Overview Potentialism Examples Conclusion Footnotes Bibliography
The following examples shall illustrate the above philosophical theory. The first example is a row of n dominoes. The arrangement makes sure that all n dominoes will topple over when the first one falls. The cause and effect theory of causality describes each fall as the effect of the previous fall and the cause of the subsequent fall. The sequence of events forms, according to this theory, a causal chain with the supportive cause and effect relation as a linking element.
In order to describe the domino effect in terms of potentialism, more substantial ideas are necessary. The fall of the dominoes is prevented by the position of their centers of gravity. It is positioned between the edges of the blocks. The gravity of the earth will pull them down as soon as this condition is eliminated. The fall of the neighbor does not knock down the next block; it changes the position of its center of gravity. Once the center of gravity has reached a certain position on the x-axis the fall is set in motion.
The energy picture of the domino effect is interesting because it is similar to certain chemical reactions that need a specific amount of activation energy and then carry on without further intervention from outside the system. Tipping a domino block lifts up its center of gravity and thus injects energy into the system. This energy is passed on from falling domino to falling domino. The fall of each domino as a realizing possibility does not cause the fall of the next block but it simply removes the inhibiting condition. It rolls back the inhibitor. Then, gravity pulls down the block. This analysis shows how potentialism simulates the cause and effect theory of causality. It achieves this by introducing an additional event. This event inhibits the effect; the former cause rolls back the inhibitor. The cause and effect relation between events can thus be analyzed in terms of potentialism.
The next example consists of an apple hanging down from the ceiling by a thread. The thread is cut by a pair of scissors. Clearly, the apple falls down. As long as the thread was intact, it prevented the apple's fall. Cutting the thread removes this obstacle and the apple falls.
Within the cause and effect theory there is another way to look at the above example. The cause of the apple's fall is the force between the earth and the apple. Generally, forces cause effects.
Can potentialism counter this critical argument? The important question is whether the force, in fact all forces, actually encourage change. Isaac Newton assumed that forces change the way mass objects move. His lex secunda postulates that objects remain in rectilinear uniform motion unless a force changes this. To counter the above argument, potentialism must interpret this force as an inhibitory effect of one mass object onto another.
The next two examples consist of random processes. The critical question is whether potentialism can explain the link between causality and randomness and, more specifically, whether increasing propensities in changing situations are due to encouraging causal influences. The first example is a three sided die that is tossed twice. The constant background conditions or events are such that three distinct possibilities exist. The propensity for each outcome is 1/3. “H,” “S,” and “T” are names for the three possible outcomes of the first throw and “HH,” “HS,” etc. are names of the possible outcomes after the second throw. The propensity of HH before the first throw is 1/9. If the first throw exhibits H, HH's propensity becomes 1/3. It has tripled. Does this warrant a theory of the causal connection as support?
The following interpretation of this example is in accordance with potentialism. The relative probability of a with regard to b measures the inhibitory influence of b on a. A measure of 1 says that a is not at all inhibited by b, but that a's complement is completely excluded. The relevant theorem of the calculus is : p(a, b) + p(ā, b) = 1. It follows: if p(a, b) = 0 then p(ā, b) = 1. A relative probability of 0 says that a is completely excluded and ā not at all. It is important to notice that the relative probability measures the inhibitory influence of possibilities on each other and not the propensity of a if b has happened. What about relative probabilities between zero and one? If p(a, b) = ½, then p(ā, b) = ½. Both a and its complement ā are inhibited with the same measure. If p(a, b) = ¾ then b inhibits a only slightly. The measure of inhibition is 1 – p(a, b). With p(a, b) = ¾ it is 1 - ¾ = ¼.
To sum up, a high relative probability conveys that only a weak inhibition is exerted onto a possibility and a strong inhibitory influence onto the complement. The increasing propensity of HH is due to inhibitory effects on its complement and not due to encouraging causal effects on itself.
Absolute probabilities measure propensities; relative probabilities measure inhibitory effects. p(HH) = 1/9. p(H) = 1/3. p(HH, H) = 1/3. H excludes a number of possibilities: p(S, H) = p(T, H) = p(SH, H) = p(ST, H) = 0, etc. p(HH) equals 1/3 if H happens. It equals 1/9 if nothing has happened. If H happens, several propensities are reduced to zero. The sum of the propensities excluded by H equals 6/9. The propensities of HH, HS, and HT increase each by 2/9 if H happens. This increase, it seems, is fed by the exclusion of formerly non-zero propensities. Specifically, p(H) equals one because all its alternatives have been reduced to zero. The following calculation determines p(HH). 1/3 = p(HH, H) = p(HHH) / p(H) = p(HHH) = p(HH). This deduction infers p(HH) from relative and absolute probabilities. Here, HHH is not the possibility that H occurs three times in a row. It is the possibility that H occurs in the first throw and HH in the second. Since p(H) = 1, p(HHH) = p(HH). The inhibitory effects of H on HH, HS, and HT are equal. Therefore, HH's, HS's, and HT's propensities are identical if H happens. Generally, inhibitory effects determine propensities.
To conclude, examples of increasing propensities under changing conditions do not refute or undermine the theory of causality as inhibition. Increasing propensities are, according to this theory, due to the elimination of competing possibilities. The possibilities left behind have, thus, higher propensity values.
The final example makes the descriptive means more realistic by introducing degrees of realization. It comprises n structures, named “towers” or “stacks.” Change in this model is the movement of blocks from one tower to an adjacent one. Each tower has an inhibitory effect on its neighbors depending on its degree of realization. This degree is simply the number of blocks on the stack or tower. With an increasing degree of realization the inhibitory effect of a tower on its neighbors grows stronger and, therefore, the propensities of those neighbors to unload blocks onto an already high tower decreases. In other words, a high tower repels blocks of adjacent towers. The stronger inhibition leads to a lower degree of realization of the inhibiting tower. A computer simulation could maintain relative probabilities as measures of the inhibitory power for each tower and calculate propensities to dump blocks on the fly. Possible variations of this model include constant degrees of inhibition and specific distributions of these degrees over the structure of n towers. These variations are not discussed here.
The one variation briefly discussed comprises a simplified view of the structure. Each tower has two values; the first represents its degree of realization, the second measures its propensity to receive a block in the next step. This propensity is the result of its own degree of realization and the inhibitory influences of the neighbors. Degrees of realization and propensities can change simultaneously. They depend on each other. From here, a direct path leads to the problem of the interpretation of the mathematical formalism of Quantum Theory. The leading question is whether the approach advanced here provides a solution for these problems.
To conclude, potentialism provides a basis for the description of the cosmos in terms of mutually dependent fields of propensities and degrees of realization.
Overview Potentialism Examples Conclusion Footnotes Bibliography