Joachim Georg Darjes: Theoretical art of reasoning (1737)

Joachim Georg Darjes (1714-1791)

Going through even the most insignificant philosophers of a certain era might seem like a complete waste of time – surely one would be better using one's time by just concentrating on the most memorable and influential figures, like Kant and Hegel. Yet, it is just by looking at these seemingly unimportant figures that one finds, on the one hand, clear trends and fashions, and on the other hand, unexpected breaks in trends and surprising novelties.

Darjes' book Die lehrende Vernunft-kunst is one of those rare works that appears to be quite traditional, but has interesting deviations from the current norm. On the surface, the book seems to follow quite faithfully the trend of Wolffian textbooks on logic, with some minor deviations. Thus, the book begins with the ontological principle of contradiction, introduces as its consequence something called a law of certainty (if something is A, then it is A), and finally mentions the principle of sufficient reason as the explanation of how actuality differs from possibility. Quite standard division of cognition into historical, philosophical and mathematical forms comes next together with a classification of philosophical sciences, which in its essentials appears quite Wolffian. Chapters on philosophical style and general need of logic show also nothing surprising.

This has all been just the preface, and when the actual book begins, Darjes starts to really use the mathematical style. A typical Wolffian textbook of the time is usually presented in numbered paragraphs. Darjes uses them also, but he also notes whether the paragraph in question is meant to be a definition, arbitrary stipulation, statement drawn from experience, proposition or corollary to be proved or just an additional remark. One at once notes that many of the propositions of the book are based on experiences, justifying Hegel's often made complaint that logic of his time was just a bunch of empirical statements. Of course, because the logic is meant to be a study of human faculties of thought, it is just understandable that introspective evidence on these faculties is required.

It is with Darjes' account of mental faculties that we find the true novelties. The description of senses, imagination, memory and reflection are sufficiently similar to Wolffian empirical psychology, although Darjes' suggestion that all sensations are produced by actual objects seems a bit naive. The truly surprising statement comes with the study of understanding and concepts, which Darjes clearly defines as representations of universals. Thus, just by stipulating, it seems, Darjes has denied the existence of individual concepts. This makes a difference in classification of concepts. While Wolff had spoken of a formal difference between concepts (their differing degree of clarity) and their material difference (whether they denote individuals or universals), Darjes can speak only of their formal differences. But the differences go even further. For Wolff, understanding was merely a faculty for analysing and breaking apart our representations, whether they be individual or universal, and thus in a perfectly Lockean fashion just a further development of our perceptive faculties. Darjes, on the contrary, redefines understanding as a faculty of generalisations. In effect, Darjes is restricting the area of understanding, but so also clarifying its role – understanding is now clearly distinguished from senses and imagination, which might be seen as a step toward the Kantian separation of faculties.

Some differences can be also found in Darjes' account of definition and especially the distinction between real and nominal definitions. Wolff had stated that for nominal definition one had to be able to distinguish the defined from similar things, while for real definition one had to know why the defined thing was possible – a preferred method was to know how to generate this thing. Clearly, nominal definitions might not be real, but also real definitions might not be nominal, because one could generate things one couldn't properly distinguish. Darjes, on the other hand, defines the two types of definitions through notion of essence and essential property. Nominal definitions mean knowing some essential property of the thing defined, that is, a property that the thing has constantly – clearly enough for distinguishing the thing, but most likely also too much. The real definition is then characterised by Darjes as knowing the essence or the ground of all these essential properties. Here, a rule for generating this particular thing should be enough, but evidently it should also involve knowing what the essential properties of the thing are and being able to distinguish it – again Darjesian real definition is far stronger than Wolffian.

I will skip Darjes' account of language, although it shows surprising familiarity with the medieval theory of supposition, that is, the idea that the meaning of the word changes depending on the context of the other words. The reason for skipping is that Darjesian classification of judgements shows considerable movement towards the later Kantian classification of judgments. I have already noted that the division of judgements according to quality and quantity were already in place in Wolff'sLatin logic. Similar classifications occur with Darjes too, although with some nuances.

The classification according to quantity is almost identical to one with Wolff: judgements are either singular, particular, universal or undetermined. The difference is that while Wolff classified singular judgements as a type of particular judgements, Darjes notes that they could be classified with universal judgements, because e.g. Socrates is everyone in the class with only him as a member.

