Sufficient reason for sufficient reason

Whenever you see a philosophical text talking about nothing, it's sure to be quite important. Although the topic would seem rather void of any content, it is at least full of all sorts of ambiguities. Kant himself noted that there are at least four things that ”nothing” or Nichts could mean, although understanding these meanings requires understanding lot of Kantian philosophy. Here I am interested of a bit simpler ambiguity.

Consider first cases where we usually apply words like ”nothing”: ”there's nothing here”, ”no one is coming” and so forth. All of these examples indicate lack of some type entities – for instance, in the second case, a lack of persons. ”Nothing” seems thus remnant of what in modern set theory is known as empty set, a set with no members. In case of ”nothing”, as used in ordinary language, this lack is undoubtedly often just contextual: the first example can be used in a room full of socks, if it is shoes we are looking for.

Now, just as extension and intension in general have often been conflated, one tends to find confusion between ”nothing” in the sense given above (lack of entities) and concept having such ”nothing” as its extension. Thus, one might find such sentences as ”gold mountain is nothing”, when what is meant is that there are no golden mountains. This is then the first ambiguity involved with nothingness.

Wolff's notion of nothing might at first sight appear to correspond with the first of the senses indicated above – or at least Wolff notes that he uses term ”nothing” as corresponding with the arithmetical notion of nullity. Yet, the very definition of nothing Wolff gives points to another direction. Nothing, says Wolff, is such that corresponds to no notion – or as he later admits, it corresponds only to a deceptive notion. Furthermore, Wolff explicates that it is the principle of contradiction that explains when a notion is deceptive – that is, contradiction makes a notion a deceptive and refers only to nothing.

What we have here is then yet another common notion of ”nothing”: lack of possibility or impossibility. And just like with the very first notion of ”nothing”, there is also the possibility to confuse lack of possibility with a concept referring to such impossibility – we can find sentences like ”round square is nothing”, when all that is meant is that there cannot be any round squares. But what is more interesting is the relation of ”nothing” as lack of possibility to ”nothing” as lack of entities: we could describe the former ”nothing” as a lack of possible entities and the latter as a lack of actual entities. When Wolff then defines ”something” as a contradictory of ”nothing”, he must be referring to a presence of possible entities – or to concepts referring to such entities.

Now, one might wonder, what has all this to do with the principle of sufficient reason? Well, Wolff's infamous proof of the principle depends very much on that ambiguous notion. Let us presume an existing thing A without any reasons, Wolff begins. Then there is a ”nothingness” of these reasons, but such nothingness cannot produce anything, which contradicts the existence of A.

This rather curious argument suffers clearly from the ambiguity of the notion of ”nothing”. What it appears to be trying to deduce at first sight is that a lack of any reasons or grounds would fail to produce anything. Yet, as we have seen, Wolffian notion of nothingness does not refer to such lack of actual entities, but to a lack of possible entities. The starting point of the indirect proof is then the assumption that thing A couldn't have any reasons, that is, that its generation would be inexplicable impossibility. This clearly would contradict the very existence of A, which would indeed have to be possible, thus leading to the sought for conclusion or the denial of this nothingness.

Wolff's argument can then be maintained, but then its conclusion comes out as rather trivial. Wolff has shown that without any possibility of generating something, this something could not be, or in other words, that if something exists, there must be some possible way it has come into existence. It is then not necessary that this possible generation process would have been a deterministic causal link necessitating it, but it merely should have been a possible series of events leading to the existence of the particular thing. On the other hand, this fits well with Wolff's wish to account for non-causal chains of grounding in human action. Motives need not determine our actions, but they just need to open up a possible path for them – it might still be down to our choice, which path is taken.

What is more difficult to reconcile with this weak reading of the principle of sufficient reason is Wolff's second argument for the principle. Supposedly one could distinguish reality from dreams only through the principle of sufficient reason: while the former follows the principle, in the latter there happen all sorts of changes just willy-nilly or according to the whimsy of the dreamer. If the principle would be taken in the weaker sense, then there would be no contradiction between it and dreams, because even the most absurd dream sequences still are possible sequences.

Now, although the dream argument appears to speak for a stronger sense of the principle, it is not impossible to make it agree with the weaker sense also. Wolff might not be thinking of dreams contradicting the principle itself, but a conjunction of the principle with relevant physical laws. Thus, while e.g. sequence of me flying above the clouds would not be impossible as such, it would be impossible given the physical laws preventing such flight. This reading would actually make more sense, because when Wolff does say that the principle of sufficient reason is derivable from the principle of contradiction, anything contradicting principle of sufficient reason would be contradictory and impossible – which appears rather confusing, when we evidently can experience dream sequences.

