After a rather modern take on logic in the so-called elementary study, Bolzano returns to the idea that logic deals with human cognitive capacities. His justification is that such epistemological considerations are necessary for evaluating the suggested rules for finding truths and for organising them into individual sciences. Bolzano states that studying cognitions means essentially studying judgements and their constituents or representations. Furthermore, he adds, since cognitions form a specific subset of judgements, because all cognitions are true, logic should also study the relation of judgements to truth. Finally, Bolzano suggests investigating the degrees of reliability of judgements.
Starting with representations, we have to emphasise that it is not what Bolzano called representations in themselves that we are dealing with here, but subjective representations, which are more like appearances of representations in themselves in some mind. He also emphasises that in difference from a common way of speaking, he does not refer by representations only to representations of absent things, but to any constituents of our judgements that are not full judgements.
Bolzano begins familiarly with characteristics common to all subjective representations, first of which is that all of them are connected to some representation in itself. He sets out to prove this statement by asking the reader to imagine someone thinking of a representation A. Then, Bolzano states, “this person has representation” is a true proposition, even if no one is thinking of this proposition. This proposition, he concludes, has as one of its constituent the representation in itself of A, corresponding to the subjective representation A. Bolzano suggests calling this representation in itself the stuff (Stoff) of the subjective representation, distinguishing it clearly from its matter – the further subjective representation, of which it is constituted – and its object, which all subjective representations might not even have.
Bolzano emphasises that all subjective representations exist. He admits that we do say that something is just a representation, but then we merely mean that it does not refer to an existing object. Although existing, Bolzano explains, subjective representation is not an independent substance, but a characteristic of some mind: not an external characteristic or relation, but an internal characteristic or property.
Bolzano moves on to consider the question when subjective representations are same or similar. He suggests that subjective representations are numerically different at least when the corresponding representations in themselves are different or when they are thought by different persons. Bolzano notes that God is always thinking of all of the representations, so that there are as many divine subjective representations as there are representations in themselves. With humans, on the other hand, the subjective representations are constantly changing, but Bolzano thinks it convenient to think of them as holding their identity, as long as there is temporal continuity, so that any discontinuity in time would make the representations different.
Similarity of subjective representations, Bolzano goes on, requires at least the same representation in itself as stuff. Clearly, he adds, we can say that two subjective representations at different times are similar, but can we have similar representations at one and same time? Bolzano notes that we can have many different representations at the same time, for example, when we are thinking of judgements. Thus, he continues, we might think that, for instance, in a judgement like “a triangle with all angles similar has all sides similar” has two similar representations of similarity. Still, Bolzano finds it more plausible that it is just the same representation of similarity that is mentioned at two spots of this judgement, thus preferring the notion that we can speak of similarity of representations only in case of representations had at different times.
As actual entities, Bolzano points out, subjective representations have different effects. Such different effects may result from the corresponding representations in themselves – for instance, thinking snakes feels different from thinking flowers – or from the relation that the representation in itself has to other representations in themselves – thinking snakes is a different experience, depending on whether we are considering venomous or non-venomous snakes. Bolzano also points out that much depends also on an internal characteristic of the subjective representation he calls its strength or liveliness: stronger representations move us more.
Evidently all divisions of representations in themselves apply also to subjective representations, but Bolzano considered only few more prominent cases. Thus, he notes that we clearly have complex representations, which means that we must also have simple representations. Bolzano thinks it plausible that we never have just a single simple representation, because we are also aware of, for instance, words describing such a representation. Then again, he carefully distinguishes thinking of a mere collection of simple representations from thinking of a complex representation, since the latter still requires combining the constituents into a unity.
Important subsets of subjective representations, Bolzano states, are that of subjective intuitions – these are simple and refer only to one object – and that of subjective pure concepts – these are not intuitions and do not also have intuitions as constituents. Bolzano argues that we have intuitions, since we have representations that we regard as effects of a single actual object represented by this representation (say, the representation of “this smell”). He also thinks that we have pure concepts, using the notion “and” as an example. Bolzano underlines as an important type of intuition those that we have of our own representations.
