Crusius, Christian August: Road to certainty and reliability – The ultimate foundations of knowledge

After propositions Crusius proceeds in a rather conventional manner to deductions or arguments, where the truth of a conclusion is based on the assumed truth of premisses. He underlines that the conclusion of a deduction is not held to be true because of its content, but because of the specific relation it has to these premisses. Thus, Crusius suggests distinguishing this relation as the form of the deduction from its individual propositions (that is, premisses and the conclusion), which then work as the matter of this deduction, while the form provides the rule that the deduction follows. He also emphasises that although we can express deductions in words and usually communicate them to others through this medium, this use of words changes nothing essential in the proceedings and can therefore safely be ignored.

Before going on to classify the rules followed by different deductions, Crusius suggests investigating the first principles on which all these deductions are based on. He begins from the capacity of human understanding to think, combine and separate concepts, but notes that it has its natural limits: there are certain seeming concepts or their combinations or separations that we cannot think of. Since human souls strive naturally toward perfection, Crusius argues, and in case of understanding this implies a natural drive to truth, we should follow this natural disposition and accept as true (and respectively as false) what we cannot think as anything but true (and respectively as anything but false).

All our thoughts originally derive from external sensation, Crusius begins his study of these natural dispositions. External sensation provides us with concepts of objects, and as long as a distinct sensation continues, he underlines, we are forced to think of these objects as existing and present. Such an external sensation also makes our internal sensation active, and through this internal sensation, Crusius explains, we become conscious of characteristics, parts and circumstances of external sensations. Then again, he adds, such external sensations induce in us also other concepts that are not externally sensuous and that lead us to universal propositions that we should think as true.

It is no surprise that the first of these universal propositions Crusius mentions is the so-called principle of (non-)contradiction. He at once adds that this proposition as such is just identical, saying nothing more than that what is, is, and what is not, is not. Thus, Crusius argues, the principle of contradiction requires the establishment of further concepts, to which it can be applied, in order to make any use of it. The established concepts might not refer to anything real, he states, and then the applied principle of contradiction has a merely hypothetical reality. Hence, Crusius insists, we must know from elsewhere that the concept in question refers to something real.

Crusius suggests as a further rule for the establishment of concepts following the essence of our understanding: combining concepts that the sensations represent as combined or that we are necessitated to think as combined, because disappearance of one makes the other one vanish also, and similarly separating concepts that sensations represent as separated. Concepts established in this manner generate propositions that are not identical and form the positive core in our knowledge, Crusius thinks: every force is in some subject, all that is generated is generated by a sufficient cause, every substance exists somewhere and at some point in time etc.

Crusius insists that these propositions are not merely derived from the principle of contradiction, but adds that this does not mean that these propositions are not certainties: it is merely a question of how they are generated in our understanding and how we thus come to know them. Furthermore, it does not mean that we could not deny the opposites of these propositions through the principle of contradiction, but only that this principle is not sufficient for establishing the concepts involved. Finally, it does not mean that the principle of contradiction itself would be uncertain, but only that it is empty and thus not the only principle of human certainty. For example, Crusius explains, the principle of contradiction easily explains that every effect presupposes a cause, but only because by an effect is meant something generated by a cause and thus the concept of effect involves the concept of cause. Furthermore, he adds, the concept of effect still refers only to a hypothetical reality, since we do not know what things are effects: even seeing something being generated doesn’t tell us that it is an effect, since causeless generation is just absurd, but not contradictory.

The argument of the emptiness of the principle of contradiction is probably targeted against the Wolffian school, who were famous of basing intricate ontological truths on it (of course, it might well be, and I’d argue that it is so, that especially Wolff himself referred by the principle of contradiction to a stronger principle that is not identical, but this is beside the point here). Crusius still finds some reasons why anyone would hold the principle of contradiction to be the only principle of our knowledge. Firstly, he says, demonstration from the principle of contradiction seems comparatively easy, since otherwise we would have to use internal sensation and attention to account for the physical possibility or impossibility of our thoughts. Furthermore, Crusius thinks, the principle is the only fundamental proposition required for pure mathematics, and someone might want to extend the indubitable certainty of that discipline to the whole of knowledge. Finally, he concludes, we are more used to deducing from already presupposed concepts than searching for the ground of reality in the establishment of concepts.

