Overview
The Problem Situation
The Tentative Solution
Critical Discussion
Correspondence
Content Logic
Class Logic
Logic of Arithmetic
Logic of Physics
Conclusion
Footnotes
Bibliography
This section first outlines a general cosmological theory, applies it to a few seemingly different areas, and, finally, presents the solution to the problem situation posed in the previous section.
The cosmological theory, or “situational potentialism” for short, is a modification of Karl Popper’s propensity interpretation of probability. 7 First, the modification is formulated and explained on the basis of an example following Popper’s explanation of the propensity interpretation, and then, the additional idea necessary to preserve the full range of consequences of the propensity interpretation is introduced. 8 In short, situational potentialism is as follows.
The cosmos changes constantly. These changes are realizing possibilities embedded in generating (background) situations. Realizing possibilities are not the only inhabitants of the cosmos; there are mere possibilities that do not realize themselves. However, only realizing possibilities creates and destroys them. In this sense, the cosmos is inherently creative. Background situations are but bundles of realizing possibilities that progress only slowly in comparison to the foreground changes.
Tossing a coin on a wooden table with a flat surface serves as a first example. There are two possibilities: heads or tails. These two possibilities are not properties of the coin; they are created by the (background) situation. The background changes slowly in comparison to the tossing of the coin. Even the shape and condition of the coin are a part of the situation and contribute to the set of possibilities created by it. The wooden table is, in itself, a realizing possibility. Although it changes slowly in comparison to the tossing of the coin and in comparison to the coin itself, it dissipates eventually.
Occasionally, changes in the background situation result in an altered set of possibilities. Carving slots into the surface of the table creates a new possibility. The coin might slip into one of these slots. On the other hand, if the wooden table were replaced by a steel table, the set of possibilities would remain the same. Thus, not all aspects of the background situation are relevant for a particular set of possibilities.
Situational potentialism is independent of more substantial theories of the physical world and can thus be combined with other theories to draw a more complete picture of the universe. The argument that there is nothing else but the void and indestructible atoms is one such theory. Even this material cosmos possesses an infinite number of possibilities to arrange its objects. A table with an ink pot, a fountain pen and sheets of paper on it is a simple model of this cosmos. The writing utensils can be arranged in different positions on the table. The flat surface and the shape of the objects create distinct possibilities, so that even in a material world, there are immaterial things: possibilities.
The main idea of the propensity interpretation of probability is the weight of possibilities to realize themselves, shown in stable relative frequencies of finite sequences upon repetition of the generating conditions. Propensities are properties of these conditions. 9 In its cosmological form, the propensity interpretation assumes that all possibilities have a tendency to realize themselves. 10
Situational potentialism seems to be a weakened version of the propensity interpretation because it abstains from assigning weights to all possibilities and assumes that possibilities without a tendency to realize themselves exist. This seemingly slight modification widens the range of situations it covers. The ink pot and the fountain pen have zero propensity to move other places on the table. Nonetheless, there are many different possible positions for the items on the table. When a philosopher is around new possibilities and propensities are created, existing propensities change. The propensity of the pen to end up in another position within a reasonable period of time jumps to, for example, one. The philosopher would not have been able to move the pen without a preexisting possibility, but he did not create the possible positions for the pen. The propensity of the pen to move to another position and the propensity of the philosopher to move the pen involve two different possibilities. The first possibility does not have a tendency to realize itself—its propensity is zero; but the second possibility is endowed with a tendency to realize itself, and its propensity is not zero.
On the other hand, situational potentialism preserves the situational aspect of the propensity interpretation of probability. It assumes that possibilities are not properties of the ink pot or fountain pen, but are created by the (relevant) situation. This assumption amounts to a change from a cosmos of objects to a cosmos of interacting events embedded in background situations. To fully analyze the interaction of realizing possibilities, a theory of causality is necessary. This essay does not discuss theories of causality or the propensity interpretation any further, but confines the discussion to situational potentialism to formulate the solution for the problem situation described above.
A further example illustrates the point made above. Consider a tiled floor and five wooden boards. Since the boards are not joined in the shape of a container, nothing can be stored in them—at least, not on a macroscopic level. The presence of nails and a hammer create the possibility of building a box. When a skilled person realizes this possibility, the new and enduring possibility is formed to store things in the box. The boards do not rearrange themselves and certainly do not fix themselves with nails. Nonetheless, the mere possibility exists, even if nobody is around to realize it ever.
A blank sheet of paper, a crayon and an artist form the next example. Before the first stroke, the possibilities of drawings on that paper are unlimited. With each and every stroke, the drawing becomes increasingly detailed; each step reduces possibilities because after a while and several strokes, for instance, a rooster or tiger appears on the paper. Beginning, for example, with a long curved stroke eliminates the chance for a ladybug, but leaves the possibility for a snake or worm. Each and every stroke is the realization of a possibility inherently found in the situation, and each and every stroke eliminates and creates possibilities that change the situation. The result, the finished drawing, creates a new set of possibilities. It might evoke astonishment in its viewers, or wonder. It might be recognized as the drawing of a tiger. The situations involving the wooden boards and the blank sheets of paper are very similar in light of situational potentialism, although the possibilities involved are quite different. The box is created by joining wooden boards. None of the boards offer the possibility of storage, but arranging them in a certain way creates a new possibility. The same holds true for the drawing. Every single stroke does not make the rooster or tiger. Several strokes arranged in a certain way, however, result in the drawing of an animal.
