Bernard Bolzano: Study of science – Intuitions and concepts

Still going on with the study of the characteristics of representations, Bolzano notes that most of the representations relate to an object and underlines that this relating is different from a proposition, where a representation or a characteristic is related to an object – this is asserting something of the object. Representations with objects or objective representations, he continues, have an extension or a sphere of objects to which they relate to, and these objects and any incomplete collection of them is said to belong to this extension. Bolzano notes that the set of these objects has a magnitude, which can be infinite. The existence and magnitude of the extension can depend on contingent matters, like the representation of the sons of Chingish Khan, but Bolzano thinks it is permanent – even a representation like “all the people living now”, since the phrase “now” fixes this particular representation to this particular point in time. Some representations, he continues , have no objects, such as nothing, round square of golden mountain. Some representations, which Bolzano calls singular representations, relate only to a single object (for instance, universe), while others relate to a finite number of objects (e.g. all the propositions in Euclid’s book of geometry).

Bolzano points out that a representation can have more parts than required for referring to its objects, for instance, a representation of a triangle that is both equiangular and equilateral. An interesting case he considers are the representations of the form “this A”: the A is superfluous, because “this” already refers to the object in question perfectly and the determining A is merely used to simplify the identification of “this” for humans. Although the notion of superfluous parts has been first defined only for representations with objects, Bolzano finds a clever way to extend it to representations with no objects, like round and angular quadrangle: we can say that some parts in such a representation are superfluous if always when we change some other parts of it and the result refers to an object, the parts in question are superfluous in the original sense.

Bolzano notes that complex representations can be contradictory in the sense that they are of the form “A that is also P”, where A implies M and P implies not-M (e.g. triangle with four sides). Such contradictory representations, he continues, have sometimes been called empty, impossible or imaginary, but these names have some room for confusion. Firstly, Bolzano explains, emptiness in this case does not refer to the content of the representation, but to its empty extension – it has no objects. Then again, he notes that there are in this sense empty representations that are not contradictory (just think of a golden mountain).

Secondly, representations as such cannot be necessary, actual or possible, since they do not exist, and not even impossible in the sense that they would otherwise be able to exist, but something hinders their existence. Such modal terms, Bolzano thinks, concern our capacity to find objects for the representations, but again, some non-contradictory representations are impossible in this sense.

Finally, he concludes, representations in themselves are never just imaginations, but we can say that contradictory representations are imaginary, because their objects can never be found outside our thoughts in existence. All other representations can then be called real, but this does not mean they have objects, because some non-contradictory representations do not have them. In any case, only complex representations can be imaginary, which implies that simple representations are always real. Furthermore, Bolzano states, imaginary representations can be parts of real representations, like in the case of a representation of a mathematician who first thought of the square root of –1.

Bolzano presents the intriguing question whether simple representations can ever be singular. At first sight, it seems apparent that limiting a representation down to one individual requires always adding new determinations. Yet, Bolzano answers, we do have simple and singular subjective representations, when we attend to immediate sensations produced by external objects for instance, for instance, when seeing a rose, we say “this is red”, “this” is a simple, singular representation. Corresponding to these subjective representations, there must be corresponding simple and individual representations in themselves, which Bolzano calls intuitions.

Another important subtype of representations, beside intuitions, Bolzano thinks, is formed by concepts. Concepts, he defines, are representations that are not intuitions and have no intuition as their part: examples include something, which refers to an infinity of objects and has no intuition as its part, because it has no parts, and representation of God, which does refer to one object, but none of its parts is an intuition. Clearly we need a third category of mixed representation, which Bolzano explains as complex representations with intuitions as their parts, for instance, rose that spreads this smell. Depending on the prominent part of a mixed representation, it can be either a mixed intuition (e.g. this that is a colour) or a mixed concept (truths contained in this book).