The true fundamentals of all our deductions, for Crusius, are then three propositions: the principle of contradiction (nothing can both be and not be at the same time and in the same sense), the principle of inseparability (things that cannot be thought without one another cannot exist without one another) and the principle of incompatibility (things that cannot be thought together cannot exist together). He adds at once the cautionary remark that while the first principle is indubitable – no understanding could think of any contradictions – the two others might mislead us, since due to our finite nature, we are sometimes incapable of thinking things that an infinite understanding can think. Especially if the two principles are used to contradict the very principle of contradiction, Crusius underlines, we should reject this use as unfounded. Furthermore, he adds, revelation by a higher form of understanding can show us truths we cannot comprehend: thus, we should accept such a revelation, especially if we can have at least a symbolic concept of what is described by the revelation. Crusius gives as an example the case of limits: we can never think anything existent without the notion of limit, but this does not mean that something unlimited couldn’t exist, just that we are too limited to think about it. Similarly, although we cannot think of two pieces of matter existing in the same place, this does not mean that God could not be omnipresent in every part of the universe.

Crusius proceeds to explain how the other true propositions can be generated from the three principles. Firstly, he begins, we can apply these highest principles to propositions discussing certain characteristics of objects that we cannot think without these characteristics: the connection between the object and the characteristic forms then an axiom. Then again, Crusius continues, we can also apply the three principles to such relations between propositions, where one proposition must be true if the other propositions are assumed to be true: this relation is inscribed in some rule of deduction or argumentation. Just like axioms are immediately connected to the three principles, the rules of deduction connect all the other true propositions to them, he concludes.

The justification of axioms and rules of deduction, Crusius insists, is an example of what he calls a subsumptive deduction, where the conclusion concerns a concept or an individual or a set of individuals contained in a concept that is the topic of the premisses. Yet, he clarifies, this does not mean that all deductions should be subsumptive, unlike the Aristotelian tradition had assumed. Indeed, he separates primary or formal deductions, which justify axioms and rules of deduction and are always subsumptive, from secondary or material deductions, which concern more specific topics and which might not be subsumptive. Thus, Crusius exemplifies, while we can subsumptively deduce from the principles the rule that if a cause brings about a whole, it brings about its essential parts, when the rule itself is used, the resulting deduction is not subsumptive. True, he admits, all deductions can be transformed into a subsumptive form, but this is just jugglery that hides the essential manifoldness of types of deduction.

Joachim Darjes: Elements of metaphysics 1 – Thinkable and possible

While philosophers of Wolffian school began metaphysics usually with ontology, Darjes starts with something called primary philosophy, which should be distinct from ontology. The main difference between the two disciplines is that only latter deals with entities (ens). I shall speak in a later post what Darjes meant by an entity, but for the moment I am concentrating on his primary philosophy.

Like all Wolffians thus far, Darjes begins his account of metaphysics with the principle of non-contradiction. It is not surprising that this principle delineates the realm of possible for Darjes. More interesting is that Darjes actually has an account of what is left outside this realm. Even Wolff did define nothing as what is impossible, but it was unclear what this nothing should be – something in our minds or something more ontologically robust. Now, Darjes notes that nothing and something or impossible and possible are simply kinds of cogitable or thinkable, while thinkable simply is what we can think. Thus, metaphysics is then forcibly defined in relation to our thought, which paves the way for a complete change of ontology into an analytic of principles, which will happen with Kant. It is also important that according to Darjes we can think even contradictions – something not admitted by all philosophers – and very telling about Darjesian attitude toward thinking, which seems then to be nothing more than mere combining words together.

Darjes notes that everything thinkable, whether it be possible or impossible, has something that makes it possible or impossible. This feature making something possible or impossible Darjes calls the essence of thinkable. Darjes thus actually has a definition for an essence, which is more than one could say of Wolff. Then again, Darjesian notion of essence is is another deviation from the usual Wolffian stand, where essences belong only to possible things. Darjes also calls essence a constitutive or adequate primary concept, implying that essences are nothing but thoughts.

