THE DIFFERENCE BETWEEN A SYMBOLIC ASSERTION AND A SPACE-TIME EVENT
If one examines the characteristic moments of the scientific method, one will discover that they are basically assertions. Even if one happens to be an operationalist and maintains that the business of science is defining the physical operations by which concepts are arrived at and properties defined, the fact remains that the terminus ad quem of the operationalist method is the scientific formula or assertion. Indeed, the operationalist cannot even express his operationalism without using assertions.
The three characteristic assertions of the scientific method are:
(1) The Naming or Classificatory Assertion. This form of the assertion is a pointing at and a naming, or, in semiotical language, an indexical sign plus a symbol.
This is grass is such an assertion. The assertion could be made simply by pointing at the grass and uttering aloud the symbol grass. So also is the scientific classification: Certain plants which bear functional similarities toward each other because of a common phylogenetic origin we agree to designate by the symbol Graminae. The latter is a scientific and definitory abstraction. But the former is also an abstraction, though of a much more primitive or “concrete” sort. Both statements assert that that something over there is one of these. The simplest act of naming and the under-standing of the act by another is the assertion and grasping of the assertion that there is a family of plants with bladelike leaves and hollow jointed stems and that that one there is one of them. The two types of classification overlap but do not coincide. The primitive classification This is grass may include grassy-looking plants which are not related phylogenetically to the family Graminae. The scientific classification Graminae, on the other hand, inCludes bamboo, which to the layman is not at all “grassy.”
(2) The Basic Sentence. This sentence asserts a scientific observation or “fact.” It can be verified by the observation or experiment of another.
Water boils at 100 degrees centigrade at 760 mm atmospheric pressure. The human heart has four major chambers. The Trobriand Islanders are matrilineal.
The form is S is P, in which S is the subject designated by the naming sentence above, P is the predicate, property or quality, “is” is the verb which specifies the nature of the relation between S and P and also asserts that it holds.
(3) A scientific law.
Bodies attract each other in direct proportion to the product of their masses and in inverse proportion to the square of the distance between them.
The glomerular filtrate of urine is a function of plasma osmotic pressure and blood pressure. Primitive tenues (k, t, p) become aspirates in Low German (e. g., English) and mediae in High German. (Grimm’s Law)
Such generalizations are of the form E = f (C), in which C represents a numerical value or a space-time configuration, E a subsequent value or configuration, f a determinate ratio of energy exchange, and “is” or “=” an assertion of identity between the two.
Each of these typically scientific statements is an assertion of sorts concerning space-time events. Even Grimm’s Law, which is about words, is not about the assertions of words but about the changes of consonantal sounds. Yet none of these statements is itself a space-time event. We can, if we like, study the energy exchanges which take place in a blind deaf-mute when he makes the discovery that this is grass. It was theoretically possible to do the same thing when Einstein conceived the relativity principle. We can observe the overt behavior of a physicist as he goes about setting up his apparatus and making measurements. But even if we had an exact knowledge of the colloidal brain events which occur in each case, these events can never be coterminous with the assertions This is grass and E = mc2. It is possible to say this, not because of our present knowledge of brain events, but because no space-time event, however intricate, no chemical or colloidal interaction, no configuration of field forces, can issue in an assertory event. As Cassirer put it, there is a gap between the responses of animals and the propositions of men which no amount of biological theorizing can bridge.
We can also make a chemical analysis of a written word or an acoustic analysis of a spoken word; we can study the science of phonetics, which traces regularities in the changes of speech sounds. But neither science will have anything to say, does not wish to have anything to say, about the assertion which these symbols convey.
In the first type of statement, the naming sentence, we may determine from an empirical standpoint that symbolization is qualitatively different from a sign-response sequence and that denotation is not a space-time relation but a semantical one.
In the next two types of assertions, S is P and E = f (C), we have two different kinds of identity asserted, one intentional and the other real.
S is P asserts what a thing is by dividing the thing from its property or definition and reuniting it in the sentence. This assertion of identity is not real but intentional.
E = f (C) asserts a real identity. It asserts that a numerical value or a physical configuration E is nothing more or less than the numerical value or physical configuration C which has undergone a determinate energy transformation or mathematical function f. The force of gravity is precisely identical with the product of the masses involved multiplied by a constant G.
I shall refer in what follows to all linguistic assertions by the form S is P, not because I am presupposing a realistic metaphysic, but because it is a convenient way to designate a sentence. To summarize: Science characteristically issues in assertions. But that which science asserts is not itself an assertion but a space-time event. Science asserts that matter is in interaction; that there are energy exchanges, that organisms respond to an environment, etc. But the assertion itself is a pairing of elements, a relation which is not a space-time event but a kind of identity asserted by an assertor.
Next week: CULTURE AS A SUBJECT OF THE SCIENTIFIC METHOD