Occasionalism is a type of Cartesian metaphysics that distinguishes between mind and body. In this system, the mind is referred to as a “mental substance” whereas the body is regarded as a “material substance”.
How is it possible for the “unextended mind” and the “extended body” to interact? It seems impossible for these unrelated entities to interact without God’s intervention. Although there appears to be direct interaction, this is actually a deceptive illusion created by God. God controls the body’s movements when the mind desires it and implants ideas in the mind when the body encounters other bodies. Descartes suggested that the mind, as an active entity capable of thought, combines with the passive, unthinking extension of the body. Together, they form a third substance known as Man.
God, as the Fourth uncreated Substance, enables direct interaction between the mental substance (God) and the material substance (the body). Foucher posed the inquiry of how a mental substance like God can interact with a physical substance such as the body. The response provided was that God created the body, possibly to facilitate interaction with it. Leibnitz expanded on this concept, stating that his Monads, which are the fundamental units of reality, do not actually react and interact. They only appear to do so because God endowed them with a pre-established harmony.
The constant divine mediation was reduced to a single act of creation, which was viewed as a logical outcome of occasionalism and its refutation through reductio ad absurdum argument. However, one may question the necessity of the fourth substance. Can all known facts be explained without it? The parsimony ratio, which measures the proportion between known facts and theory elements/entities used to explain them, becomes relevant here. Each newly discovered fact either strengthens the existing worldview or necessitates the introduction of a new one, often resulting in a “crisis” or “revolution” (as described by Kuhn’s abandoned phrase “paradigm shift”). The new worldview does not necessarily need to be more parsimonious.
One possibility is that when a new fact emerges, it can lead to the creation of multiple new theoretical entities, axioms, and functions (represented by curves between data points). Defining the boundaries of a field of study restricts the number of relevant facts that can significantly impact the existing worldview. By establishing quantitative or qualitative limits of relevance and negligibility, we can achieve parsimony. This process of simplification occurs through idealization.
Despite the importance of maintaining a delicate balance between relevant and irrelevant information, essential and non-essential elements, and the extent of explanation within research boundaries, excessive adherence to this equilibrium can lead to structural breakdown. However, this does not address the underlying question of why simplicity is often favored over complexity. Throughout history, influential figures like Aristotle, William of Ockham, Newton, and Pascal have all advocated for parsimony and viewed it as a fundamental principle in scientific pursuits.
Both biologically and spiritually, our inclination is to prioritize things that are essential rather than those that are not. Additionally, we tend to favor things that are necessary over a combination of necessary and unnecessary items. This preference stems from the fact that necessary things are vital for survival and enhance its probability. The development of economic theories also contributes to survival. As a regular part of our daily routine, we all engage in the formulation of theories.
One theory suggests that seeing a tiger indicates danger. Theories that require fewer assumptions are processed faster and improve the chances of survival. In the case of the tiger example mentioned above, the effectiveness of the theory lies in its simplicity: one observation leads to one prediction. If the theory had been more complex, it would have taken longer to process and the prediction would have been unnecessary. Ultimately, the tiger would have won.
Humans can be described as Parsimony Machines (also known as Ockham Machines) because they prioritize selecting the shortest and most efficient path to generate true theorems based on a given set of facts and theories. Another way to understand the function of Ockham Machines is that they aim to produce the maximum number of true theorems in a specific time period, using the same set of facts and theories. Poincare, a French mathematician and philosopher, believed that Nature itself adheres to parsimony. He argued that simplicity in mathematics indicates truth. Even with the influence of theory and language, a mathematically simple Nature would still appear simple.
The world exists because it is the simplest option compared to other possibilities. It is the most parsimonious choice, which is a necessary requirement for a scientific theory. However, being scientific does not guarantee parsimony; it can also exist within a non-scientific framework.
Parsimony is a tool employed in theory construction, as theories are not solely determined by data. The reason for this is that an infinite number of theories can explain a finite amount of data. This discrepancy arises from the contrasting sizes between the myriad cases encompassed by a theory and the limited available data, which only represents a subset of those cases. Hence, parsimony acts as a heuristic to guide us towards theories with higher chances of success.
In essence, the ability to choose a theory as the prevailing worldview depends on new data that can challenge it. However, there is an unanswered question about how we determine if we are applying parsimony. What are the specific requirements for parsimony? To be considered “parsimonious,” any law or selection method must meet the following conditions: it must explore a higher level of causality that includes the previous one and other seemingly unrelated phenomena.
The purpose of the law is to explain a set of data that was previously explained by another cause or reason, as well as additional data. William of Ockham, a Franciscan monk, always sought a primary cause. The law should contribute to an integrative process, whether it leads to it or is a part of it. This implies that when previous theories or models are thoroughly and accurately joined together, certain elements of these theories may become unnecessary.