Darjes also introduces at this point the primary division of complex and simple, although he extends this classification to all thinkables. His method is to introduce these notions through the idea of essence. Essence of something we can think might be resolvable into further thinkables. If it is, the corresponding thinkable is complex, while if it isn't, this thinkable is simple. Note that we still appear to be moving in the level of thoughts, since Darjes especially calls the parts of essences or essentials partial or inadequate concepts. Further evidence that we are here dealing with thought is provided by Darjes' statement that division of complex thinkables must inevitably end with something simple, because we simply cannot think a bottomless series of constitution. Furthermore, Darjes notes that all impossible thinkables – nothings – must be complex, since simplicities cannot contain contradictions (another assumption that Wolff never made).

Beyond essence and its constituents or essentials, what is thinkable has what Darjes calls affections or adjuncts, in relation to which the thinkable is a subject. Knowing a bit about Wolffian tradition, one might suspect that Darjes would mention attributes and modes at this point. He will mention them, but in a completely different place, because his division of characteristics of thinkable is much more fine-grained than with earlier Wolffians. Still, something similar is in Darjes' mind, when he mentions that affections can be divided into two sorts. Some of them the thinkable has absolutely – that is, they characterise the thinkable in any situation whatever, for instance, like triangle is characterised by certain sum of angles. Some affections, on the other hand, are hypothetical, that is, characterise the thinkable under some conditions, such as when a triangle could be characterised by a certain colour, if it happens to painted in some manner. While the former affections are stable, the latter could be changed without any contradiction.

Beyond essence, essentials, attributes and modes, Wolffians also mentioned relations and Darjes makes no exception. For him, relation or extrinsic determination is something external to a thinkable which it characterises, that is, even when we have assumed the existence of the thinkable, we still need to assume the existence of something else, before this determination could hold of the first thinkable (for instance, one cannot be a child without someone else, whose child one is).

An opposite of an extrinsic determination is, of course, an intrinsic determination, that is, a determination that characterises a thinkable, even if there were no other thing to relate it to. Darjes doesn't leave this class of characteristics here, but goes on to divide intrinsic characteristics further. At first sight the division appears to just repeat the division between extrinsic and intrinsic determinations- some intrinsic determinations can be conceived without other things, some cannot. Yet, it is the word ”conceive” which is obviously important here – a determination might ontologically not be dependent on relations with other things, but we might epistemically require such relations.

The first part of the division or qualities is an easy thing to understand, and for instance, essence and essentials are obviously qualities in this sense. But what belongs to the other category? Darjes suggests that at least quantities belong to this class of intrinsic determinations. Clearly, quantity is an intrinsic determination in the sense that a thing can be of certain size without any thing external to it. Yet, if thing has a size, it must, firstly, be a complex and contain other things as its constituents. These other things or parts are then what is required for conceiving that a thing has a certain quantity – for instance, to say that a field is four acres large, we must think of field as consisting of acre-sized parts.

A thinkable with a quantity should not just consist of parts, but of parts that are in some sense same – this if how we can say e.g. that a field is six acres in size or that there are six wolves in a pack. This sameness, Darjes defines, means that these thinkables can replace one another, at least in some respect (just like if wolves are required, one wolf is as good as another, and that's why we can determine the size of a wolf pack). Darjes goes into more details of various kinds of sameness – identity or sameness of all characteristics, equality or sameness of quantities, similarity or sameness of qualities etc. - but none of this is surprising.

The one final thing to discuss at this point is Darjesian notion of existence. Unlike Baumgarten, Darjes does not try to beat Wolff in finding a definition for existence, but like Wolff, he merely accepts it as a given notion, which is related in a certain manner to the notion of possibility – what exists is possible, but something might be possible, without existing. Thus, Darjes divides possible essences into two kinds – ideal or merely possible essences and real or actual essences. The ideal essences Darjes also takes as a kind of nothing. That is, they are not nothing, in the official Wolffian sense of the word of being impossible – in other words, they are not complete negations of all existence. Instead, Darjes calls them nothing in a privative sense – they could exist, but happen to not exist.

We've already seen how innovative Darjes is in his use of the absolute and hypothetical viewpoints on various notions, and possibility is not an exception – in addition to absolute or intrinsic possibility or non-contradictoriness, Darjes mentions hypothetical or extrinsic possibility, that is, potentiality in some specific conditions. Another and more interesting use of these viewpoints concerns Darjesian differentiation between possibles of first and second order – possibles of first order absolutely cannot fail to exist,while possibles of second order cannot fail to exist under some hypothetical condition. We are obviously already speaking here of absolute and hypothetical necessity, although the term necessity hasn't yet been introduced. Darjes also makes a quick interesting remark about absolute necessity. He notes that while a thing exists, we cannot really distinguish between the essence and the existence of the thing. We can do this separation only with things that at some point won't exist and with things that must exist essence and existence just cannot be distinguished.

