The second question of Bolzano’s fundamental science concerns knowledge or cognition (Erkenntniss), but before we can understand what it is, he says, we must first understand what judgements (Urteil) are. Judgement is, again, a term that Bolzano cannot give a definition of, so he suggests just that he is using it in the regular sense of the word. Since this is a rather meager explanation, he gives a further detail that judgements are the common element in e.g. decision, opining, belief and assent.
Bolzano goes on to indicate some further characteristics of judgements. Every judgement contains a proposition, and depending on whether the proposition is true or false, the judgement is correct or incorrect. As something belonging to the human mind, Bolzano thinks, judgement exists, but then again, its existence is not independent, but dependent on the person who makes the judgement. He emphasises that judgement is different from mere representation of proposition, which does not assert anything. Thus, Bolzano suggests, God judges every true proposition, but only represents false judgements.
What then does it mean to make a judgement? Bolzano observes that it is an activity that requires that we have first decided to consider representations, where this consideration has led to a confidence that some proposition is true. He notes that the force of this confidence can have different degrees and that we cannot decide what this degree is. If it happens that a proposition and its opposite seem equally probable, we cannot judge, but only doubt.
Knowledge or cognition, Bolzano defines, is a judgement that contains a true proposition: thus, all cognition involves judgement, but some judgements do not involve cognition. True, he admits, we sometimes speak of erroneous cognition, but then we mean that cognition is mingled with some errors. When Bolzano is thus asking whether we humans can know or cognise anything, he means to ask whether any of our judgements can be true. He clarifies that he is not taking a stance on whether children or mentally ill people can do this, but wants to know just whether his readers can know any truths.
The target of Bolzano is a full skeptic who does not accept any truths. Such an extreme skeptic, he says, could not even make judgements, because this would require considering something as true. Indeed, if they said that they doubted something, they would appear to know at least this doubt. A wary skeptic might avoid this trap by not even committing themselves to their own doubt. But if they say that they doubt this doubt, don’t they admit then this second-level doubt? This takes us to an infinite regression, but we can cut the escape of the skeptic short, Bolzano thinks, by pointing out that in all these discussions the skeptic constantly has representations and can know it.
Having found this certain truth, Bolzano continues, we can say with certainty that we know it. Indeed, the judgement that this judgement is a truth is a further truth and thus something we can know. Since we can clearly repeat this same procedure over and over again, there are innumerably many truths we can know.
Bolzano notes that the proofs he has just given satisfy the skeptic for a single moment, but a complete cure requires further convincing, which he puts in a form of dialogue, which begins by the skeptic denying that they can admit having representations, because they do not even know whether there is any I that would have them. Bolzano is convinced that the skeptic cannot really doubt their own existence, once they think about the issue, and even if they do not happen to consider their existence, they need not make any judgement about it in order to notice that they are having representations. The skeptic concedes this, but raises the further doubt that this is all just their peculiar judgement that is skewed to regard everything erroneously. Bolzano assures us that even such an erroneous person would be right in assuming that they have representations and do exist.
Skeptic moves on to a new level of attack by admitting that Bolzano has managed to show that seemingly good grounds justify the truth of some of the judgements, yet, the question is whether these grounds themselves are true. Bolzano answers that the grounds are immediately certain. Furthermore, he continues, although these grounds presuppose the truth of what is to be proved, knowing the truth of the conclusions does not presuppose knowing the truth of the grounds, just like our belief in seeing does not require belief in the existence of the eyes, although the existence of eyes can be proven from the fact we do see something.
The skeptic is still afraid of the possibility that the judgement about the representations is just an error. Bolzano suggests that the question is not anymore about being convinced of the judgement, because just attending to it makes the answer obvious and even being deceived presupposes having representations. Perhaps, he says, the question is that the skeptic does not understand why they are so convinced. Bolzano really doesn’t have any answer: our power of cognition is behind it, but we do not know how it works – then again, we only need to know that it does work.
The skeptic changes tack and questions the worth of knowing the existence of representations. Bolzano admits this is not much, but at least it assures us that our power of cognition is not completely faulty. Skeptic finds this hard to believe, since we cannot know whether our representations correspond to the objects in themselves, because we can’t compare representations with their objects. Bolzano finds this whole question deceiving: because the very idea of comparing representations with objects is irrational, the truth of our judgements cannot depend on this. Sometimes, he continues, we know our judgements to be true, because this is evident from the very concepts used: this happens especially in mathematics. At other times, our judgements are based on immediately certain intuitions, just like when I say that I see red. Finally, Bolzano concludes, sometimes our judgements concern causes of our intuitions, and these judgements are based on probable information about the possible effects of objects, received through constant occurrence of some types of intuitions together.
The skeptic is relentless and notes that despite all these cognitive tools, humans still manage to make many errors. Bolzano points out that immediately certain judgements cannot be doubted and neither can correct deductions. This leaves still probable arguments, and he admits they can lead to errors, but adds immediately that it is not reasonable to not assent to very probable judgements. The skeptic points out that in dreams and confused states our cognitive tools do not work. Bolzano thinks that even in these states the errors do not concern immediately certain judgements, but only consequences deduced from them: thus, although it is certain even in a fevered state that if I feel cold, I truly feel cold, it is wrong to conclude that this feeling is caused by coldness of the air surrounding us. Even so, he continues, these problems do not concern us in a healthy state. The skeptic makes the obvious retort that in a dream or confused state we often cannot recognise that we are in an abnormal situation. Crusius agrees, but thinks the important point is that in a healthy state we can distinguish it from abnormal state. The skeptic makes the final suggestion that perhaps we will have quite different experiences in the afterlife. Bolzano is sure of that, but asks the reader to focus on our current judgements that concern our current life.
After this long detour, the skeptic accepts that they do know some truths, but still asks for a criterion to recognise truths. Bolzano suggests as a criterion that a judgement is reliable, if it is ascertained always when tested. The skeptic still raises the possibility that their memory might be in error, but Bolzano finds this very improbable.
Bolzano notes in the end that these kinds of investigations are usually not included in logic. Instead, he continues, their place is often taken by the so-called laws of thinking, such as the law of contradiction. Bolzano notes that often these laws concern things in general and not judgements, making them more fit for ontology than logic.
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