La falsedad u omisión de datos: la necesidad de oír al interesado

We have mentioned above that it is possible to talk about scientific knowledge with- out the use of the unclear terms ‘theoretical’ and ‘nontheoretical’. Though it is possible to use the same terminology and make the sense clearer by redefining the terms, it is always a better approach to name them differently, for it would cause least confusion. Another reason why we think that the term ‘theory’ makes epistemological analysis difficult is because in most uses of the term it refers to a very large body of scientific knowledge. For reasons already explicated we will defend here a view of scientific knowledge which is seen as a collection of a large number of independent structures, each with its corresponding domain of application.

We therefore propose a distinction between structure-dependent and structure-independent

concepts to replace the traditional distinction between theoretical and nontheoretical con- cepts. The distinction that we are proposing here is not the same as the observation-theory dichotomy, because, on the basis of the distinction being proposed, certain notions which we will regard theoretical may be observational according to the older dichotomy, and vice versa. In order to bring out the distinction we shall compare the structural features and certain applications of natural numbers and integers. Consider a situation of loss and profit in a monetary transaction. In order to know whether a person incurred a loss/profit of some money in a transaction, we need to relate (compare) one state-of-affairs with another. Since we can make sense of the meaning of being in a state of loss/profit/balance only in relation to another state-of-affairs or situation we can say that the meaning of some terms,

such as ‘loss’/‘profit’ gets generated only within a relationship. We can call the form of that

relationship a structure, and the terms that find their meaning in relation to the structure

can be called structure-dependent.

164 Chapter 6. Inversion

them at a bank counter. Each time we count we count them directly, and quite independently of other states-of-affairs. In this case the amount counted will not have any ‘tag’ attached, except possibly the units of currency, unlike the above case, where special mention is always made of whether the amount is to be regarded as loss or profit or balance. Since the de-

scription of the latter situation does not involve any other situations, we call this structure

independent.

In the former case the three different possible situations can be described in terms of positive, negative or zero situations, depending on whether a person is in profit, loss, or balance. This should be the nature of the state-of-affairs to apply a system of integers

because there is a clearisomorphism between the three possible states and the three ‘kinds’

of integers.

It is important to note that when a person says he is in a ‘zero’ state of economy in the former case, he does not mean that he has no money at all with him. Rather he is referring to a no loss and no profit situation (or neither-nor-situation). So ‘0’ when used in

this case has a different meaning from ‘0’ when used to refer to an empty purse. The two

meanings of ‘0’ mentioned are incommensurable, for they are entirely different measures.

Thus while counting currency notes at the bank counter, we don’t make use of negative numbers, nor do we use positive numbers, we use numbers pure and simple. This therefore is a state-of-affairs that needs natural numbers. When integers and natural numbers are used in entirely different situations, how can we say that integers are ‘superior’ to natural numbers? For a mathematician whose main concern is to solve algebraic equations, to be in possession of integers, rationals, reals, etc., is naturally preferable.

Are the operations involved in the two cases the same? No, because in the former

case where we need to state either loss or profit, somecalculation is necessary, while in the

latter case we engage in only simple counting. Isn’t calculating different in nature from

counting? Counting may be involved in calculating, but calculating involves more than counting. Calculation is structure-dependent, while counting is not.

Doesn’t counting involve any structure? After all the series of natural numbers also has a structural form. But the ‘linear’ order of natural numbers and denomination of currency are presupposed in both the cases. Since what is common to the two situations does not enter into consideration when we make comparison, the stated distinction is independent of these other situations. Thus the crucial point that determines the distinction is whether the structure that is involved is a pattern suggesting any situational variance or not. We will see below that proportionality relations that scientists often assert between varying parameters

are structure-dependent in this sense. Since natural science, in the state in which it is today, is inconceivable without proportionalities, this distinction is crucial for bringing out its essence. Another example may make the intended distinction clearer. When we apply color concepts to describe objects, each application of a kind of color to a state-of-affairs is inde- pendent of the other, because each color forms a separate category. Different color concepts generally do not possess any structural relationship with one another. We can say that our

knowledge of colors at this stage isamorphous, in the sense that the place of different colors

in that abstract class of all colors is not in relation to any other colors. However, when we start understanding some relationship between colors, such as when the three primary colors are seen as giving rise to the rest of them, our knowledge enters into structural form. This structure has an order that can lead to what can be called ‘the chemistry of colors’, and is still not ordered in a manner that can suggest any mathematical order.

On the other hand when a scientist says that an object is emitting a radiation of a particular frequency, our knowledge of that object’s radiation property is structure- dependent, because it presupposes the structure of a wave with a specific frequency, wave- length, amplitude, and velocity of propagation. Here in the specific use of the term ‘frequency’ its meaning is not independent of the other properties a wave would have. This structure de- pendence is usually formulated in the form of a mathematical equation because the structure is a relationship that exists between other parameters of a light wave.

Though we might say that emitting a specific frequency by an object means it has a specific color, this ‘equation’ or ‘reduction’ is misleading just as different uses of ‘0’. Once we understand the coextensional relationship between a color concept and a particular frequency, there occurs a transformation in our knowledge of what a color is. This is similar to the kind of transformation that took place in the case of numbers. Though we continue using the same symbols they do not refer to the same object. In ordinary usage color concepts are used to describe objects, while in the case of scientific usage though such a description is possible, the

uniqueness consists in the ability to describe the object color. That is to say that different

kinds of radiation distinguished are different independent objects that scientists talk about. In this sense the objects of scientific inquiry can be stated to be qualities. The process of transforming a quality into an object of study is essentially what is involved in making a

quality measurable.8 _{Since the knowledge of light in terms of frequency, wavelength etc., is}

based on proportions (see _§6.10 page 195), while the notion of identity employed in the case

of colors is of the type-token kind (see _§6.5 for distinction of types of identities, page 174) no

8

This is what, we think, is meant inhypostasizing qualities as explained by E. Meyerson, E. Cassirer and recently by E. Zahar. See§6.7 below.

166 Chapter 6. Inversion

identity of the notions can be claimed. In a similar manner the common man’s usage of the term ‘massive’ is different from the scientist’s usage of the term ‘mass’.

The nature of the distinction that we are proposing is more or less absolute,unlike

the distinction between theoretical and non-theoretical functions proposed by Sneed and

Stegm¨uller, which is relative. As already stated we think that all scientific knowledge is

structure-dependent, while commonsense knowledge is structure-independent in the relative sense (because commonsense knowledge is not free of abstractions though free of scientific abstractions). Since we see a possibility of demarcating scientific structures from non-scientific structures on the basis of inversion, we think that the dichotomy being proposed should ultimately enlighten us on the nature of scientific and non-scientific knowledge. The kind

of relativization as proposed by Sneed and Stegm¨uller would help us in understanding the

distinctions within the body of scientific knowledge, and cannot help us to distinguish science from non-science. This is because their definition of a scientific theory does not answer the question: What character is in the structure of a theory as a function of which it can

be said to be a scientific structure? We propose that inversion is that character which

differentiates scientific structures from non-scientific structures. This is our specific criterion

of demarcation.

In the sections that follow, we introduce the sense in which inversion becomes an es- sential character of scientific knowledge. In the section that follows we shall contrast negation with inversion in an attempt to demonstrate that inversion is as fundamental as negation.