rotten.

Now, if we can account for all truth requirements or conditions of a judgement or proposition, we would be certain of the truth of that judgement – we would have all the reasons to believe in that proposition. Then again, we might have only insufficient account of these conditions, in which case the proposition would be only probable and not certain. Wolff suggests some basic laws that hold for probable propositions, such that syllogisms which have one certain and one probable syllogism lead to just probable conclusions, and recommends the study of probability as a future task of logic, because it is something required in empirical studies, where full certainty is often impossible to achieve.

The difference of probability and truth leads us finally to the difference between the three levels of certainty, which I have already discussed in another post. Actually, I failed to mention there that Wolff also considers a fourth level, namely, the level of error, and indeed, in Latin logic he uses considerable time to go through various forms of spurious reasoning. I shall just mention the basic difference between sophism and paralogism, the former of which is a hidden type of spurious reasoning, while paralogism makes its mistakes explicit: we shall later on see these concepts with Kant.

The notion of different levels of truth-likeness raises a question far more serious than the supposed logication of Wolffian ontology: how does Wolff account for the normative element of logic, that is, for the fact that e.g. certain forms of deduction are said to be better than others, and in general, that methods for finding truth are to be followed more than methods for finding erroneous views? Certainly Wolff could turn his logic into hypothetical imperatives of the form ”if you want to find truth, use these syllogisms”. Then again, one might ask if logic even requires more than just hypothetical imperatives. The relevant categorical imperative would be something like ”try to find truth in all circumstances”, but logic itself does not appear to dictate that one should attempt to find truths.

So much for truth, next time we shall see Wolff's methodology for finding it.

Christian Wolff: Reasonable thoughts on God, world, and human soul, furthermore, of all things in general - Truth vs. dreams

At least since the days of Descartes the problem of the reality has perplexed philosophers. Is the world that we perceive truly real, and not a mere dream, hallusination, figment created by a powerful daemon or mere fiction fed into our brain by a mad scientist? Wolff himself notes the problem, but apparently fails to take it very seriously. Wolff simply decrees that in dreams all processes are less ordered than the truth. By order Wolff means the occurence of some similarity, that is, of a pattern or a rule, which the things follow. Ultimately the basic criterion is the principle of sufficient reason or causality: processes in dreams do not follow any causal laws.

Wolff's criterion is perhaps enough for distinguishing our usual dreams from what we happen to call reality. He is not interested of a possibility that a new, even more real world might be discovered beyond the world of experience. This might be a consequence of Wolff's pragmatic nature – after all, there has to be some limit for the demand of indubitability. Furthermore, Wolff could continue, if we some day discover that we have been dreaming all along, at least this discovery will be made through the very same criterion of the regularity of processses. Here Wolff is once again paving the way for German idealists, who also had some doubts about the need to find any ultimate reality beyond the world of experience.

In modern analytic philosophy one is accustomed to mean by truth a characteristic of propositions, beliefs etc., while here Wolff essentially refers by truth to the reality. Furthermore, he almost instantly extends the notion of truth to apply to all sorts of processes. Truth thus becomes a quantifiable characteristic: the more regular and law-governed a thing is, the truer it is.

Wolff also introduces the notion of perfection (Vollkommenheit), which he then immediately characterises as a coherence of a manifold, which is yet another form of regularity in addition to truth as a regularity of processes. The regularity in its various guises appears then to be the primary value characterising simple things: the goal the finite simple things try to acheive is the regularity both in their internal processes and in the system of things they causally engage with.

Like with truth, Wolff also suggests that perfection is a quantifiable characteristic. Indeed, he appears to suggest that there could be a calculus of perfections for counting from individual perfections the quantity of their combination. Yet, the value of this combination is not a simple sum of the perfections, because one must also take into account how well the perfections fit together. For instance, the perfection of a house is not to be determined by its beauty and its utility, but one must also consider how well the beauty and the utility serve one another.

A complex thing with several constituent perfections might not then be perfect as a whole, if the perfections clash with one another. Similarly, harmony of apparent imperfections can produce a greater total perfection. It takes no Leibniz-scholar too see where this line of reasoning is heading to – we might indeed live in the best possible world, although its individual elements might seem quite unpleasant.

Before moving to the next issue, I will shortly recapitulate what Wolff has to say about the division of things. We have essentially three possible types of entities. Firstly, there are the complex finite things, and we know from experience that they exist all around us. Indeed, the whole world is a complex of all finite things. Then there are the finite simple things, and we know that at least some of them must exist – otherwise we wouldn't have even complex things to discuss about. Furthermore, although we do not yet know it, our own soul will also probably be finite, but simple. Finally, there might be an infinite thing, although we do not yet know whether there is any actual infinite thing – if there is, it will play the traditional role of God. Thus, even in his ontology Wolff has preliminarily outlined the three other parts of metaphysics: cosmology, psychology and theology. Next time, we shall move to the more concrete parts of Wolffian metaphysics.