From subjective representations, Bolzano moves to judgements. He underlines that judgements are not representations – if we just represent a proposition, we do not judge or assert the matter to be so. Still, he admits, judgements do share some characteristics with subjective representations. Both have a stuff: with subjective representations it is an objective representation, with judgements it is a proposition. Furthermore, just like subjective representations, judgements are actual, but only as adhering to a soul.
Propositions are constituted of representations, Bolzano reminds us, and so should judgements consist of subjective representations. He states that parts of a judgement coexist or at least the earlier parts have not completely vanished when the later parts occur in our mind. Then again, Bolzano adds, just like coexistence of representations does not mean that a combined representation exists, the coexistence of the parts of judgement does not mean that the judgement exists. He also suggests that the formation of judgements is not completely voluntary, although we can affect it by choosing what representations we attend to.
Just like with representations, Bolzano finds it convenient to speak of one judgement, when the same person judges the same objective proposition uninterruptedly. This means that judgements are different, if they have different propositions as stuff, belong to different thinkers or are discontinuous in time. Bolzano also suggests that similarity of judgements presupposes at least that they have the same proposition as their stuff.
Bolzano thinks that many other features and types of representations apply also to judgements. Examples of these include clarity, distinctness and liveliness (then again, he notes that confidence or certainty is a feature unique to judgements). Other classifications, such as the distinction between analytical and synthetical, judgements derive from propositions.
Just like representations, Bolzano points out, our judgements come and go: indeed, it is very common that our opinions change over time. Judgements also leave traces on our soul, which makes it possible to recollect our judgements. Of course, Bolzano adds, we may deny a judgement we recollect asserting in the past or our confidence about it might have changed.
Bolzano moves on to the question how our judgements are generated. Some of them, he points out, have been caused or mediated by other judgements through the use of inference. Bolzano recognises three types of mediation: firstly, that based on objective consequence relation, secondly, that based on other relations of derivability, and finally, that based on probability. He finds the first two unproblematic: objective grounds can also cause judgements in us, while knowing relations of derivability is just something where we resemble God, although in a restricted manner. Probability relations, on the other hand, are something God in their omniscience cannot be dealing with. Indeed, Bolzano suggests, using probabilities in inferences arises from the limitedness of our powers of cognition – great enough of probability makes us confident of a judgement, and after a time, we forget that it is just probable and remember only the judgement.
Mediated judgements must ultimately be based on some unmediated judgements, Bolzano argues. These include, he says, judgements like “I have the appearance A”, where A could be, for instance, a representation, a judgement, a sensation or a decision, and also judgements of the type “this, what I intuit here and now, is an A”, where the A could be something like red, fragrant or sour (he does note that sometimes the latter kind of propositions are mediated, for instance, if we know that something that we see is of a kind that is salty, we can deduce that this what I see is salty). Bolzano calls immediate judgements of both kinds perception judgements, while all mediated judgements referring to intuitions he names experiential judgements.
All mediated judgements cannot arise from mere perceptual judgements, Bolzano contends, for instance, because we need something more to show that our intuitions presuppose some external thing that has generated them. Thus, he concludes, we need pure conceptual judgements that describe connections between pure concepts. In this way, Bolzano goes against any mere empirical explanation of the origin of our judgements. This does not mean, he adds, that just insisting on two sources of judgements – intuitions and concepts – is enough.
Bolzano goes into great detail in studying especially the views of Kant and some of the more prominent Kantians, but finds their explanations unsatisfying. While Kant found the explanation of analytical judgements simple, Bolzano thinks these judgements contain unexpected difficulties. Analytical judgement, as defined by Kant, should be such that the subject contains the predicate – so basically, Bolzano notes, of the form “something that is both A and B is A”. Although seemingly self-evident, he points out, they presuppose that there is some A that is also a B (taking the often used example, “all bachelors are unmarried” presupposes that there are bachelors, that is, unmarried men).
Bolzano’s take on Kant’s analytic judgements might seem a bit pedantic (and dependent on his reading of universal propositions as making an existential commitment), but his take on what Kant calls a posteriori judgements is more interesting. Kant had suggested, Bolzano says, that such judgements are based on intuitions. Bolzano thinks this is an inadequate explanation, since singular intuition cannot justify universal judgements like “all bodies have weight”. Indeed, he goes further and insists that even a singular judgement like “this body has weight” is not explained by mere intuitions. Either the notion of the weight is simply included in our intuition of this body, and then we would be discussing simply an analytic judgement, or more likely, this singular judgement says something like “this body that is the cause of other intuitions (e.g. colour, smell etc.) is also a cause of our intuition of weight”, which is something not justified by mere intuitions.