This conclusion appears rather interesting, because early on it was the dream argument that was emphasised by the followers of Wolff. It seems plausible that this argument was chosen over the official proof of Wolff himself, because it was easier to reconcile with the stronger version of the principle of sufficient reason. In effect, the dream argument then gives a criterion for recognising reality: it is the lawlike nature of the reality that distinguishes it from dreams. One might even find such emphasis on lawlikeness in Kant's description of experience as regulated by the category of causality. If the weaker reading of the principle is correct in case of Wolff, his description of reality is far more modest: it is not the lawlikeness as such that distinguishes reality from dreams, but the fact that reality follows laws not followed by dreams.

So much for sufficient reasons, next time I'll look at essences.

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.

Thoughts concerning Mr. Christian Wolff's LOGIC, or so-called RATIONAL PHILOSOPHY (1729)

None of the philosophers I've dealt with so far can be called a philosophical celebrity – I'll hit that milestone when I reach Kant – and even from the viewpoint of the circle of German philosophy scholars, several of these philosophers have been rather obscure. Even among these unknown figures, Adolph Friedrich Hoffmann shines with his apparent anonymity. Hoffmann's fate was to be placed between two more philosophers with more fame, as a mere mediating point of their philosophical development.

Hoffmann's teacher, Rüdiger, was known in his time through his medical writings and was also famous as a counterforce against Christian Wolff. Hoffmann's pupil, Crucius, was to be known as yet another critic of Wolffians, but also as an influence on Kant's thinking. Hidden between these two, it is not unsurprising that Hoffmann's writings never really circulated that much – and indeed, when Lewis White Beck, in his study of early German philosophy, notes that he had the opportunity to see one of the copies of Hoffman's major writings, he also points out that this was one of only three copies of the book.

Hoffmann esteemed his mentor highly, and when Rüdiger's book criticising Wolffian psychology  received no answer from Wolff himself, Hoffmann became incredibly displeased. Now, Wolff probably felt that he had adequately answered his critics in his earlier works, and in any case, he was engaged with writing the Latin versions of his works. Still, Hoffmann thought that Wolff could have spared some time after completing his Latin logic for consideration of Rüdiger's text. As the situation was what it was, Hoffmann rebuked Wolff by attacking the just published Latin logic in a writing aptly called Gedancken über Hn. Christian Wolffens LOGIC, oder sogenannte PHILOSOPHIAM RATIONALEM. As far as I know, this was the first time when someone had made critical remarks on Wolffian logic, whereas Wolff's pietist opponents had just ignored this part of Wolff's philosophy.

Hoffmann closes his article by explaining the purpose of the book and also by invoking the simile of the world of letters as a republic, in which the only crime is bad reasoning and the only judges are learned fellows of Europe. Hoffmann thus considers himself to be engaged in a trial of Wolffian logic. He concentrates his questions mostly on the theoretical part of logic, the only exception being Wolff's notion of truth. Hoffmann's criticism shows how well he truly found the weak points of Latin logic – Hoffmann points out how ridiculous Wolff's definition of truth sounds, and in fact, I noted recently that this definition is truly difficult to interpret.

A considerably large portion of the article deals with Wolff's consideration of demonstrations and especially his attempt to incorporate all sorts of deductions in syllogistic guise. Hoffmann argues that there are actually many types of deduction that do not have syllogistic form, such as the immediate deduction from the sentence ”all As are Bs”, to ”some As are Bs”. Wolff of course knew about these cases, but thought them to be at least implicit syllogisms. Thus, one could add an identical proposition ”some As are As” and from this and ”all As are Bs” one could syllogistically prove ”some As are Bs”.

Hoffmann notes that Wolff's moves for syllogising all deductions are rather unsuccessful. For instance, adding the identical proposition ”some As are As” adds nothing new to deduction in hand. One might think that Hoffmann had an unclear intuition of a deep thought developed later in more detail by Lewis Carroll in his famous dialogue between Achilles and turtle. The point of the dialogue is that adding mere premisses to a deduction is never enough to make it valid – for example, if Achilles says ”A, and if A then B” and turtle asks how Achilles could justify the move to ”B” after this, Achilles cannot just add a new premiss ”if A and (if A then B), then B”, because turtle can just ask for the same question again. What the turtle requires is not new premisses, but rules for what to do with those premisses. Similarly, one could say that the identical proposition above is just a description of a rule stating that one could apply everything applicable to members of a class to members in any part of the original class.

