If the first part of Bolzano’s logic – the fundamental science – was rather an outlier in a logic book, the next part – the elementary science – seems at first sight much more traditional. Thus, Bolzano notes that since logic deals with the question of dividing science into groups of truths that are presented in scientific treatises, we must investigate the characteristics of truths. Before we can get into truths or true propositions, he continues, we must first deal with characteristics of propositions in general, and before that, we must deal with characteristics of parts of propositions, which he calls somewhat unexpectedly representations. Furthermore, Bolzano adds, we should also deal with a useful subset of propositions and truths that indicate that certain propositions can be derived from others – these are deductions. Thus, Bolzano’s elementary science, so named because it deals with the ultimate elements of scientific treatises, deals almost traditionally with representations, propositions, truths and deductions, with some of the nomenclature and the inclusion of truths the seemingly only peculiarities.
Starting with representations (Vorstellung), Bolzano notes that they have internal characteristics that require no comparison to anything else and external characteristics that arise from relations to other things. The latter he then divides into characteristics in relation to other representations and characteristics in relation to other things, like propositions. But before going into any of these, Bolzano states, we have to investigate the very notion of representations in themselves.
Bolzano begins by noting that he has used the term “representation” earlier, but only in what he takes to be its common sense or then in contexts where it is evident what is meant. Just like with propositions, he wants to distinguish representation in itself from this common meaning, which he calls a thought of representation or subjective representation. ; In comparison, Bolzano states, representation in itself could be called an objective representation and it refers to any constituent of a proposition in itself that is not yet itself a proposition.
Bolzano notes that his explanation of representation might not be enough, since the very notion of proposition in itself was somewhat mysterious, so he tries to give another explanation. He starts from representation in the common sense or the subjective representation – whenever we are perceiving, imagining or thinking something, without making any explicit judgements or assertions, we are representing, and since all of these activities suppose a subject who does these, they could be called subjective representations. As mental states, Bolzano adds, these subjective representations have actual existence.
Now, Bolzano continues, every subjective representation has a content or material and this material is the objective representation in itself. This representation in itself does not require any subject, but then again, it also does not exist. Because representation in itself is not connected to any particular subject, it can be thought by a number of different persons and still remain the same representation – this is why it is called objective, Bolzano explains. He even suggests that there are representations that are not thought by anyone beyond God, like the number of grapes in southern Italy this year.
Bolzano goes on to distinguish representation from several other notions. Although representation was called the material of subjective representation, he begins, it is definitely not the object to which subjective representation refers to: indeed, a representation can refer to many objects, like the representation of an ancient Greek philosopher refers to both Plato and Aristotle. Another clear distinction between the two, Bolzano adds, is that the representation in itself does never exist, but objects of representation can exist – then again, they do not always exist, for instance, if the representation in question is the notion of a proposition. He even fathoms that some representations do not have any object, giving as an example the square root of –1.
Bolzano also emphasises that representations are not words, since these are always sensuous objects, either sounds or written signs. Furthermore, he adds, some representations are not connected to any words, while other representations can be signified by many words. Bolzano notes that sometimes even propositions and judgements are taken as representations, e.g. when philosophers speak of true and false representations. Bolzano thinks it important to separate these notions, although representations can include propositions as parts: think, for instance, the representation of a conjecture that God is omnipotent.
Bolzano admits that the notion of representation in itself is strange, but necessary for logic. Although representation in itself does not exist, it can have what he calls Gegenständlichkeit (objectivity), by which he means simply that the representation is connected to Gegenstand or an object. In addition to this connection with reality, Bolzano argues, representations in themselves are a necessary assumption, if we want to speak of constituents of propositions and truths in themselves. He admits the name is not perfect, since representations suggests something mental, but no better is available: best option would be concept (Begriff), but Bolzano notes that this term is often reserved for a subset of representations (representations that are not intuitions).
Bolzano points out that just like in case of representation, there really isn’t any satisfactory definition of representation. True, he has managed to describe representations as constituents of propositions, but he also considers this a mere external characteristic of representation, not its essence. Even worse in this sense is the description of representation as a material of thoughts, since this ambiguous term might in another sense refer to the objects of thought.
As difficult as defining representation in itself, Bolzano finds defining subjective representation. He has described it as an appearance of some object in a thinking mind, but here the word “appearance” is just another word for representation, so the definition is actually circular. Bolzano considers other suggested definitions, but rejects all of them. Subjective representation is not an image, except in a metaphorical sense, but then it could be applied to other mental phenomena, since even chest pain could be called a metaphorical image of a heart attack. Subjective representation is also not a symbol referring to some thought or concept, and it also not a sign in the sense that smoke is a sign of fire.
Bolzano still considers whether other philosophers had any inkling of the representations in themselves, but finds nothing certain, although some of them had noticed that the same concepts could be thought by different persons. Yet, he does not want to be harsh with them, since even the easier notion of propositions in themselves had escaped them. Indeed, Bolzano says, representations have often meant something completely different, with the meaning varying from one author to another, and each of these uses have probably delineated important notions in other disciples. Yet, he concludes, the notion of non-propositional parts of propositions is important for logic, and since no better nomenclature is available, he will call these representations.
