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.