Just like the study of propositions was followed by the study of truths, Bolzano moves from the study of judgements to consider their relation to truth. More precisely, his question is how both true and false judgements are generated. Knowing especially the sources of error, Bolzano suggests, helps us to avoid them altogether. On the side of true judgements, he adds, it should be helpful to know if our knowledge has any intrinsic limits.
Before getting to the actual investigation, Bolzano wants to define the notions of knowledge and error and also the related notion of ignorance. He suggests first defining knowledge as truthful judgement, but quickly notes that with this definition, something we weren’t asserting at the moment would not be knowledge. Thus, Bolzano finally lands to the definition that knowledge is a truthful judgement that we have assented to at some point and that we can recollect and would continue to assent to, when explicitly asked.
Bolzano notes that the concept of error refers to judgements. We do say, he admits, that we have an erroneous concept of a thing, but then we just mean that we make erroneous judgements about the thing. Similarly, Bolzano contends, ignorance should refer to judgements, since in case of concepts we can instead speak of their absence. Thus, he defines ignorance as not having a certain piece of knowledge, regardless of whether the respective judgement has never been made or whether it is just not recollected. Error, then, is for Bolzano a false judgement that one has assented to at some point and that they can recollect and would continue to assent to. He also points out that assenting to propositions that imply a specific knowledge or a specific error is still not enough for having this specific knowledge or error without an explicit assent.
Bolzano states that we are clearly ignorant of infinitely many truths, because our mind is too finite to contain all of them. More precisely, he adds, we are ignorant of truths, because we do not have the relevant representations, or in case of mediated judgements, because we haven't been able to do the proper inference, either because the required premisses are never at the same time in our mind or because we lack the capacity for the required inference.
Bolzano starts his investigation of errors by noting that it is not rational to doubt the truth of our immediate judgements: If we doubted one of them, we should doubt all of them, since they are all generated in the same manner, and in fact, we would have to doubt all of judgements, since ultimately they are based on immediate judgements.
Moving on to discuss derived judgements, Bolzano notes that we really cannot doubt the basic rules of inference we use, again, because that would undermine our reliance on all of our derived judgements. What we can doubt and what can cause errors, he suggests, is when our inferences involve probability. In other words, it is not their probability that is to be doubted, but our instinctual habit of accepting highly probable propositions as true, although there is a slight possibility they are not. This means, Bolzano argues, that any entities, like God, that do not use probable inferences, are incapable of error. Furthermore, he adds, erroneous judgements are not completely certain, but they do have a deceptive look of a truth, due to their high probability.
Most judgements based on probability are experiential, Bolzano thinks, but he does not rule out purely conceptual judgements that use probability. Indeed, he states, every time we use recollected premisses in our inferences, we are involved with probabilities, since we cannot be completely certain on what basis we accepted them.
Bolzano notes that the general description of the cause of errors does not yet give us proper tools to avoid errors, since we cannot just reject all probable inferences. Thus, he gives a more detailed explanation on the causes that especially make us think false propositions as probable. The list is not very original, as Bolzano himself admits: ignorance, reliance on incidental connections, unreliable memory, too weak or too lively imagination, inclinations of our own will, ambiguousness of words and influence of other people are all among possibve causes of errors.
The discussion of error has taught us, Bolzano continues, that judgements are necessarily true, if they are immediate or derived from immediate judgements by inferences that do not involve probability. Mediate judgements can be at times or accidentally true, even if derived by probable proofs, he adds, and even if they are derived from false judgements through inferences.
Bolzano reminds us that some of our true judgements are based on knowing the ground of that truth. The question is can we know truths otherwise than from their grounds. Bolzano answers at once that at least immediate judgements are not known from grounds. Then again, he continues, some truths have no ground – these are the so-called fundamental truths. Could all our immediate judgements be fundamental truths? Bolzano denies this, because our immediate perceptual judgements have a ground, since perceptions have a cause. Furthermore, he continues, knowledge based on probability does not presuppose knowledge of the ground, and in fact, when making judgements of experience, we seem to never know the grounds before the consequences. This leaves still the question of conceptual truths, in finding of which we require probability at most for recollecting earlier known truths. Immediate pure conceptual truths could be taken as fundamental truths, Bolzano conjectures, but he is apprehensive about truths derived solely from such fundamental truths: since there usually are many possible ways to prove them, but there should be only one ground for one consequence, we most likely do know some derived conceptual truths on the basis of something else than their ground.
If a judgement is not immediately made, Bolzano reminds us, it is derived from other judgements, which are then the cause of the first judgement. If the first proposition is true, the collection of the judgements from which it is derived could be called the ground of this knowledge – actually, Bolzano thinks, it should be more proper to call them the cause of knowledge, but this is not a commonly used term. Grounds of knowledge can, of course, contain false judgements and they need not be grounds in the proper sense of the word, thus, Bolzano divides them into objective grounds of knowledge, which are also proper grounds, and subjective grounds of knowledge, which are not.