Situational potentialism in this rudimentary form, without a theory of causality, suffices to determine the relationship between sentences and contents. When sentences are concerned, naturally, words are involved. The roles of words and sentences are the same as the roles of the boards and the box and of the strokes and the drawing, respectively. Single words cannot provide the content, but arranged in a certain way, words form sentences that create new possibilities: contents. The main thesis is that sentences create possibilities and that contents are possibilities. More precisely, the whole relevant situation creates these possibilities and not just sentences by themselves. One important aspect of these situations is that words name objects in a constant way. Interpreting a word as the name of a different object changes the content of the sentence that includes the word. Whether sentences are spoken, signed or written is, on the other hand, not relevant to the content. All these presentations create the same content; but removing every other character from a printed version of a text probably destroys its content. As possibilities, contents are immaterial—in the sense explained above. Since they are bound to sentences, they are bound to sheets of paper; they are not part of anyone’s mind; they exist independently and are objective in this sense. Moreover, sentences do not designate contents. Words designate objects outside language, but this does not mean that sentences designate things too. Words can designate inner pictures of a person’s mind, but sentences built with these words create contents independent of minds.
At this point, the usefulness of the modification of the propensity interpretation of probability becomes clear. Situational potentialism assumes the existence of mere possibilities. Contents are not propensities but mere possibilities. Reading a book and picturing its content leave the content of the book untouched, just like crossing a river over a bridge leaves the possibility of crossing the river untouched. Nonetheless, the physical properties of a book play a role in the process of reading it. Analyzing this process requires a theory of causality and a full understanding of the mind-body problem. These issues are not discussed here.
Not all the possibilities attached to sentences are objective contents. Every spoken, signed or written utterance can evoke emotions. One consequent of the main thesis is that these emotions are not part of the objective content. These subjective aspects are real, but different from the content, and they must be described in psychological terms. The same holds true for the wooden box. Geometrical terms describe its shape; physical terms describe its stability. What kinds of terms are suitable to describe contents?
The final example leads the way to an answer. Consider the following two texts.
“Once upon a time, there was a young girl. Because she wore a hood, everybody called her ‘Little Riding Hood.’”
“Once upon a time, there was a young girl. Because she wore a red hood, everybody called her ‘Little Red Riding Hood.’”
The second text provides more details. In logical terms, the content of the second text excludes more. The content of the first version is compatible with mutually exclusive contents attributing any color to the hood. A subjective analysis misses this point because different readers create different pictures in their minds. Some readers may even be unaware of the difference between the two texts altogether. Therefore, logical terms must describe objective contents of sentences, and logic becomes the theory of contents, their logical forms, levels, and relations.
Ultimately, words do not create contents, nor do sentences designate things; but words designate things and sentences create contents. As sequences of characters, words are physical objects and therefore endowed with possibilities. The most important possibility is forming clusters that create new possibilities: contents. These contents are either true or false. Sentences do not have this property. Sentences are sequences of graphic symbols imprinted on sheets of paper. They provide the material substrate for contents. Logic is the theory of contents.
From now on, this essay uses single quotation marks to create names of contents and double quotation marks to create names of sentences. Although both types of quotation marks frame individual sentences, there is a significant difference between them. Double quotation marks create names of individual sentences or classes of similar sentences, 11 regardless of their contexts; single quotation marks create names of contents formed by the surrounding situation. This notation depends on the understanding that the relevant conditions outside the sentence do not change. Only in this case, the denoted content does not change. Some misunderstandings can be attributed to changes to relevant conditions. For example, when the assignment between expressions and denoted objects is changed, then singly quoted sentences denote different contents. This discussion will continue in later sections. A few examples shall introduce this notation.
“Socrates was the wisest man in Greece” is an English sentence. It is grammatically correct. “Sokrates war der weiseste Mann in Griechenland” is a German sentence. ‘Socrates was the wisest man in Greece’ is true. “Socrates was the wisest man in Greece” and “Sokrates war der weiseste Mann in Griechenland” create the same content. ‘Socrates was the wisest man in Greece’ and ‘Sokrates war der weiseste Mann in Griechenland’ are identical.
The remaining sections discuss this tentative solution. Leading questions are: Does the introduction of variable names of contents make variable use in logic and mathematic consistent with the rule that constant names substitute variable names? Can a philosophy of content logic adapt Tarski’s semantic theory of truth without losing its insights into the hierarchical structure of language? These are not the only problems relevant to the critical discussion.
Overview
The Problem Situation
The Tentative Solution
Critical Discussion
Correspondence
Content Logic
Class Logic
Logic of Arithmetic
Logic of Physics
Conclusion
Footnotes
Bibliography
[Download a pdf version: Contents, Sentences, and Possibilities]