Examples of intuitions we know of, Bolzano notes, belong to the realm of actuality as certain changes in our soul. He adds that these are probably the only intuitions we humans can know, since the only simple representations of an individual object we are aware of seem to be those caused by something actual. We cannot intuit all actual objects, Bolzano states, but for each actual or non-actual object that we have an exclusive representation of we can form a representation with intuition as a part, by relating the original intuition to other things that we can intuit (e.g. seed of this flower). According to Bolzano, with few exceptions, such as God and the universe, we cannot construct from pure concepts a representation that would pick out exclusively one object. Even if we managed to pick a set of characteristics that seem to individuate a finite substance, in the infinity of things there might be lurking another one with the very same set.

Bolzano points out that we can never have the same intuition twice, because the object of an intuition is a certain change outside or inside us causing this intuition and this exact thing cannot occur twice, although there can be representations similar to it. In the same manner, no one can have the same intuitions as I do and intuitions cannot be transmitted, unlike pure concepts. True, Bolzano admits, we do say that we transmit intuitions, but actually we just tell others of their characteristics, for example, by indicating that they are caused by a certain external object.

If interactions with a certain object are frequent, we may even give it a name, which is then a mixed representation (“object that has been the cause of such and such intuitions”). This is true, Bolzano notes, even of names of long gone objects (“person who lived in ancient Athens and was called Socrates”). In any case, he underlines, names are reserved only for some objects, and usually we just use words like “now”, “then”, “here”, “this” etc. and sometimes add some species for explanation (e.g. “this rose”). The last, which is a designation of a mixed representation, Bolzano muses, could be used in scientific treatises as indicating pure intuitions that otherwise are difficult to express.

Bolzano notes that every language has words that are used sometimes for pure concepts, sometimes for mixed representations, especially when speaking of natural objects. He gives as an example the concept of a human being. By human, Bolzano says, we can mean any reasoning creature (pure concept), whether they live on the Moon or Earth, but often we restrict the concept of humans to reasoning creatures on Earth (mixed representation, due to the reference on Earth). We can also find cases with a converse relation, Bolzano thinks and explains that by gold we have originally meant substance connected to certain intuitions, but we can purify this into a pure concept by describing it as substance causing certain changes in humans etc.

Bolzano considers the question whether the names he has picked for intuitions and concepts are suitable. His answer is that intuitions usually mean singular subjective representations, and that he has just extended the concept to objective representations. Then again, Bolzano notes that the term “concept” has often referred to objective representations, except that concepts have always been taken as either consisting of multiple parts or as having an extension with multiple objects. All in all, Bolzano is not very satisfied with the way intuitions and concepts have been treated by his predecessors, who generally recognised them as subjective representations.

All intuitions are simple and singular, Bolzano notes, but there’s more variety with concepts. Evidently there are complex concepts, but there must be also simple concepts, because all complex representations need at least the help of the simple representation “and”, which isn’t an intuition (other similar notions include such terms as have, should etc.) Some concepts have an infinite extension (e.g. created substance), some a finite extension (e.g. one of the cardinal virtues), some only a single object (e.g. community of all morally good entities) and some none (e.g. means for undoing past).

Bolzano considers also a question, important from the time of Kant, whether time and space are intuitions or concepts. Bolzano notes that there are actually many temporal and spatial representations, and for some the question has an obvious answer: general notions like moment in general and point in general cannot be intuitions, because they have many objects – thus, they must be concepts.

This still leaves unanswered the case of temporal and spatial representations with only one object, such as the whole infinite time or space and this particular point in time or space. Bolzano argues that none of these can be an intuition, because they do not have any existing objects: space and time have no effect on anything, and if they seem to, like when we say that time heals wounds, we actually mean that some object has this effect. Indeed, he concludes, they must be pure intuitions, since none of their parts is an intuition.

Although not really a task of logic, Bolzano quickly defines what space and time are. All existing things, except perhaps God, he says, are at a certain time. Thus, we could define time as the determination in something actual that must appear as a condition, in order that we can truly ascribe to it any characteristics. A similar definition can be given of space or a sum of all places, Bolzano suggests. All actual objects act and are acted upon, and the characteristics of these interactions depend on the forces of the objects and their places. Bolzano can then define the place of an actual thing as a determination that must be added to the forces of the thing, in order to comprehend the changes that they generate in one another.