As Bolzano has stated a number of times, we can know only a finite amount of truths at a time, but this does not yet imply that there would be a definite limit on what we can know. Considering what finding limits of our knowledge would mean, he first suggests simply that it would imply determining what we can know what we cannot. Then again, Bolzano reminds the reader, we can know truths accidentally even through errors. To make the idea of the limits of knowledge more stable, he then suggests including within them only truths that we can reach in a regular fashion.
Bolzano continues by stating that the notion of the limits of knowledge is still ambiguous: we might speak of limits for a certain purpose, my individual limits or limits of all humanity or even limits for all conscious beings, limits for the time being and limits for the end of times. He suggests that the aim of determining these limits in logic should be to show where we need not put our efforts in searching for the truth. Thus, it would make sense to speak either of our own or of the limits of humanity. It would also not be useful to know only the current limits of our knowledge, Bolzano suggests, since those can change in the future.
Going to the concrete question of determining these limits, Bolzano notes that this cannot be done by simply stating the truths we cannot know, since then we would in fact know them. He suggests that we could instead mention generally the objects, of which we can know nothing, but notes at once that we can know something of every object, for instance, characteristic it shares with all objects in general: and indeed, even the judgement “we can know nothing of this object” would also be a truth we know of this object.
Moving further with the idea, Bolzano suggests that maybe we could point out objects, of which we cannot know anything that is proper to these objects. His answer is that since we have to be able to have a representation of the object even to speak about it, we do know something that is proper to it (this representation). Another possibility is that the limits of knowledge would limit knowing any such proper characteristic of the objects in question that are not included in their representation. Bolzano thinks proving such unknowability would have to be based on the proper characteristic of the object included in its representation, but admits knowing no such proof. In addition, he sees a possible contradiction lurking here: if we could probe unknowability in this sense, it would actually be a characteristic proper to the object, but not included in its representation.
The only possibility Bolzano can think of anymore is that we might point out propositions of which we could never know whether they are true or false. The problem is that he sees no way to prove propositions to be unknowable: although we haven’t decided their truth now, we could find means to decide the issue in the future. Indeed, Bolzano states, it has sometimes taken hundreds of years to find out proofs for conceptual truths, and in case of judgements with experiential elements, further experiences in the future might decide the issue about their truth,
Bolzano again admits that his conclusions on the limits of knowledge are not revolutionary and points out that most non-sceptical philosophers would agree with him. The clear exceptions are Kant and his followers, who thought they could define strict limits to human knowledge. Bolzano has already rejected some key elements of Kant’s philosophy, which underlie also Kant’s notion of the limits of knowledge. Still, Bolzano criticizes the idea yet again from another angle.
Bolzano finds even Kant’s division of proper sciences into just four parts (logic, arithmetic, geometry and pure physics) faulty, because it lacks all practical sciences and aesthetics. He also considers it absurd that Kant insisted logic would consist of mere analytical judgements. Indeed, Bolzano lists many synthetic judgements of logic, such that there are representations and that every proposition can be divided into at least three parts. Even rules of inference are synthetic judgements, he thinks. Then again, as we have already seen, Bolzano considered arithmetics to be more analytical than logic and definitely not dependent on any intuition of time. What Bolzano finds particularly faulty in Kant’s notion of the four sciences is that they contained only universally recognised truths, because he thinks their great certainty rises only from the ease of empirically testing their most important theorems, possibility to infer the rest of their theorems and lack of human passion concerning them.
Kant especially thought we could not say anything about supersensuous objects, because we can make synthetic judgements only of what we perceive immediately, since space and time are a necessary condition on what we can know. Bolzano thinks it not at all clear what we should include among such objects. Usually, he says, by sensuous objects we mean such that can generate perceptions by affecting our organs, that is, bodies, which would mean that simple substances, of which bodies consist, are not sensuous – still, they exist in time and space. Similarly, Bolzano continues, the soul should be supersensuous (since we do not perceive it as such), but it also exists in time (because it changes) and in space (because it interacts with things in space). In fact, he concludes, only God is not in space and time, because God does not change, although in a sense God is in all space as time as their creator.
Bolzano also thinks that there are many true metaphysical judgements about these supersensuous objects that we know – his examples include “God exists”, “no simple substance can be destroyed”, and “representations can occur only in simple substances”. He admits that we have not found the proper grounds for these judgements, but they still are known to be true judgements, and indeed, we still lack proper foundations in most of our sciences, since we haven’t been able to properly define even such crucial notions as space in geometry.
Bolzano goes into great detail in pointing out missteps in Kant’s proofs of antinomies and we need not follow him there – the faults of these proofs have been many times attested by several philosophers. Instead, we should point out that Bolzano finds Kant’s notion of practical proofs of God, freedom and immortality preposterous: surely we cannot first suppose that we ought to strive for some end (in Kant’s case, the greatest good) and then just say that the preconditions of this end must be possible, but instead, we should first ascertain that achieving the very end is possible and only then conclude that it is something we ought to strive for.
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