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.  

Hoffmann: Study of reason – Principles of deduction

After judgements, a study of different modes of proof follow – this has been the official order since someone decided to place Analytics after On Interpretation in Aristotelian corpus. Somewhat refreshingly, Hoffmann leaves the classification of various types of proof to the practical part of logic, where we shall find it later. In theoretical part, he instead concentrates on some general features of all proofs and especially on various principles followed in proving.

Just like in case of judgements or propositions, proofs are not just strings of propositions for Hoffmann, but instead, processes of human thinking, in which we feel ourselves forced to move from some judgements to a new one. Note that Hoffmann is not yet interested whether these proofs have any connection to truth or not – this is the topic of the next chapter. Indeed, he admits outright that some proofs lead to false conclusions, even if they are so seductive to follow. Yet, now it is time only to describe the very act of following a proof, not give rules for determining a validity of a proof.

What is interesting in proofs is that we feel forced to follow them, no matter what the matter, that is, the topic in question. If propositions assumed just are of certain structure, then we feel obliged to draw some conclusions of them. It is then the form of proofs, embodied in some grounding principles, which are the topic now – nowadays we might speak of rules of inference, and it is important that Hoffmann clearly separates them from mere axioms, which by itself or as mere propositions do not force us to make any conclusions.

While Hoffmann accepts a number of grounding principles, he thinks they can all be based on three most basic principles. The first one should amaze no one. What understanding finds the easiest to deal with, Hoffmann begins his introduction of the principle, are those thoughts that require least amount of analysis. Such thoughts are being and non-being, which understanding at one notices to be impossible to combine. This is the basis of the principle of non-contradiction. Just like with Wolffians, the principle is for Hoffmann ontological, while the corresponding logical principle ”nothing can be both true and false”is based on the ontological principle.

For Wolff, the principle of contradiction was not just ontological, but apparently covered all cases of incompatible properties, since he used ”wooden” and ”iron” as an example of contradictory characteristics. Hoffmann, on the contrary, notes that, while undoubtedly a rule that understanding follows, such denial of incompatible properties must be based on another principle – what is incompatible in understanding must be accepted as incompatible in reality. Third is the corresponding positive principle – what is necessarily conjoined in understanding must be accepted as conjoined in reality.

This is actually all that Hoffmann presents as a theory of proofs – except he uses these basic principles to derive some further principles. I shall leave most of them unmentioned and concentrate on the most interesting of them, that is, the principle of sufficient reason or ground.As we have seen earlier, Hoffmann doesn't buy the Leibnizian principle as it is, but makes an important emendation – actions started by an immediate use of a force that does not need any external determination do not need to have any sufficient reason. The principle of sufficient reason in its Hoffmanian guise is based on the principle of necessary conjoinment – we must always connect an event to some force starting it, thus, it must have begun by an active force just described or by a force determined by something external.

What Hoffmann is suggesting is that a sort of Humean account of causality as a string of events with no intrinsic connection is just so alien to human thinking that we cannot accept it. Of course, this does not yet prove whether this human way of thinking is true – that type of question we have to leave to the next post.

Primary philosophy or ontology (1730)

After concluding the Latin version of his logic, Wolff moved on to translate his metaphysics. Just like with logic, the latinization added a huge amount of pages to the German version. Thus, Wolff actually divided his metaphysics into five parts, each corresponding to a chapter in the German metaphysics. This series begins with Prima philosophiae, sive ontologia, Wolff's Latin take on ontology.

As a careful reader might notice, there is no book corresponding to the first chapter of German metaphysics, the Cartesian beginning establishing the existence of human consciousness. Instead, Latin ontology begins with a general examination of the nature of ontology. Like the title of the book says, ontology is primary or first philosophy, on which all other philosophical disciplines should be based. This means that even logic or the very methodology of science is based in Wolffian scheme on ontology. What Wolff means is apparently that we couldn't be doing science, or indeed, doing anything, if we, among other things, did not exist.

