Bolzano defines certain or secure judgement as being generated in such a manner that there is no possibility of error. He notes at once that certainty in this sense is a contextual notion, related to a certain thinker who holds a judgement to be true. Thus, Bolzano says, for God, all truths are certain, while for us, only those are certain that we know immediately or that we have derived from immediately known truths without probable inferences.
Bolzano divides erroneous judgements into four groups, on the basis of whether all the premisses of these judgements are true or whether at least one of them is false and whether the judgement in question is a probable conclusion of the premisses or whether it is just imagined to be so. He manages to simplify this classification by noting that in cases of imagined inference, we could take the erroneous rule of probable inference as one premiss, which of course is then a false premiss.
Bolzano divides probable judgements into those where we know their probability and those where we don’t know it. If we know the probability of a judgement, he continues dividing, the judgement might be either held to be true or not (in quantitative terms, this depends on whether the value of probability is greater than ½ or not). If a probable proposition is held to be true, this probability can be either real and objective, if all its premisses are true, or then just assumed and subjective, if some premisses are false. In case of objective probability, Bolzano suggests, the premisses are then partial grounds of the probability of judgement – he emphasises that they are not grounds of the judgement, although they are causes of us having the judgement (that is, what he earlier has called grounds of knowledge).
Bolzano also divides probability into contextual or relative and complete or absolute probability, depending on whether the probability of the judgement is calculated in relation to just a part of judgements held to be true by the thinker or in relation to the whole collection of them. If the absolute probability is so high that it would be ridiculous to even consider its negation to be true, Bolzano calls the judgement believable or morally certain.
Bolzano returns to the notion of confidence in judgement, which has earlier just mentioned in passing, characterising it only as coming in degrees. The question is why we have different degrees of confidence: could it be that before we even assent to a judgement, we ascribe to it a definite degree of probability, on the basis of which we decide how confident we are in its truth? Bolzano admits that this might be the case sometimes, but certainly not with all judgements, because ascribing a probability to a judgment is a new judgement, leading us to an infinite regression, since our degree of confidence in this new judgement would require another judgement on its probability. He notes that especially immediate judgements are not preceded by a judgement of their certainty, since otherwise they wouldn’t be immediate. Furthermore, Bolzano continues, not even all mediate judgements cannot be preceded by a judgement of their probability, because this latter judgement would again be a mediate judgement, leading us to a new infinite regression.
Bolzano suggests as an answer that the probability of judgements, even when it goes unnoticed by us, is connected to a force that the judgement has to affect our confidence in it. Thus, he concludes, our confidence in a judgement is determined, firstly, by the absolute probability of the judgement in relation to all the current judgements in our minds, and secondly, by the degree of confidence these previous judgements have in our minds. Bolzano considers the question, whether there might be other influences, and at once rules out the possibility that forgotten judgements had something to do with our confidence. He does admit that differences in our attention and our wishes on truth or falsity of some matters might affect our confidence, but suggests that this influence happens mediately through judgements they evoke.
Bolzano suggests enumerating our degree of confidence in the immediate judgements and judgements derived from these with no use of probable inferences as 1 – this would be the highest quantity confidence could have. Our confidence in judgements derived with probable inferences would then be less than 1. Bolzano suggests calling such a less than fully certain confidence a moral confidence or conviction, if the respective probability is so high that the judgment is morally certain, while otherwise the judgement would be a mere opinion.
How is the degree of confidence then calculated? If the probability of a proposition is ½, Bolzano thinks, our confidence in it would have to be 0, since then we are not at all confident in the judgement, and indeed, do not even hold it or its negation to be true. Thus, he suggests defining the confidence in a judgement as the difference of the probability of the judgement and the probability of its negation, that is, if the probability of judgement is presented as a fraction m/n, then the confidence would be m/n – (n – m)/n = (2m – n)/n. Bolzano notes that the confidence in a judgement could then get negative values up to –1, but this means just that our confidence in the negation of the judgement has the respective positive value.
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