Etapas de la Inducción de Personal

Imagine that an actual situation of the world, say the fact that this red apple is on this brown

table, is represented in three different ways: by means of a three-dimensional, grey clay model

where a piece of clay in the shape of the apple is sitting on top of a piece of clay in the shape of the table; by means of a two-dimensional, red and brown painting, where the apple is drawn in red on top of a table drawn in brown; and by means of a proposition written in black ink on white two-dimensional paper (e.g. ‘This red apple is on this brown table.’).

The depicted fact this red apple is on this brown table decomposes into a number of coloured points arranged in three-dimensional space at a particular time. These points ultimately decompose into a vast number of states of affairs made up of Tractarian objects. According to our Ontological Model, these states of affairs will each comply with the general form of states of affairs: a simple

property is instantiated at the point fixed by the combination o f three simple spatial locations,

at a simple point in time. The combination of these states of affairs will yield, on its own, the

redness of the apple and the brownness of the table, their three-dimensional shapes, the spatial relation of the apple to the table (i.e. ‘being on top of), etc.

Let us consider the analysis of the two iconic pictures of this fact: the grey clay model and the red and brown painting. Once this is done, it will be easier to understand how propositional pictures differ from iconic ones.

The clay model and the painting can be viewed in two ways. They can either be regarded as pictures of the fact that this red apple is on this brown table, that is as representational facts depicting another fact, or they can be regarded as non-representational complex objects in their own right. To view them in the latter way is to view them divorced from any possible representational role that can be ascribed to them. Now, the clay model and the painting will have different analyses depending on whether we are considering them as representational facts (i.e. as pictures) or as non-representational complex objects. For, when we analyse a picture into simple signs, we are not looking for the things we look for when we analyse a complex object into simple objects. In the former case, we aim at uncovering the simple signs designating the simple objects that ultimately constitute the depicted state of the world. In the latter case, we are trying to discover what the ultimate, simple constituents of the complex object are. In other words: in the former case we look for those items which cannot be further analysed without ceasing to act as the representatives for the objects making up the depicted state of the world; in contrast, in the latter we look for those items which cannot be further analysed without ceasing to be genuine Tractarian objects.

When the painting and the clay model are regarded as pictures, they will be ultimately analysed into a logical product of elementary pictures made up of simple signs. If these signs genuinely act as the representatives for the simple objects in the depicted fact, they will have to be regarded as simple names. If it seems strange to speak of an iconic picture ultimately decomposing into simple names, note that Wittgenstein himself suggests that this is the case:

A proposition possesses essential and accidental features.

Accidental features are those that result from the particular way in which the propositional sign is produced. Essential features are those w ithout which the proposition could not express its sense. (7 1 /’3.34)

same sense have in common.

And similarly, in general, what is essential in a symbol is what all symbols that

can serve the same purpose have in common. (TLP 3.341)

So one could say that the real name o f an object was what all symbols that signified it had in common. Thus, one by one, all kinds o f com position would prove to be unessential to a name. (T I f 3 3411)

If the simple signs into which a painting, a clay model and a proposition are ultimately analysed designate the same objects, as they would have to here (since all of these pictures represent the same fact), then these signs, whatever their appearance, will express the same names. Indeed, as pointed out before, there is, at the ultimate level of analysis, a one-to-one relation between simple names and simple objects. (More will be said on this issue below.)

Consider how this would work: the grey clay model, regarded as a picture of the fact that this red

apple is on this brown table, decomposes into grey clay points arranged into a particular three-

dimensional shape. Each of these points represents a point in the depicted fact. Imagine that a given grey clay point in the three-dimensional model (let us call this point designates a given red point made of apple stuff in the three-dimensional apple (let us call this A). According to our Ontological Model, A would be equivalent, in terms of analysis, to the logical product of the facts [redness is instantiated at the complex location in space fixed by three particular simple

spatial locations at this simple point in time ] and [the property of being made out o f apple stuff

is instantiated at the complex location in space fixed by these - i.e. the same - three simple

spatial locations at this simple point in time]. Thus, if in the clay model stands as a representative

of A in the apple, would have to be regarded as being equivalent to the logical product of the propositions: ‘the property of redness is instantiated at this complex location in space fixed by three particular simple spatial locations at this simple point in time’ and ‘the property of being made out of apple stuff is instantiated at the complex three-dimensional location in space fixed by these (i.e. the same) three simple spatial locations at this simple point in time’. This would have to be the case even though A^, when the clay model is regarded as a non-representational complex object, does not possess the properties of redness or of being made out o f apple stuff.