A very common way to divide subjective representations, Bolzano points out, has been that between clear and obscure representations, but he finds most explanations of this difference lacking. The best explanation suggested, Bolzano thinks, has been to define clear representations through our being conscious of them, but what does this consciousness mean? Clearly, if we judge that we have a representation, this is a clear representation we are conscious of, but Bolzano deems the existence of such a judgement to be a too strong demand of clarity: picture two otherwise similar representations, only one of which we judge to be our representation – wouldn’t both still be clear? Of course, at least an ability to make such a judgement characterises our consciousness of representation, but Bolzano finds an ability to do something a rather weak basis for a definition.
Bolzano continues by noting that in order to judge that we have a representation, we need a representation of this representation. Then again, the converse is not true or we can have a representation of a representation without judging that we have this representation. Thus, Bolzano suggests as the first definition of clarity of a representation that we have a representation referring exclusively to this clear representation. He notes that this definition still leaves undetermined whether the representing representation is an intuition or a complex representation. Considering the complex representation of a representation we have a month ago, he states that it is obvious that only intuitions can be representations representing a clear representation. Bolzano also points out that mere ability to intuit a representation is not a sufficient mark for its clarity, since it is the actual intuition that gives our representations clarity, for instance, when we actually intuit having pain, instead of just being in pain, but not intuiting it.
Armed with this definition of clear representations, Bolzano thinks it obvious that we do intuit some of our representations. He is also adamant that some of our representations are obscure or such that we do not intuit them. Otherwise, Bolzano argues, we would have infinitely many representations, since we would intuit a representation, then intuit this intuition and so forth.
Another common division of representations is that between distinct and confused representations, and Bolzano follows the usual definitions quite faithfully. Thus, he takes distinct representations to be such where we know its possible constituent representations and how they are combined. A clear difference in Bolzano’s definition from those of some of his predecessors is that he can accept also simple representations as distinct, as long as we just know that it does not have any constituents. He also notes that distinctness has degrees and defines a complete distinct representation as such where we know how it is formed of its ultimate, simple constituents.
Bolzano has already stated that God’s subjective representations are eternal, but is it so with humans? Looking specifically at intuitions of external things, Bolzano notes that they are caused by external things affecting us, thus, making at least their come and go with this interaction. Then again, other representations are more dependent on our own activities. For instance, intuitions of our own representations depend on our attention toward our own mind, while simple concepts, Bolzano explains, are generated together with activities by which form representations from other representations (e.g. the concept of “not”) or judgements from representations (e.g. the concept of “having”). Thus, he concludes, these representations come and go together with such activities.
Although representations come and go, Bolzano suggests that they do leave some traces in our soul. Such traces, he explains, are the main reason why we can later draw from our memory representations that we know resemble those that we have had earlier. This drawing of memories or recollection follows the so-called laws of association, which Bolzano reduces to the single rule that when we have regularly had two representations of a certain kind occur at the same time in our mind, the existence of one type of representation can awaken also a representation of the other type. The possibility to recollect has degrees, he notes and surmises it has something to do with the strength of the representations in question.
A special case of recollection Bolzano considers is such where one representation is supposed to refer to an object and we then generate another representation or image of this object (Bolzano also calls this image scheme, which is a term reminiscent of Kant’s philosophy). The image is often more determined than the original representation – for instance, when we imagine a triangle with a definite shape, when thinking of triangles in general – and we might have such an image even of things we cannot actually perceive (e.g. God) or even of completely imaginary things (say, when we think what a body limited by ten regular figures would look like).
Bolzano goes into great detail to discuss the use of representations as signs for other representations, which obviously leads to the formation of language, but he mostly suggests some simple definitions, so we can skip this part of his account. A more interesting digression is his suggestion that especially in case of complex representations formed in early childhood, we are not aware of their constituents. This is especially true, Bolzano thinks, with generic representations related to intuitions, like “red”, “blue”, “sweet”, “bitter” etc. These must be complex, he insists, because they are not intuitions, which always refer to just a single object (in other words, we have intuition of this particular red we sense now, but not of red in general), and also not simple concepts, since they do not have as clear limits (for instance, the line between red and orange is fuzzy). Indeed, Bolzano goes even so far as to deny that they can have intuitions as their constituents, since they do not have any reference to a specific moment in time (as my representation of e.g. my parents do). Instead, he suggests, these generic representations must be concepts of laws describing how certain types of intuitions can occur in our soul through interaction with other objects.
Bolzano ends his discussion of subjective representations with the rather obvious point that there are representations that we do not at the moment have and even never have had. Indeed, since intuitions are dependent on interaction with external objects, there are many objects we have never had interaction with and thus have never intuited.
