Bernard Bolzano: Study of science – Can we know any truths?

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.

Bernard Bolzano: Study of science – Are there truths in themselves?

The purpose of fundamental science, the first part of Bolzano’s logic, is to remove all doubt that prevents any use of human reason. This task, he says, has two parts: first, we have to show that there are what he calls truths in themselves, and then, we have to show that humans can know at least some of these truths. Bolzano notes that one might doubt the meaningfulness of both of these tasks, since true skeptics wouldn’t even believe in the existence of other people and wouldn’t then even listen to any of their arguments. Bolzano notes that even if we cannot save such extreme doubters, we can convince people who are in danger of becoming skeptics. Furthermore, he adds, even the most stubborn skeptics live unskeptically and thus have the opportunity to be at least internally convinced, even if they refuse to admit this.

As a preliminary to the first task, Bolzano introduces the notion of proposition in itself (Satz an sich). He does not explain the phrase immediately, but only through comparison with other types of propositions. In other words, Bolzano says that uttered propositions are spoken phrases indicating something that must be either true or false, while a thought proposition is such that is not spoken, but only thought by anyone. Yet, he adds, propositions need not be said or thought at all, and if we ignore the question whether they are or not, we are dealing with propositions in themselves.

Bolzano is at some pains to explain why he can use the German word Satz for the notion he is describing: Satz is etymologically related to the verb Setzen, which implies that there is some person “setting up” this proposition. He explains that the etymology should not be taken literally here, just as a mathematical root of an equation is not at all like a root of a plant. Besides, he states, the concept is needed, and any other possible designation, like judgement (Urteil), would point even more to a thinker behind it. Indeed, Bolzano emphasises again and again that proposition is nothing anyone needs to be thinking (although it can be). This implies, he notes, that propositions in themselves do not exist, although thought of a proposition can exist. Then again, Bolzano points out, propositions in themselves can still concern thoughts (think of a proposition like “I am thinking myself”).

Bolzano is assured that previous logicians have at least implicitly used the concept of proposition in itself: for instance, they have admitted that the order of propositions in syllogisms is irrelevant, which would not be true, if they described the order of thinking and not relations of abstract propositions. True, he admits,they have not spoken of propositions, but judgements, mostly because many of them supposed that the phrase Satz referred only to a subclass of judgements, namely, assertions. Bolzano notes that even the suggested other types, such as questions, can be also seen as assertions: question just is an assertion saying something of the form “I ask this and this”.

Bolzano admits that his description of proposition is no true definition. His excuse is that no proper definition is simply available. The best historical alternative – that it is something that can be true or false – is not a classical definition, according to Bolzano, because it contains a disjunction. Other suggested definitions, he notes, have often concerned thoughts of propositions or then they have assumed the concept to be defined.

Bolzano has introduced the notion of a proposition in itself only to explain the further notion of truth. Words “true” and “truth”, he says, can mean many things, but the most appropriate is that truth is a characteristic of certain propositions in themselves, whether they are asserted or thought or not. Sometimes, Bolzano continues, we speak of truths, when we mean these propositions that have this characteristic. An even further deviation is to speak of true thoughts or judgements that contain true propositions or of collections of propositions or judgements. The least appropriate meaning, Bolzano thinks, is that of speaking of e.g. true friends, where we are referring to an object that truly is what it is described to be.

Just like there are propositions in themselves, Bolzano says, there are truths in themselves or objective truths, that is, truths no matter whether anyone says or thinks it. Just like propositions in themselves, he thinks, truths in themselves do not exist, except when thought by someone. Bolzano does admit that metaphysically speaking, God does know all truths, but this does not lie in the very concept of truth: truth in itself differs from a known truth. Furthermore, he continues, truth differs from certainty, which is a property of judgements, and from existence, although truths can refer to something existent. Interesting is the relation of truth to thinkability and knowability. Bolzano notes that all truths are thinkable, but not everything thinkable is true. Even more, he adds, all truths are knowable and everything knowable is true, but the concepts are still different, because knowledge and thus also knowability have degrees, but truth does not.