What Kant finds truly difficult, that is, the so-called synthetic a priori judgements, but insofar as they coincide with what Bolzano himself calls pure conceptual judgements, he thinks they are rather unproblematic – we shall see a bit later how Bolzano accounts for them. On the contrary, Bolzano finds Kant’s explanation of them wanting. Kant’s solution is to rely on the so-called pure intuitions of space and time, but if they are supposed to work like the regular intuitions with a posteriori judgements, Bolzano argues, they do not work at all.
Bolzano goes further to analyse the Kantian notion of pure intuition, which should differ from empirical intuitions by not being generated by actual objects, but by imagination. Bolzano wonders why this would make any difference, since imagined objects are just less lively than intuitions of actual objects. Of course, Kant had suggested that it was not regular imagination that he was discussing, but pure imagination – Bolzano finds this a meaningless wordplay. Kant did suggest as a difference that empirical imagination generated images and pure imagination only pure schemes, that is, rules for finding images for a concept. Bolzano finds this even more perplexing: why call such a scheme an intuition? Indeed, he says, Kant’s scheme seems to coincide with what was traditionally called a genetic definition, which is essentially something conceptual.
Looking at concrete examples of synthetic a priori judgements, as discussed by Kant, Bolzano comes to the conclusion that Kantian notion of pure intuition shows infatuation with the idea that geometric proofs are based on constructions of figures in our imagination. Bolzano himself suggests that using such constructions as substantial steps in geometric proofs just shows the still inadequate condition of this science. Indeed, while they make proofs more lively in simple cases, with more complex figures they soon become too imprecise.
Bolzano finds even more to complain in Kant’s extension of the need of construction to arithmetics. Looking at the famous Kantian example, 7 + 5 = 12, Bolzano contends that a true notion of arithmetic sum would imply its associativity, that is, the fact that (a + b) + c = a + (b + c). If numbers are then defined by their relation to the predecessor (e.g. 7 = 6 + 1), proving the required judgement becomes just a simple task of using these definitions and associativity. True, Kant insists that such a process would require using time, but Bolzano finds this objection preposterous: equally well one can say that any sorites, that is, combination of several steps of syllogisms, takes up time, but Kant is still not saying that they require construction in time.
Returning to Bolzano’s own explanation of the origin of judgements, the immediate judgements he finds easy to account for. The first type of perceptual judgement, “I have appearance X”, just requires that we can have clear representations of our mental phenomena. With the second type, “what I intuit here is A”, the only problem Bolzano finds is that A can be a very complex representation, but he suggests that even such complex representation could be gradually built over time, when we attend to changes in our soul. The immediate conceptual judgements Bolzano finds even more unproblematic: we just require an ability to generate the pure concepts in question, perhaps occasioned, but not justified by other judgements, while combining these pure concepts into judgements is based on nothing more than immediately observing their relations.
The only real problem, Bolzano argues, is that many of our judgements have been generated at such an early time in our life that we are not anymore aware of the inferences we have required in generating them. Especially our judgements of temporal relations are problematic, he emphasises and adds that Kant never really addressed this question, at least when it comes to temporal relations of our representations, just assuming that we have an immediate awareness of some of our representations being earlier than others. Bolzano contends that this is something we cannot intuit immediately, but then again, we cannot derive it from observing external changes, since seeing something as change already requires an understanding of temporal relations.
Bolzano suggests as an ultimate basis of temporal judgements that we must be able to perceive that our mental phenomena occur at this moment, now. Furthermore, he continues, we can also observe that some of our representations conflict with one another in the sense that they cannot occur at the same time (for instance, judgement that A is true and judgement that A is false, or wish and sensation of its fulfilment). Sometimes, Bolzano argues, we are aware of an appearance as occurring now and a trace or a memory of a conflicting appearance. Thus, he suggests, we get our first notion of some of our appearances occurring at different times: we remember something that occurred, but is not occurring now. Series of representations can form even our first, although rather crude way of measuring time (think of a person counting in their head “one, two, …”).
According to Bolzano, we can distinguish between external and internal intuitions, and of the former we know that they have been brought about by external objects with an ability to generate intuitions in us (apparently this is based on a conceptual judgement on the nature of external intuitions). If we have similar intuitions, he continues, we can draw the probable conclusion that they have been generated by the same thing: this is not a certain conclusion, because sometimes different things provide similar intuitions. Furthermore if a group of intuitions always occurs at the same time, we can draw the probable conclusion that they have been caused by one thing with different powers. We still have to explain why this thing does not cause these intuitions always, and in some cases, the examples of which we do not need to deal here, we can infer that it has been a question of our spatial distance from the thing being different.
Bolzano goes into more details in his explanation of these processes. The important point here is that these inferences, as they occur in an animal or in a small child, are more like associations that slowly build up a set of judgements. Of course, they are not clear judgements, that is, judgements that the animal or the child would be aware of. In case of a child, Bolzano states, when they reach a suitable age, the resulting judgements start to gain clarity.
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