In other words, if A,„ genuinely stands for A in the depicted fact, then it would have to be regarded as equivalent to the logical product of these propositions, even though, when considered as a point in the non-representational clay model, it is grey, not red, and it is made of clay, not of apple stuff. In turn, given our Ontological Model, since ‘redness’ and ‘being made out of apple stuff are not simple names, the propositions containing them will have to be analysed further until we obtain a logical product of elementary propositions complying with the generalised form

‘a simple property is instantiated at the spatial location fixed by three coordinates at a simple point in time’.^ The coordinates and the names for the simple properties and simple points in time making up these elementary pictures would be the simple names revealed when the clay model, regarded as a picture, is fully analysed.

The same occurs in the case of the painting. The painting decomposes into a series of red and brown dots made out of oil paint and arranged on a two-dimensional canvas. Imagine that a particular red dot in the painting regarded as a picture (let’s call it ‘Ap’) represents point/I in the three-dimensional depicted fact (i.e. the point also represented by A^’), where A is made out of apple stuff and not of oil paint on canvas. Ap’ would have to be analysed into the logical product of the propositions 'the property of redness is instantiated at this complex location in space fixed by three particular simple spatial locations at this simple point in time’ and ‘the property of being made out of apple stuff is instantiated at the complex three-dimensional location in space fixed by these (i.e. the same) three simple spatial locations at this simple point in time’. This would again be the case, even though A, as a point in the non-representational object, is made of oil paint on a two-dimensional canvas, and not of apple stuff. From this point onwards, the analysis of ‘Ap’ would be the same as that of ‘\ ’. Hence, the clay grey model and the red and brown painting, when they are regarded as pictures of the same fact (e.g. of the fact that this red apple is

on this brown table) have the same ultimate analysis: they are both be analysable into the logical

product of the same elementary propositions made up of the same simple names. Given our Ontological Model, these elementary propositions would all be of the generalised form ‘a simple property is instantiated at the spatial locations fixed by three coordinates at a simple point in time’.

The deep level structures of these two pictures, as revealed by their complete analysis, is therefore the same, and this will be the case in spite of the fact that their structures as non-representational complex objects differ. Their deep level structure as pictures is given by the logical product of the elementary propositions revealed through their complete analysis.

The structures of the painting and of the clay model, when these are regarded as representational facts, differ, however, from the structures they have when they are regarded as non-representational

® As we saw before, it was Wittgenstein’s hope, when he wrote the Tractatus, that colour properties would ultimately be analysable into simple properties meeting the logical independence constraint.

complex objects in their own right (that is, in isolation from the way in which they can be used to represent the fact that this red apple is on this brown table, or any other possible situation of the world). For, when we analyse the painting and the clay model as non-representational complex objects, we do so with a view to uncovering the simple objects which ultimately constitute these complexes.

Let us use again the Ontological Model in order to illustrate this point. Consider the grey, clay model. The clay model decomposes into grey, clay points. Let us take point \ in the clay model.

is one of the grey, clay points making up the three-dimensionally shaped model. It is clearly not a simple object, since it is made of the material properties oigreyness and of clayness. In order to reach a full analysis of the clay model regarded as a non-representational complex object, we therefore need to analyse (and all other points belonging like it to the model), until we discover what its ultimate simple constituents are. Hence, will be shown by this analysis to be logically equivalent to a combination of states of affairs, which, according to our Ontological Model, will all comply with the generalised form: a simple property is instantiated at the spatial

location fixe d by three simple spatial locations at a simple point in time. The structure of the

clay model as a whole, when regarded as a non-representational fact, will therefore be given by the logical product of states of affairs whose simple objects will all combine according to this generalised form of states of affairs (given our Ontological Model). And the same would hold for the painting.