The only concepts that we should include in the new worldview are the ones that are absolutely necessary. We need to test the predictions of the law of parsimony scientifically and make sure that they align with our observations. The worldviews based on the law of parsimony should also be semantically accurate.
Constant use of these methods will result in a transformation (either gradual or sudden) of the actual language used to express the perspective of the world, or at least key components of the language. Even the wording of the inquiries to be addressed by the worldview will be impacted. In extreme scenarios, an entirely new language must emerge, developed and structured in accordance with the principle of simplicity. However, in most situations, weaker language is simply replaced by a stronger meta-language.
Einstein’s Special Theory of Relativity and Newtonian dynamics demonstrate a clear linguistic transition that occurred through the courageous use of the law of parsimony. It is essential that laws of parsimony are fully governed by the laws of Logic and Nature and do not lead to contradictions or tautologies. In the field of physics, these laws must adhere to causality or correlation and avoid teleology. Moreover, laws of parsimony should be able to handle paradoxes effectively.
Paradox Accommodation involves adapting theories, theory elements, language, and an entire worldview to prevent paradoxes. One possible approach is to minimize the goals of a theory or its domain to avoid paradoxes. However, the process of adaptation is also accompanied by a mechanism of adoption. In some cases, a law of parsimony may result in the adoption of a paradox. Therefore, both sides of a dilemma are accepted. This ultimately leads to a crisis that can only be resolved by introducing a new worldview.
New assumptions are adopted parsimoniously, eliminating the paradox. Accommodating paradoxes is a key characteristic of a genuine law of parsimony. Additionally, paradox intolerance is significant. Laws of parsimony allow theories and worldviews to disregard paradoxes that are beyond the scope covered by the concise set of data and rules. Conflicts often arise between non-parsimonious sets and the parsimonious one, resulting in paradoxes which serve as powerful tools for the non-parsimonious sets.
The law of parsimony should clearly and unequivocally guide us in determining when to embrace a paradox and when to reject it. To accomplish this daunting task, each law of parsimony is accompanied by a metaphysical interpretation that aims to convincingly address lingering paradoxes and questions. This interpretation places the findings of the formalism within the framework of a purposeful universe, offering a sense of direction, causality, order, and even “intent.” The Copenhagen interpretation of Quantum Mechanics exemplifies this type of interpretation.
The principle of parsimony applies to both the entities in a theory and the observable results, which are both part of a coherent, internally and externally consistent, logical (or scientific) theory. This principle is characterized by divergence and convergence: it diverges from strict correspondence to reality during theorizing but converges with it when testing the predictions generated by the theory. While it is uncertain whether quarks exist or not, their effects are observable. The law of parsimony should remain invariant under all transformations and permutations of the theory entities. It is almost tempting to demand symmetry for this law, but this requirement is often violated and is merely an aesthetic aspect. The goal of the law of parsimony is to minimize the number of postulates, axioms, curves between data points, theory entities, etc.
The principle of maximizing uncertainty states that the more uncertainty is created by not explicitly postulating assumptions, the stronger and more rigorous the theory or worldview becomes. A theory that only assumes one entity and one theoretical construct leaves much of the world in a state of uncertainty. This uncertainty can be eliminated by using the theory, its rules, and applying them to observational data or other theoretical constructs and entities. The goal of the Grand Unified Theories in physics is to eliminate four separate powers and gain one unified power instead.
The application of a law of parsimony should result in a sense of beauty, aesthetic superiority, acceptability, and simplicity. These sensations are often mentioned by scientists as influential factors in favor of a particular theory. Laws of parsimony involve choosing specific facts, observations, and experimental results to include in the parsimonious set. This selection process is closely connected to the concepts of negligibility and the methodology of idealization and reduction.
The concept of parsimonious selection is akin to a strategic move in a finite game with a fixed number of players and established rules. When a new player enters the game, such as an observation or experiment result, it can either transform the current game or create an entirely new one. All players are then transferred to the new game and must adhere to its rules. This process has the potential to result in an endless loop. To achieve parsimonious selection, a theory must be present to govern the selection process. However, this theory must also abide by a principle of parsimony, meaning it must selectively choose its own facts, among other things.
In order for a lower-level theory to implement its own parsimonious selection and adhere to the tenets of a law of parsimony, there must be an existing meta-theory that informs it. This meta-theory applies the principle of redundant identity, in which two facets, aspects, or dimensions of the same thing are seen as one rather than separate and independent entities. A law of parsimony invalidates anything that does not follow its principles, considering superfluous entities not just unnecessary, but likely false. Theories that have not undergone tests of parsimony are likely not only lacking rigor, but also incorrect.
The laws of parsimony impose “back determination” on all applicable theories and worldviews. A range of parsimony sets can be suggested for a given data set and set of rules. Additional facts are required to choose among them. These facts will be discovered in the future, thus determining the correct parsimony set. It is possible that there is a finite parsimony group from which all temporary groups derive, or there may be no such group and an infinite number of parsimony sets are possible, representing an infinite number of data sets. This implies a form of pluralism, albeit subtly expressed.