But the true controversial topic is the relationship between mathematics and philosophy. It is clear that Wolff himself thought mathematical method to be suitable even in philosophy – this will be argued for in more detail in his Latin ontology. Now, Wolff himself had suggested that philosophy was essential for knowing causes of things, and mathematics would then be of use by revealing dependency relations through correlations of quantities. Hoffmann makes the correct remark that mere quantitative relation does not always mean a causal relationship. For instance, people who frequent most doctors usually have diseases more than other people. Still, this does not mean that visiting doctors would be bad for your health. On the contrary, people happen to visit doctor, whenever they are ill, which explains the correlation more naturally. Hoffmann has thus uncovered the familiar sophistical move from mere correlation to causation. This simple methodological remark does hurt Wolff's credibility more than all the criticism about his Spinozism.

So much for this critical book, next time we shall return to Wolff and his ontology.

What use of logic?

In case reader would still be perplexed after all the pages as to what use logic is, Wolff kindly considers at the very end of Latin logic how logic can help one also in every-day life. In particular Wolff is speaking of artificial logic, as he has no doubt that everyone concurs that natural logic or the natural capacities of knowledge seeking are quite useful. In fact, advantages of artificial logic lie mostly in the refinement of these natural capacities: we can more easily detect erroneous thought patterns by knowing just few tricks of trade.

Still, the main point of application for logic is academic life, which Wolff divides into three broad subfields. Firstly, a learned person is in business of searching truths – this task has been covered by the majority of Wolff's logic. Secondly, a learned person must engage herself with books – she must write them, but also read and evaluate them. We covered this part of academic life in the previous blog text.

The final field where a learned person can apply logic is then interaction with other people. She must be able to demonstrate what she claims to be true or at least make it sound convincing. She must also refute views she finds false and she must be able to defend her own position from refutations of other learned people. All these tasks use essentially similar rules of logic, just applied at different stages – indeed, best defense of one's viewpoint is just demonstration of its truth.

The work of demonstrating, refuting and defending overlaps somewhat with the publication of books, as most of scholarly discussion happens through text. Yet, there are places where a learned person must come to actual contact with other people. This is especially true of public debates, part of education of a learned person, in which one has to defend a view, possibly even such which the defender doesn't really endorse. Art of disputation is then for Wolff nothing else but application of the arts of demonstrating, refuting and defending – there is no place for rhetorical niceties in Wolff's idea of disputation.

If disputation is two-directional interaction, teaching Wolff sees more as unidirectional. In fact, Wolff's philosophy of education is rather meager: all one needs to do is to take care that students understand the definitions and axioms and then it is just simple application of the rules of demonstration in the correct Euclidean order.

Here finally ends the tale of Wolff's logic. Next time, I shall finally move on to the next generation of the critics of Wolffian philosophy.

Taxonomy of books

When I investigated Wolff's German logic, I skipped a detailed take on most of the last half of the book, because it appeared to contain little of philosophical interest and seemed more like a haphazard collection of different topics. With Latin logic, I think I have a duty to be as thorough as possible and discuss also the final sections of the book, especially as the book is better organised, even if the topics dealt with would have no apparent philosophical interest.

Wolff's aim is to provide his students with a book on methodology. In addition to seeking truths, new scholars have to acquire new skills, one of which is the ability to write, read and review books. But before one can learn how to do all this, one must know what different types of books there are, because writing and reading, say, a historical treatise requires different things than writing and reading mathematics.

Every librarian knows that trying to place books into a neat taxonomy is ultimately a hopeless task: there's just too many possibilities to choose from. Wolff's approach begins actually from the standpoint of the method of book. Some books are merely historical or merely describe experiences concerning some specific topic. Thus, we have books on natural history, telling e.g. how cats reproduce, books on civil history, telling what has happened, for instance, in France and Germany in last couple of decades, and biographies that describe morally uplifting facets of someone's life (Wolff clearly lived before the age of rock stars).

In addition to historical, there are also dogmatical books, which are more about general theories than experiences: if you describe all the various changes of climate near the coast of Britain, you are doing history, but if you attempt to explain these changes, you are writing a dogmatical book. Note that there are clearly two ways to approach dogmatics. One can either just describe theory, without trying to justify it – this is essentially a historical take on dogmas – or one can use demonstrations based on axioms, definitions and reliable experiences and prove the dogmas – this would be a truly scientific treatise.