The description of ontology as a philosophical discipline is also important. Just as we can distinguish natural logic or natural means of cognizing from philosophical or artificial logic, similarly there is a natural ontology, or in other words, we humans have a natural tendency to categorize and conceptualize things that exist. Just like natural logic was not enough for Wolff, he is certain that natural ontology also requires some improvement. This was already attempted in scholastic philosophy, which tried to define ontological concepts more carefully. Yet, scholasticism was sterile, Wolff thinks, and the reason of its sterility was hidden in its lack of scientific form. That is, Wolff explains, scholastics failed to base their ontology on demonstrations starting from evident axioms and reliable experiences.

Wolff's evident attempt is to fix the mistake of scholasticism and to base his ontology on the most certain principle of contradiction. As one might remember, in German metaphysics Wolff wanted to justify the principle through the Cartesian beginning of the whole book: if the principle wouldn't have worked, neither would have the beginning been indubitable. Here Wolff does not have the luxury of assuming the existence of anything. Yet, he also does not just want to accept the principle dogmatically, but tries to give some justification for his position. Wolff's justification is what would later be called psychologistic or it bases theories of what there is on assumptions of what (human) mind can do. Anyone would notice that we cannot think of one thing having two sets of contradictory predicates at the same time, Wolff remarks. The easiest way to explain this is to assume that this repugnant nature of contradiction just follows an ontological truth: things really cannot have and not have some property at the same time.

Indeed, as we already saw when dealing with German metaphysics, the principle of contradiction is an ontological and not merely logical principle for Wolff. What this ontologicity means might be difficult to understand. In German metaphysics it all ultimately led to God, who thought of all possible worlds, but could only will one to existence, because these worlds cancelled one another. Here Wolff is dealing only with ontology and God must still be left out of the equation.

Instead of God, Wolff then bases the principle on what is ontologically primary according to him, that is, individual things – Wolff is a committed nominalist denying the literal existence of e.g. universals. Individual things then cannot have a property (e.g. redness) and at the same time not have it, that is, have a property cancelling the first one (blueness or any other colour beside redness). Possible characteristics, as it were, battle over individual objects and just by their presence exclude other characteristics. It is then redness of this individual that contradicts blueness of the same individual, and the more general contradiction between e.g. redness of all members of a genus and blueness of one member of this genus is just an abstraction out of the concrete relations between individuals.

Yellow and white battling over the supremacy of the ball surface.

Although the principle of contradiction should be the highest principle of philosophy, Wolff does not mean that all things could be proved from it – we just have to remember the possibility of using indubitable experiences as further premisses. Yet, he is willing to allow that we can deduce something out of it. For instance, Wolff thinks that the principle of identity, ”what is, is what it is” could be easily derived from the principle of contradiction. Indeed, one would hardly want to deny that the two principles are quite closely related. Well, Kant did deny this, but he was probably reading the principles in a strict logical sense: because negating and affirming are two different activities, there must be different principles governing them. Ontologically, on the other hand, it seems more reasonable that by excluding certain characteristics a thing must presents others.

A more difficult to explain is Wolff's willingness to deduce the principle of excluded middle from the principle of contradiction, especially as we know that the two principles are actually independent of one another. How so, you ask? Think of the principle of contradiction saying that a proposition cannot have both the values 1 or true and 0 or false and the principle of excluded middle saying that its only possible values are 1 and 0: then the first principle does not preclude the possibility of a proposition having a third value (say, ½), while the second principle does not say that it couldn't have two values at the same time.

Judging by Wolff's actual proof of the principle of excluded middle, it appears that there's a hidden ontological presupposition behind it. We are still thinking of individual objects and their possible characteristics. Now, denial of one characteristic of a thing (say, redness) means just insurgence of another characteristic of the same type within this thing (say, blackness). In other words, there are no bare or characterless particulars in Wolffian scheme of things. Then the law of excluded middle becomes a triviality. If you would deny a property A of a thing, this means that another property of the same sort, but incompatible with A arises, and if you deny property non-A, that is, all the properties of the same type than A, but incompatible with it, then A itself must arise. Thus, if you deny both A and non-A, you are actually also letting both A and non-A exist within the same individual thing, which then contradicts the principle of contradiction.

The most famous is undoubtedly Wolff's apparent attempt to deduce the principle of sufficient reason/ground from the principle of contradiction. I myself have already tackled the issue earlier, but I think the topic deserves a second chance. But that's something for the next post.