The classification according to quality shares similar resemblance with the Wolffian classification. Both Darjes and Wolff start by dividing all judgements into affirmative and negative, although Darjes apparently has rather idiosyncratic way of understanding negative judgements as attaching ”not” to the subject of the judgement. Then, while Wolff thought infinite judgements to be a type of negative judgements, Darjes takes them to be a type of affirmative judgements: affirmative judgement is either finite (its predicate is positive) or infinite (its predicate is negative). Similarly Darjes then divided negative judgements into conditionally and simply negative judgements.

The true innovation of Darjes lies in his third method of classifying judgements according to their ”whatness”. This rather obscure name hides behind it, among other things, both Kantian classifications of relation and modality. The basic division of judgements into simple and complex hails already from Wolff, although he understood also hypothetical judgements as simple, while for Darjes the only simple judgements are what Kant would later call categorical assertoric judgements.

Darjes then divides complex judgements into distinctly and indistinctly complex judgements. Starting from the easier subdivision, distinctly complex judgements are those which clearly consist of many judgements. Such judgements either hold that some subjudgements must hold together or deny that such subjudgements cannot hold at the same time. In the first type, the judgement could be simple conjunction saying that two subjudgements do happen to be true (”A is both B and C”), but it might also just state the hypothetical that one subjudgement is a condition of the other (”If A is B, it is C”). The second type contains then similarly judgements that state the fact that some subjudgement holds and another not (”A is not B, but C”), while it might also just present a disjunction of alternatives (”A is either B or C”). This side of the classification of complex judgements contains then two divisions from the Kantian classification of judgements according to their relation.

Indistincly complex judgements then contain words that somehow modify the basic sense of the judgement. A major part of such indistincly complex judgements are formed by what would be later called modalities, but what Darjes names explicative judgements – words like ”possibly”, ”impossibly”, ”necessarily” and ”contingently” explicate the relation between the subject and the predicate. Showing again his interest in medieval philosophy, Darjes notes that unlike what Michael Psellus said, ”truly” and ”untruly” are not similar explicators, but more like second-order statements about the truth or falsity of the judgements. The rest of the indistinctly complex judgements exclude something (”only A is/ is not B”), restrict the validity of a judgement (”in so far as p, q) or make some comparisons (”A is more B than C”). All in all, quite a mixed bunch, but most important is the inclusion of modalities, which has been the first time in my reading list that they appear in a logic book.

Like in most books on logic at the time, I can easily skip the part on syllogisms, because nothing significantly new comes up in that section. Then again, this does not mean I could close the text here, because there's still the final section on demonstration to go through. What is interesting in this context is Darjes' account of what he calls undeniable and deniable judgements or propositions. At first sight, there's nothing particularly strange about Darjes' definition of undeniable judgements – in an undeniable judgement, we can by having a distinct representation of the subject of the judgement say immediately that the predicate belongs to it. Well, the definition does have some superficial resemblance to later Kantian notion of an analytic judgement – and the feeling of resemblance is heigtened when one finds out that Darjes thinks the principle of contradiction suffices as a criterion of truth for undeniable judgements.

What makes Darjes' definition distinct from later Kantian notion of analytic judgements is his insistence that beyond definitions and tautologies judgements based on experience are also undeniable. Although this might at first seem rather unintuitive, Darjes does have a point. Consider the subject of an experimental judgement – this is just an individual we happen to represent. Now, it is quite clear that a judgement based on nothing but experience merely states some characteristic that is already evident in this representation – we see a duck and note that it seems white. In this sense the judgement is also based on the principle of contradiction – if the object seems white, we cannot but affirm this.

The difference with Kant arises probably from the fact that Darjesian definition of undeniable judgements speaks of representations in general, while Kantian definitions of analytical and synthetical judgements are made in terms of concepts. Indeed, Darjesian judgements of experience are always singular - we experience only individuals - and thus their subject cannot be or refer to universal or concept.

Of course, most of our judgements supposedly based on experiences actually overstep the limit of individual experiences just by making generalisations out of individual experiences (ironically, many of the supposed experiences in Darjes book appear to do do). The account of such judgements, Darjes tells us, should be based on probability – which apparently should be handled on the second part of Darjes' book. Unfortunately, I haven't been able to find this second book on ”übende Vernunft-lehre” or practical logic, and I cannot even say whether Darjes ever published it.

All in all, Darjes' book with all its small deviations and original quirks is a sign for an end of an era. Another sign will be seen in next post, when we say farewell to a certain opponent of Wolff.