Wolff's classification is meant to give a clear answer to how such books are to be made and on what criteria they are to be judged. Here the methods for writing and judging books are parallel in the sense that the rules of good writing are essentially criteria for evaluating what is good. In historical books, one must consider especially the end of the book and on that basis decide what is to be told and in which order. An important question with historical books is the reliability of what is told – note that when you are reading a historical book, you can at most reach the level of Glauben or faith.

The methodology of scientific books is essentially the methodology Wolff has presented earlier. Thus, a scientific book should define its concepts as explicitly as possible, use only such premisses that are already known to be certain, that is, are either axioms or demonstrated propositions, or at least use only so-called lemmas that have been proven in other books – all standard Euclidean stuff. A point of interest is that Wolff notices the possibility of and condemns the habit of plagiarism, that is, an uncredited use of works of other authors.

While there are then strict criteria by which to decide the worth of a book, Wolff also suggests certain leniency in evaluation. Reader should especially try to interpret confusing words and propositions in the best possible manner which would make the most sense of the text – this is what is nowadays known as a principle of charity.

Wolff extends the use of the principle of charity also to hermenutics of sacred writings. The ultimate source of these texts is supposed to be God, whom we must assume to have perfect cognitive skills. Thus, what these texts say must indeed be true. Yet, because the writers of the texts have been imperfect human beings and God has just imported the thoughts contained in these texts directly to their mind, these texts are bound to have metaphors and even paradoxes, when the complexity of these thoughts has reached over the limits of the writers.

So much for books, next time we shall see what else was part of scholar's life in Wolff's time.

A posteriori and a priori

Wolff is interested not just of truth and probability, but of different methods for discovering true and probable statements, that is, scientific and philosophical methodology. Now, as we have seen, Wolff has made the bold statement that logic is all that one requires for methodology, and at least when it comes to truth, logic is essentially based on demonstrations. This rather stringent description is easier to understand, once we remember that Wolff would accept also empirical statements as premisses of demonstration.

What I find remarkable is that Wolff mentions two different methodologies: a posteriori and a priori. In all external appearances, we are moving towards Kant, yet, there are still crucial differences. While for Kant a posteriori would mean all knowledge based on experience, Wolff limits the range of a posteriori to mere experiences. Thus, when Kant says that a posteriori knowledge cannot be universal, his statement is far stronger than Wolff's. Indeed, Wolff would verbally accept Kant's statement, but it would mean something less than with Kant – it would be just tautology because individual experiences are always singular.

Now, if a posteriori has no other meaning for Wolff, but individual experiences, a priori must then get everything else, that is, the class of a priori contains all bits of knowledge requiring demonstration. Now, demonstrations as meant by Wolff here can be either direct or indirect, while a priori can be either intuitive or discursive. Intuitive a priori has a nice paradoxical feeling to it, somewhat reminiscent of later and more famous synthetic a priori, yet, is not completely identical with it. Intuitive apriority characterises all those truths that can be directly intuited as true, just by carefully reflecting on the elements of the supposed truth. The class of such truths contains analytic axioms of logic, but also immediate truths about causes and effects, which Kant would have classified as synthetic a priori.

The final class of knowledge statements contains then discursive apriorities, that is, demonstrated truths. As one should remember, these demonstrations could have reliable experiences as premises. Furthermore, Wolff also included inductions as just one modification of syllogistic reasoning. Wolff's class of discursive apriorities contains then a lot that Kant would have classified as a posteriori, and in fact is probably the largest of the three classes.

Within this threefold classification Wolff places his main methodological considerations: when is experience to be relied upon, when can we say that something is a cause, when can we use experiences to draw general conclusions etc. I shall refrain from going into intricate details, and instead, I shall next time look at how Wolff thinks scientific conclusions should be presented.

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.

Syllogistic 102 revisited

Just like the the investigation of judgements, the investigation of syllogisms is much more extensive in Wolff's Latin than in his German logic. While German logic concentrated on the so-called first figure of syllogisms and noted that all other figures could be reduced to the first figure, in Latin logic Wolff goes through even the second and third figures of syllogism. As I have adequately dealt with all these figures, I shall not touch this topic anymore.

This still doesn't mean that I could leave the rest of this text blank. The three figures all have categorical judgements as premisses, thus, syllogisms of these figures could be called categorical. As categorical judgements are the simplest type of judgements, Wolff also calls them simple syllogisms. In addition, we might also have syllogisms with non-categorical premisses, which appropriately are then called complex syllogisms. Wolff goes on to note that complex syllogisms include at least hypothetical syllogisms, with one hypothetical judgement as a premiss, and disjunctive syllogisms, with one disjunctive judgement as a premiss. There is no indication that these two are all the types of complex syllogisms, although Kant will later appear to assume this.