Bolzano could not define propositions in themselves, but he suggests we can define truths in themselves. Propositions always have a subject or a topic, of which they figuratively say or predicate something. Propositions are true, Bolzano underlines, if this subject actually has what the proposition predicates of it. The only weak point in this definition, he says, is the word “actually”, which in this context means the same as “truly”. Still, Bolzano thinks, this is no problem, since we can do without this word: proposition is true means that proposition predicates of its subject what the subject has.

Bolzano considers several alternative definitions of truth, dismissing quickly the so-called metaphysical definition, equating truth with existence. A more interesting definition is that of truth as correspondence between thought or representation with its object. Bolzano cannot, of course, accept this definition, because it speaks only of thoughts or representations of truths. Furthermore, he says, no one has really been able to explain what this correspondence is supposed to be. If it is meant to say just that a representation represents its objects, well, Bolzano thinks, this is what representations always do. If it means that representations within a proposition have the same relation to one another as their objects, this cannot be literally true, he points out, because e.g. a representation of God is not the cause of a representation of the world.

Further suggested definitions of truth Bolzano finds even less convincing. Truth cannot be just universal validity, since every person does not know every truth. Furthermore, truth cannot be defined as agreement with the rules of thinking, because these rules are either defined in terms presuming the notion of truth or then the definition also includes probable propositions that are still not true. Finally, truth is not defined by permanence, which is at most a sign of truth, not its essence.

Bolzano criticises attempts to extend the notion of truth. Firstly, he is not fond of the concept of subjective truth or of truth relative to a person, since we already have notions like opinion. Similarly, Bolzano forbids the idea of a formal truth, which at best means something like non-contradictoriness, which should not be confused with truth.

With all these preliminaries taken care of, Bolzano can finally move to his actual task, that is, proving that there are truths in themselves. This does not mean, he underlines again, that we should prove that such truths exist, but only that at least one proposition in itself is true – or to put it in other terms – that the proposition “no proposition is true” is not true. This, Bolzano quickly notes, is evident because “no proposition is true” contradicts itself: if it were true, it would itself not be true. Thus, there must be at least one truth. Even further, Bolzano points out, the same proof can be applied again. Say that we know there to be a certain number n of truths. Well, if we pick out these n truths and consider the proposition “no proposition beside these specific truths is true”, we note again that this proposition contradicts itself and that there are more – and indeed, infinitely more – true propositions.

Bolzano notes that a hardcore skeptic might not be impressed with this proof. They would object that if they are to be convinced by this proof, they must already suppose that they have a capacity to know truth, thus already presupposing that there are truths in themselves. Furthermore, Bolzano continues with the skeptic’s objections, the proof assumes the premiss that “no proposition is true” is a proposition in itself, thus assuming another truth before we showed that there are any truths. Bolzano is not afraid of these objections. Firstly, he admits that the person convinced of the proof must have a capacity to know truths, but they themselves need not explicitly have this as an opinion. Secondly, Bolzano agrees with the skeptic that the mentioned premiss is true and goes even so far as to suggest that its truth is immediately convincing. Yet, he adds at once, this is no problem, but another proof for what we set out to demonstrate. The method Bolzano used was chosen just because it so forcefully showed the self-contradictoriness of all skepticism, but this does not mean that there aren’t other ways to do the same thing.

Bernard Bolzano: Study of science (1837)

(1781–1848)

Hearing the title of Bolzano's magnum opus – Wissenschaftslehre – makes a student of German idealism instantly think of Fichte's similarly named treatises. Despite Bolzano's cries against this, the two do share something in common, namely, the attempt to set up a kind of metascience or a science of sciences that acts as a foundation for all other sciences.

The similarities between the two projects do not go far beyond this very abstract foundation. Bolzano's Wissenschaftslehre is a much more modest affair. For Bolzano, science is just a convenient chunk of the sum of all human knowledge that could be presented in an easy to understand and convincing book or treatise presentable in a book. Wissenschaftslehre, for Bolzano, is then in essence a science of rules for making books or treatises from sciences.

Bolzano emphasises the literary character of Wissenschaftslehre: it should not include didactics, which he defines as the science of oral teaching of sciences. Even so, an inevitable question is whether it is possible to write a scientific treatise on Wissenschaftslehre, before one has such a treatise from which to learn the skill. Bolzano notes that it is possible, because it is possible to follow the rules without knowing them distinctly.