James Mill, Analysis of the Phenomena of the Human Mind 2

Second volume of Mill’s work on philosophy of mind clearly divides into two different parts, and I shall treat the latter part in a writing of its own. The first part continues the discussion Mill started in the first volume, that is, the analysis of common concepts pertaining to human cognition.

The first of these concepts are relational terms. You might remember from my previous post that Mill appeared to accept only monadic predication, which seems, of course, problematic for understanding relations. Mill’s solution is to suggest that relational terms like “parent-child” are actually names for a single phenomenon, consisting of two things. The different names just emphasise different aspects of this same totality. Connected to this notion is Mill’s idea that difference and opposition is necessary at least for such conscious entities as us - we do not really sense or think anything, if there is no change in our sensations and ideas. Together these ideas suggest surprisingly close tendencies with broadly Hegelian philosophers, who view the world as an necessarily interconnected system of oppositions.

Mill goes into great details classifying the various possible relations: difference and sameness of sensations, sensations as preceding one another, spatial relations of objects, temporal relations of objects, quantitative equality and inequality of objects, qualitative likeness or unlikeness of objects, same or different composition of ideas and ideas as preceding one another. A clear fault in Mill’s schema is the ignorance of relations with more than two relata. The closest Mill comes to discussing them comes with spatial relations, as he admits that even the idea of position of an object involves relations to all other objects. Still, even here Mill tries to simplify matters and concentrates on juxtaposition of two objects and such pairs like high and low or front and back.

If we inspect Mill's account of spatial relations in more detail, we find him, in a manner reminiscent of Fichte, reducing the genesis of our experience of space into muscular exertions, by which we move ourselves or things around us. In another sense, Mill’s notion of space reminds one of Leibniz, because just like him, Mill says that space is nothing but an abstraction from all the concrete positions and spatial relations between things. While Kant would object that surely space is prior to positions in it, he might approve Mill’s admission of a subjective element in our notion of space - we always associate a place with a further place, thus making our notion of space infinite.

A further peculiar element in Mill’s notion of space is that when we think of empty space, he insists, we think of something positioned in that space and then the absence of this something. This is a feature of Mill’s general theory of privative statements - he insists that thinking of absence of something, we think of both that thing and its absence (e.g., when thinking of darkness, we think of light and its absence). In case of space, this would mean that by empty space, we always mean space empty of something. Indeed, he confirms, because our experience of space is intrinsically related to the idea of something resisting our efforts, we cannot think of any space empty of everything.

Mills account of time is similar enough to his account of space that we do not have to deal with it in great detail - like space is for Mill just an abstraction of all positions, time is nothing more than just an abstraction from all successions. Reminiscent of Kantian tradition, Mill connects numbers also with successions. In other words, he points out that although numbers are used to count the greatness of synchronously existing objects, the act of counting happens through some successive operation.

Mill also investigates the notion of personal identity, especially over time, and reflection. His basic solution to this conundrum is to point out that personal identity is just a special case of any identity. Identity as such, say, of other persons, we come to know by seeing a person and remembering that we saw her earlier. Similarly, Mill says, we are always conscious of ourselves, remember being conscious of ourselves and hear testimonies of others concerning us at times, which we don’t remember.

Mill’s explanation seems flawed in many ways. Firstly, one might point out that he hasn’t ever really explained what it means of being conscious of oneself, because saying that consciousness in general is just a general name for sensations and ideas explains nothing about self-consciousness - what are we conscious about when we conscious of ourselves? Secondly, Mill’s explanation would at most tell what evidence we use to justify our assertions of self-, or indeed, any identity, but not what it means that something is identical with itself. Finally, while it is undoubtedly obvious that our assertions and experiences of self-identity are particular examples of assertions and experiences of identity, one might wonder, in the manner of Fichte, whether e.g. our experience of self-identity underlies our experience of all other identities (that is, whether we must be able to identify ourselves, before being able to identify anything else).