Just like with the three figures, Wolff is eager to show that we can simplify the variety of syllogisms. Now, I failed to mention last time that Wolff appears not to take disjunctive judgements in the form of the current propositional logic, that is, as a combination of propositions (p or q). Instead, he favours the notion of disjunctive judgements as a combination of concepts: A is B or C. Furthermore, while in modern propositional logic ”p or q” is meant to include the possibility that both p and q are true, Wolffian ”A is B orC” is clearly meant to indicate that A cannot be both B and C at the same time. Thus, a disjunctive syllogism is then of the form

A is B or C

A is / is not B

Then A is not / is C

Wolff points out that we could then understand the judgement ”A is B or C” as a combination of hypothetical judgements ”if A is B, then it is not C” and ”if A is not B, then it is C”. Clearly then disjunctive syllogisms can be reduced to hypothetical judgements.

Wolff continues by noting that an important part of hypothetical syllogisms, including all the disjunctive syllogisms, could be reduced to categorical syllogisms, namely, those in which both the antecedent and consequent of the hypothetical judgement have the same subject, in other words, if the syllogism is of the form:

If A is B, then A is C

A is B

Thus A is C

Wolff suggests that we could always read such a syllogism in the following form:

All Bs are Cs

A is B

Thus, A is C

Problem is that in the original syllogism the hypothetical might hold only for As. Consider the following deduction:

If a triangle is a figure with two equally large angles, then it is an equilateral triangle

This triangle is a figure with two equally large angles

Thus, it is an equilateral triangle

Clearly the corresponding categorical premiss ”all figures with two equally large angles are equilateral triangles” is false. A possible solution is to restrict the scope of the middle term in the following manner:

All As that are Bs are Cs

This A is B

Thus, A is C

Still, even if the reduction works with these hypothetical syllogisms, Wolff has to admit that it isn't so easy in those cases, where the hypothetical judgement doesn't have a subject shared by its antecedent and consequent.

Wolff also considers incomplete syllogisms, which Aristotle had in his Rhetoric called enthymemes. In practice, such entyhmemes are nothing but hidden syllogisms, where we leave some premisses implicit. Thus, if I deduce ”I am hungry, therefore I must eat” I am actually assuming the general premiss ”if someone is hungry, he must eat".

An important subdivision of enthymems is formed by so-called immediate syllogisms, which according to the tradition could be used to prove something without full syllogistic trappings: an example includes ”All As are Bs, thus, some As are Bs”. Wolff points out that we could add as a new premiss the tautology ”some As are As” and then we would have a normal categorical syllogism, albeit one with a tautology as a premiss.

Somewhat more surprising is Wolff's view that even inductions are enthymemes or deductions with implicit assumptions. Namely, if we conclude from the fact that certain individuals or species of things have a feature that this feature is shared by whole of their common genus, we have assumed a further premiss that what holds for an individual or a species holds also for superior genera. It appears problematic to suppose that induction could be deduction, but I would like to point out that it is not meant to be valid deduction, because one of the premisses might well be untrue – the inductive principle or possibility to generalise might be wrong either absolutely or under some circumstances.

I might finally note that Wolff describes a possibility to concatenate syllogisms to form chains of deduction or polysyllogisms and that the highest form of deduction or demonstration can use only axioms, definitions, indubitable experiences and previously proven propositions as premisses. Next time we shall see what all this has to do with truth.

Syllogistic 101 revisited

When I for the first time spoke of Wolff's theory of judgements I was perplexed by the question where did Kant actually get his twelve-part classification of judgments, on which his scheme of categories is supposedly based. Wolff's more extensive treatment of the topic of judgements in his Latin logic is still far from Kant's neat classification, but is at least a step towards it.

It is easy to start from what has not changed: there's still no account of modalities as a logical question. There's also no division of judgements according to relation in the Kantian sense. Wolff does distinguish categorical from hypothetical judgements, former thought to be true in all circumstances, latter, on the other hand, only under some express circumstances (note that the ”if-then”-clause is not viewed as an operation for forming new judgements, but as an expression of the conditionality of the consequent, which is the true judgement in this case). Yet, this is a division and not trivision, like with Kant. Furthermore, both categorical and hypothetical judgements are apparently classified as simple propositions and distinguished from the class of complex propositions, which then contains disjunctions as one member, but in addition, e.g. conjunctions.