The first possibility is that there is a finite number of facts, observations, or experiments needed to determine the correct parsimony set. However, there is also another option: there could be a single parsimony set that is everlasting, and all our current sets are only approximations of it. This would essentially be monism in disguise. Additionally, there appears to be an intuitive conflict between parsimony and infinity.
A law of parsimony appears to contradict the principle of multiplicity of substitutes. This observation is based on empirical and pragmatic evidence: When one element or entity is removed from a theory, it is typically replaced by two or more elements or entities in order to preserve the theory. This principle often leads to scientific crises and revolutions. Entities tend to multiply, and Ockham’s Razor is rarely employed until it becomes necessary to completely replace the theory.
This text emphasizes that the collapse of worldviews is not a necessary outcome of scientific progress, but rather a psychological and social phenomenon. Ptolmey’s cosmology was replaced by the Copernican model not only because it was more efficient, but also because it contained fewer theory elements, axioms, and equations. To prevent this from happening, a law of parsimony should discourage and restrain the inclusion of excessive elements in theories or, if necessary, deliver the final blow to an ailing theory. Moreover, the law of parsimony should allow for the complete conversion of the phenomenal to the nuomenal and the universal to the particular.
In simpler terms, a law of parsimony cannot support the idea of distinguishing between our data and the “real” world. It also cannot allow for the existence of Platonic “Forms” and “Ideas” that are not fully reflected in specific instances. The law of parsimony suggests that there must be necessity. Assuming that the world is contingent means suggesting the presence of another entity on which the world depends for its existence. This is theorizing about another principle of action. Contingency leads to an increase in the number of entities and goes against the principle of parsimony.
Of course, causality and contingency should not be mistaken. Causality is deterministic while contingency is the result of free will. The explicit parsimony, which is formulated, formalized, and analyzed, is connected to implicit parsimony and latent parsimony. Implicit parsimony refers to the rules and assumptions of formal logic. Latent parsimony allows for a (relatively) smooth transition between theories and worldviews during crises. These rules of parsimony govern scientific revolutions.
The latent rule stated in article (a) is that the transition between old and new theories must involve a shift from a lower level of causality to a higher one in order to be valid. The following approaches do not achieve efficient, workable parsimony: association, which involves forming networks of ideas through verbal, intuitive, or structural links; this does not lead to more parsimonious results. Although this technique can reveal syntactic, grammatical, structural, or other theoretical rules, scientists must distance themselves from associative chains to discern such rules and adopt a broader perspective. Alternatively, scientists may isolate a specific part of the chain for closer examination, whether arbitrarily or not.
The act of association frequently results in an abundance and overwhelming variety. This concept can be applied to other methods of linking, connecting, and networking. When something is incorporated without being fully integrated (meaning, without removing unnecessary duplications), it creates hybrid theories that are not sustainable in the long term.
The motivation behind incorporation lies in the conflict between entities, postulates, or elements of theory. Those who defend the “old truth” hope to prevail through incorporation, which serves as an intermediate stage between the old and the new. However, this tactic often backfires on the instigators, leading to the creation of a new theory. It is important to note that incorporation is driven by political motivations and is considered a sworn enemy of parsimony.
Everyone is kept happy by not sacrificing anything and collecting entities, which is toxic and undermines the entire hyper-structure. This accumulation of entities goes against contingency (refer to (r) above), whether through strict monism or pluralism (refer to (o) above). In order to prevent simplicity, comprehensiveness is necessary.
To achieve a concise description of the world in accordance with the law of parsimony, it is necessary to disregard numerous elements, facts, and observations. Godel demonstrated the inherent paradoxical nature of a comprehensive formal logical system. However, a complete depiction of the world would require an unlimited number of assumptions, axioms, theoretical entities, elements, functions, and variables. This goes against the principle of parsimony. The aforementioned impedes the convergence of parsimony and monovalent correspondence. It would be unlikely for an isomorphic representation of the world to the worldview, a realistic portrayal of the universe employing theoretical entities and other linguistic elements, to possess simplicity.
The use of theory elements would result in a multitude of entities. Realism can be likened to operating a supercomputer with machine language. The alignment with both the world and the predictions from the theory leads to an abundance of categories, with each one having few examples. There is an overabundance of species and genera. The worldview becomes cluttered with numerous unrelated observations and excessive details. If the field of research is defined too narrowly, it can hinder the formulation of meaningful questions and the anticipation of meaningful experimental outcomes.
The psychophysical problem may be too narrowly defined, as it is heavily influenced by physics and tends to bias or exclude certain questions. However, maybe a Fourth Substance is actually the simple and efficient solution.