Bolzano notes that his planned Wissenschaftslehre is not a new idea, but has been studied under many different names, most often under the name of logic. True, he admits, logic has never really been defined in the same way as he does, probably because the rules of making scientific treatises have formed just a small part of logic. Bolzano finds no difficulty in this, since these other topics are preliminaries we must learn, before getting to the writing of a scientific treatise – a phenomenon familiar with other sciences also.

Reverting to the more familiar name, Bolzano notes that by logic we can mean logic in objective sense – sum of logical truths, no matter whether they are actually known by anyone – logic as an individual treatise and logic in subjective sense – sum of opinions on logical topics of a certain person or subject. Logic in the subjective sense can then be divided into natural logic – sum of logical insights that anyone has without any learning – and artificial logic – sum of logical information gathered through various means of learning. Furthermore, Bolzano notes, logic in the subjective sense can be distinguished from a capacity to follow logical rules, because it is possible to follow logical rules without knowing them and know the rules without being able to follow them. Logical capacity finally divides into innate logical talent and logical art acquired through, for instance, study of sciences.

Bolzano points out that even if we have innate logical skills, studying logic is still good for avoiding mistakes and false deductions and especially useful for very subtle disciplines like metaphysics. In addition, Bolzano says, a logical treatise gives a good example of what a scientific treatise should look like. Still, he does not encourage teaching logic to very young children, because it requires very much abstraction, its topic being so far removed from sensuous matters. Instead one should first study easier disciplines, like natural sciences and a priori sciences that can be sensuously represented, such as geometry.

Bolzano considers some questions about the nature of logic, such as whether it is more of an art or a science. According to his definitions, it is actually both. Crusius defines art as a practical or technical science, that is, a science, the essential content of which lies in rules of behaviour, or in a more stricter sense, as a scientific description of processes one must do to put rules of technical science in practice. Logic, he thinks, is at least a technical science and maybe even art in a stricter sense.

Another question is whether logic is a formal science. Bolzano has some problems understanding what the question means. In a sense, he says, the answer might be positive: logic deals, for instance, not with any determined propositions, but with kinds of propositions (such as affirmative and negative propositions) that might be called their forms. Then again, Bolzano adds, if by formal is meant such a science that abstracts from all differences of objects, logic does not fit the description, because it deals e.g. with difference of empirical and non-empirical truths or that of analytical and synthetical propositions. Even more so, Bolzano states, if by formal science is meant a mere collection of analytical truths, logic, and indeed no real science, is such a collection.

Bolzano considers also the relation of logic to other sciences: is logic dependent on some of them or an independent science? He explains that by a science being dependent on another he means that a treatise of the first science must contain in its demonstrations propositions belonging to the second science. Bolzano points out that very few sciences are independent in this sense. Logic particularly, in his opinion, depends at least on empirical psychology.

The only task left to do for Bolzano before actually starting logic is to consider what preliminaries to study before dealing with the proper science of sciences, that is, showing how the field of truth should be divided into individual sciences and what rules these sciences should follow. Before we can get to the business of constructing sciences, he says, we must obviously have truths to make them. Thus, Bolzano concludes, logic must also contain heuristic or art of finding truths.

Bolzano notes that the proper science of sciences and heuristic cover much of what is usually named methodology. In fact, he says, they contain even more, since usually methodology is taken to be a part of pure logic, containing only truths applicable to all thinking beings, while his science of sciences and heuristic are explicitly dealing with the question of how humans find truths and make sciences out of them. Because of this, Bolzano suggests, logic must also investigate the question how humans can in general know truths, that is, it must deal with epistemology.

It was commonly thought the methodology presupposed what was called elementary science that dealt with concepts or representations, propositions or judgements, deductions or syllogisms and often also truth. Bolzano also accepts this elementary science as a part of logic, since understanding these elements is necessary for understanding how truths can be known and found out. He does make a significant change: while usually the elementary science was meant to be a study of e.g. truths as thoughts, Bolzano argues that it should study something more fundamental, in other words, truths in themselves that need not be thought by anyone.

Elementary science, as conceived by Bolzano, has one further presupposition: in order to study truths in themselves, we must at first ascertain that there are such objective truths, not dependent on any thinker, and that we humans can have access to them. This final – or actually the first – part of logic he calls fundamental science, because all other sciences presuppose it. Next time, we shall start our journey through Bolzano's logic with this fundamental science.