It is the divisions of quality and quantity that are almost in the shape that we will later find with Kant, and Wolff even uses the terms quality and quantity to indicate the special characteristics of these divisions. Thus, in addition to affirmative and negative judgements, Wolff does speak of infinite judgements, which are affirmative in their form, although they have some indication of negativity in them, that is, hidden in the predicate (e.g. ”this creature is immortal”, which seems affirmative at first sight, but contains the negative prefix ”im-” and therefore negates the proposition ”this creature is mortal”).

Still, Wolff appears not to take the affirmative, negative and infinite judgements to form a trivision of judgements of equal stature. Instead, he calls infinite judgements a species of negative judgements, which appears to suggest that it is more a question of first dividing all judgements into affirmative and negative, and then negative judgements into properly negative and infinite judgements. Wolff thus first asks whether the judgement contains some indication of negativity and then distinguishes case where the indicator is explicit ”not” attached to copula from a case where a more implicit indicator of negativity is attached to predicate.

Kant's trivision of judgements according to their quantity in universal, particular and singular judgements is also seen in Wolff's Latin logic. An interesting point is that Wolff does not classify singular judgements with universal judgements, although their behavior as describing one set of things (with only thing) would make it possible. Instead, Wolff supposes that all singular terms are implicitly part of some species and then singular judgements could be regarded as just explicit forms of some particular judgements.

In addition to these three judgement types Wolff also mentions an undetermined judgement, in which it is not indicated whether it is universal or particular. In some cases such indeterminate judgements would be universal – if I say ”triangles are figures”, I certainly mean all the triangles. Then again, if a guardsman had yelled ”Turks are at our doors” during the siege of Vienna, he wouldn't have meant that every single Turk was there, but only some of them.

In addition to undetermined judgements, Wolff also notes that some apparently universal judgements are actually singular. He means cases like ”all the soldiers form an army”: clearly none of the individual soldiers forms an army by himself, but only the whole group of them. Wolff is thus referring to cases where we speak of a collection of things as a single individual: later on this intuition was developed in more detail with set theory.

Despite all this variety, Wolff is quick to point out that we can actually do with a simpler classification: infinite judgements can be viewed as affirmative or negative, singular judgements as particular and indefinite judgements as either universal or singular. The main reason for this tidying up is undoubtedly the use of judgement forms in classification of syllogisms. Another reason lies in the neat application known as square of opposition:

The basic idea of the square is to represent some important relations between different statements that differ only by their form (in Kantian terms, their quality and quantity), but share the content or concern same concepts. Thus, universal affirmative judgements and particular negative judgements are contradictories, and same goes for universal negative judgements and particular affirmative judgements. Contradictories, then, are such pairs of judgements, only one of which can be true and one of which also must be true: for instance, ”all spies are Finnish” and ”some spies are not Finnish” cannot both be true, but one of them must surely be true.

Universal affirmative judgements and universal negative judgements are contraries, that is, only one of them can be true, although it is possible that neither is true, in the case that both particular affirmative and particular negative judgements are true (e.g. if some roses are red and some are not, then neither are all roses red nor all roses not red). The latter two judgement types are called subcontraries, that is, both of them cannot be false, although both of them could also be true. Finally, particular affirmative or negative judgements are subalterns of corresponding universal judgements, which means that a universal judgement implies the corresponding particular judgement (if all humans are rational, then certainly some particular humans, like Inuits, are also rational).

We have to make the reservation that the square of opposition might fail, if we allow concepts that do not refer to any real objects, such as round squares. All round squares are clearly round, but as squares, none of them are round: both of the judgements can be true, because there are no round squares. It is then a matter of whether we prefer the beauty of the square of opposition over the possible use of such empty terms: both of them cannot be accepted.

Note that the judgements I have been speaking of are in Wolffian logic combinations of concepts, that is, something within consciousness. Just like mental concepts can correspond to linguistic, communicable, words, similarly mental judgements can correspond to linguistic, communicable propositions or combinations of words. Wolff does note that the correspondence might not be perfect – something that Aristotle already noted. What we say, might actually refer to different thoughts in different contexts, for instance, when we say ”it was a fluke”, we might refer to a fish or to a stroke of luck: this phenomenon in case of single words we would call homonymy. Similarly, we could use different expressions to convey the very same thought, which in case of single words we would call synonymy.

So much for judgements, next time we once more enter the proper syllogistic.