Bolzano begins his study of the characteristics of representations with a preliminary plan: he shall begin with characteristics common to all representations, then move to remarkable types of representations, first to general types and then to types specified by parts of representations. Starting with the characteristics common to all representations, he notes a couple of features that have surfaced in his discussions earlier. Firstly, Bolzano notes, representations in themselves do not actually exist: thoughts of representations do, but representations in themselves are not thoughts, but their content. Secondly, no representation in itself is either true or false. Bolzano admits that sometimes representations are called true or false, but thinks these cases are clearly derivative. For instance, sometimes we say that a representation is true, if we apply it to some object and want to indicate that this object fits with that representation, which is a proposition, the truth of which is actually in question. Furthermore, sometimes we call a representation true, if we want to suggest that there are in general objects that fit representation, and similarly another representation – say, a square circle – false, if no object fits that representation: Bolzano underlines that this is not the original sense of true and false.
Bolzano points out that many representations are constituted from parts that are also representations, just like our thoughts of these representations consist of parts. He makes the observation that in this case the representation is not a mere sum of its parts, because the way these parts are connected also affects it: for instance, a poor brother of a rich father is different from a poor father of a rich brother. Although Bolzano’s discussion about the parts of representations seems to hinge on what words are used to describe the representations, he notes that sometimes the verbal expression of a representation is deceptive. For example, we have a habit of making implicit restrictions of the words we use, for instance, when we speak of animals and mean specifically animals. For this reason we have often a need to use a term like “animal in general”, which does not mean that something would be added to the representation of animal, but only that we want to remove all possible implicit restrictions. Similarly, Bolzano thinks, words like “every” or “the” do not really add anything to a representation: “humans are mammals”, “every human is a mammal” and “the human is a mammal” all mean the same.
Bolzano discusses further the features of the parts of representations, such as the fact that the parts can of course have their own parts. This is especially clear in a case where the parts are not representations, but propositions, like the representation of a creature which lives on Earth – “which lives on Earth” is a proposition with its own parts. Bolzano points out that in some cases the parts of representations connect one another immediately like not and being in not-being, while in other cases, the connection of parts requires mediation of other parts, like in the case of the creature which lives on Earth, where the part “which” connects a representation and a proposition into a whole. Bolzano also notes that in some cases, like the now many times mentioned creature which lives on Earth, the parts have an intrinsic order, with “creature” being in a sense earlier than or prior to the other parts – he is adamant that this order is not temporal, since representations do not exist. He also emphasises that not all parts of a representation need to have such an order, when a representation could be called just a sum of its parts, like “red and round”, which is the same representation as “round and red”.
We have already met representations with the form “A that is x”. Bolzano notes the language sometimes hides deceptively this form: the memory of Julius Scaliger means the memory which Julius Scaliger had. Similarly, constructions like righteous person can be easily turned into this form (a person that is righteous), but Bolzano suggests being cautious at times: painted fish is not a fish which is painted, but a painting, which represents a fish. Furthermore, he notes, an expression of the form “this A” can in some contexts mean “this which is A”. but in other contexts just the A (these assertions are the assertions, which we are currently engaged with.
Another common form Bolzano mentions is that of “something that is A”. He calls such a representation concrete, while the A is then an abstract representation of characteristic. Bolzano also notes that some representations are neither abstract nor concrete, like something, nothing, this A and Socrates. Bolzano also warns the reader that verbal expressions do not always reveal what representation is concrete, for instance, when we speak of animals, we actually mean something that has animality. Sometimes the same word can in some contexts refer even to concrete and in others to abstract representation, for instance, virtue usually means characteristics, but sometimes something that is virtuous.
Bolzano moves on to define simple representations as such that have no parts. It is at first problematic, whether any representation is simple, but Bolzano is convinced that finitely complex representations must have simple representations as parts. He also suggests that infinite wholes, like space, must also have simple parts, such as points in space. While representations thus have a lower limit, Bolzano thinks they cannot have any upper limit: to any representation could be added more and more things, like new characteristics (is the creature that lives on Earth a plant or an animal?) or even propositions (e.g. the truth that earthly creatures exist).
Bolzano notes that philosophers have sometimes insisted that representations should correspond to their objects. He has difficulties in even understanding what this correspondence means. It cannot mean that the representation should have the same number of parts as its object, because there are representations without any objects. Even if we restricted the notion of correspondence to representations with objects, we would still face the difficulty that some representations have propositions as their parts. Bolzano suggests the emendation that in these cases it would be parts of the proposition that would have to also correspond to their object. Yet, he quickly discards this solution, because in a representation like “land that has no mountains”, the concept of mountains should not correspond to anything in the land, which should be a land with no mountains.
Another possible interpretation of the notion of correspondence is that the parts of representation should correspond to the characteristics of the corresponding object. Yet, Bolzano points out, there are parts of representations that are not characteristics of its object, such as the already familiar something and which. Furthermore, he adds, there are characteristics of objects that are not part of the corresponding representation, for instance, because many objects simply have characteristics that we are not aware of. Indeed, Bolzano adds, in some cases there can be two different representations that have the same object, but different content, such as the notions of equilateral and equiangular triangle. There are even, he thinks, objects with an infinite number of characteristics (say, an irrational number, expressed as an infinite sum), although we certainly cannot think of all of them.
Bolzano’s latest arguments seem suspect, because they concern not representations in themselves, but only our thoughts of representations. Yet, he emphasises, the same is true even of representations in themselves, since although e.g. all equilateral triangles are also equiangular, equiangularity is not a part of the representation of an equilateral triangle: it is certainly not a part of the representation of a triangle – since not all triangles are equiangular – and not even a part of the representation of equilateral – this is obvious, once you think of an equilateral quadrangle or parallelogram that is not equiangular.
Bolzano goes on to give further arguments for his position, now from a different angle. Simplicity, he says, is a characteristic of a simple representation, but it is clearly not part of this representation, since simple representations should have no parts. Furthermore, Bolzano adds, simple representations usually represent something and thus have the characteristic of being something, but this being something is again not their part for the same reason that they are simple and thus have no parts. Finally, if we have several representations, then the two representations differ, but this difference is not part of either representation.
Bolzano is again a pioneer on the issue, as most earlier logicians, in Bolzano’s opinion, apparently had very different ideas on what composition of representations means. Most of them had ascribed themselves to the opinion that parts of a representation form like a sum, forgetting parts like “something”, “which” and “is”. Furthermore they had often confused parts of a representation, on the one hand, with parts of its object, and on the other hand, with characteristics of representations that are not its parts. Indeed, Bolzano observes, these differences are what underlies the Kantian notions of analytical and synthetical judgement – analytical judgement merely points out some constituent parts of the subject representation, while synthetical judgement moves on from this to further characteristics of the subject – although Kant and his followers did not properly understand the difference.
Ei kommentteja:
Lähetä kommentti