Note that the Tractarian objects ultimately making up the clay model will differ from those objects ultimately making up the painting. According to our Ontological Model, both the painting and the clay model ultimately decompose into simple spatial locations, simple points in time and simple properties. But the simple spatial locations making up the clay model differ from those making up the painting, since the clay model and the painting cannot be in the same place at the same time. Similarly, the simple spatial locations in the clay model are such as to produce, by combining with each other, a particular three-dimensional shape, whereas those in the painting combine with each other to produce a particular two-dimensional shape. The simple properties making up the clay model also differ from those making up the painting in that the former are such that their combination produces the properties of clayness and oigreyness, whereas the latter are such that their combination produces the properties of redness, brownness, being

As we saw above, the pictorial form of a picture is what is shared by the picture and the depicted state of the world which enables the former to have a structure which mirrors that of the latter in

the particular way it does. The three-dimensional, grey clay model, shares with the depicted fact

(i.e. with the fact that the red apple is on the brown table) its particular three-dimensional shape. It is because the points in the model are arranged three-dimensionally in a particular way, that the structure of the model mirrors that of the depicted fact. Hence, what allows this structure to represent that of the depicted fact in the particular way that it does, and what is shared by the clay model and the represented fact, is the fact (in a non-Tractarian sense) that the simple spatial locations that ultimately constitute them, though different (since the clay model and the fact cannot be in the same place at the same time) combine to produce three-dimensional shapes which resemble each other. It is because the clay model, regarded as a complex object in its own right, is made up of objects which combine to produce this particular three-dimensional shape, that the clay model depicts the fact that the red apple is on the brown table in the particular way that it does. The pictorial form of the clay model will therefore consist, at least in part, in the fact (in a non-Tractarian sense) that the objects that ultimately constitute it produce a particular three-dimensional shape.^’ In contrast, the two-dimensional, red and brown painting shares with the fact it depicts its red and brown colouring. It is partly because the painting is an arrangement of red and brown dots that its structure can mirror that of the depicted fact in the particular way that it does. The pictorial form of the painting will therefore consist, at least in part, of the fact that some of the objects that constitute it combine together to produce redness greenness,

just like some of the objects that make up the depicted fact.

To sum up: the structures of the painting and of the clay model regarded as non-representational complex objects differ from the structure they have as pictures of the fact that this red apple is on

this brown table. Although the painting and the clay model have different structures as complexes,

they have the same structure when they are regarded as pictures of this fact. What allows the structures of these pictures to mirror the structure of the fact they depict in the particular way

that they do is that the painting and the clay model are ultimately constituted by simple objects

which resemble and, at times, may even be identical with the simple objects constituting the depicted fact: the painting, like the depicted fact, is for instance, ultimately made up of simple properties capable of combining together to produce redness and brownness, whilst the clay

^ I say ‘at least in part’ because there will be other elements to the model’s pictorial form, such as the fact that the v coordinates of the points making up the clay apple will be larger than the y coordinates of the points making up in the clay table, reflecting the fact that the real apple is on top of the real table.

model, like the depicted fact, is ultimately made up of simple locations in space capable of combining together to produce a specific three-dimensional shape. This therefore constitutes, at least in part, their pictorial forms.

To be ultimately made up of constituents that resemble (or are identical with) the constituents of the depicted fact does not, however, suffice for a complex object to become a picture and thus to possess a pictorial form. Part of the reason why the painting and the clay model can be regarded as pictures is that their ultimate constituents designate the ultimate constituents of the depicted fact. In other words, it is partly by virtue of their pictorial relationships that non- representational complexes become representational pictures possessing a pictorial form and a structure which mirrors that of the depicted fact. Which is why, as was noted above, Wittgenstein’s comments on the pictorial relationship serve to expand on and qualify his remarks on pictorial form (see again TIP 2.15, TLP 2.151, TIP 2.1511, TIP 2.1512, IIP 2.15121, TIP 2.1513, TIP 2.1514, and TIP 2.1515, quoted above).

In contrast, the representational forms of the painting and of the clay model encapsulate the criteria for correct representation which belong to their particular mediums (TIP 2.173). I cannot, for instance, represent the fact that the red apple is on the brown table by painting a canvas in one colour all over, although I can represent this fact by painting a blue apple on top of a green table. Similarly, I cannot represent this fact by means of a piece of clay which has been extended and thinned out to become a two-dimensional sheet, although I can represent it by fashioning a piece of clay in the shape of a cone and putting it on top of a two-dimensional sheet of clay. That a monochrome painting and a two-dimensional clay model cannot represent this fact is determined by the rules for the depiction of possible states of the world which characterise the media of paintings and models.

Finally, consider the logical form of the painting and the clay model.

What any picture, of whatever form, must have in common with reality, in order to be able to depict it - correctly or incorrectly - in a n y w ay a t a ll, is logical form, i.e. the form o f reality. (JLP 2.18) [My italics]

Wittgenstein tells us in this entry that reality has a form, which is logical form, and that this logical