A Realist view of logic and physics

 Realism: A Journey through Logic and Physics

“I know three things will never be believed - the true, the probable, and the logical.”

- John Steinbeck 

 

In a time scale of the sun's age we we can confidently say that we have not made the world, compared with the changes achieved by animals and plants. Yet we have created a new kind of artifact which promises in time to work changes in our corner of the world as great as those worked by our predecessors, the oxygen-producing plants or the islanding building corals. These new products, which are decidedly of our own making, are our myths, our ideas, especially our scientific theories: theories about the world we live in. 

I suggest that we may look upon these myths, these ideas, and theories as some of the most characteristic products of human activity ( as said by Karl Popper).  They are organs evolving outside our skins per se these are exosomatic artifacts. 

Thus we may count among these characteristics products especially what is call " human knowledge" where we take the word 'knowledge' in the objective or impersonal sense, in which it may be contained in a book, stored in a library, or in the internet. 

" Knowledge produced by a person is analogous to honey produced by bees". Bees produce, store, and consume honey, but typically, a bee does not just eat the honey it has produced. Drones, which don't make any honey, also consume it, and bees can lose their stored honey to bears or beekeepers. Interestingly, worker bees need to consume honey, often made by other bees to maintain their ability to produce honey.

This concept largely applies, with minor differences, to oxygen-producing plants and theory-producing humans. Like bees with honey, we are both producers and consumers of theories. We must consume others' theories and occasionally our own to continue generating theories. Here, 'to consume' primarily means 'to digest,' similar to bees. However, it extends further: consuming theories involves critiquing, altering, and often dismantling them to make way for better ones. These processes are essential for the advancement of our knowledge.

Humans produce not only scientific theories but also a variety of other ideas, such as religious or poetic myths and friction. What distinguishes a scientific theory from a work of fiction? It's not just that theories might be true while fictional stories are not, though truth and falsehood are relevant. The key difference is that theories and stories are embedded in different critical traditions. They are judged by distinct traditional standards, despite having some commonalities. 

A scientific theory is characterized by its purpose as a solution to a scientific problem. This problem may have emerged from previous critical discussions of tentative theories or may have been discovered by the theory's author within the realm of scientific problems and solutions. However, this is not the whole picture. The scientific tradition, until recently, has been defined by what can be termed scientific realism. This means it was driven by the idea of finding true solutions to its problems that correspond to the facts. This regulative ideal of seeking theories that match facts is what makes the scientific tradition a realist one. It differentiates between the realm of our theories and the realm of facts to which these theories pertain. Furthermore, the natural sciences, with their critical methods of problem-solving, and some social sciences like history and economics, have long represented our best efforts in problem-solving and fact-finding. By fact-finding, I mean discovering statements or theories that correspond to facts. Thus, these sciences generally contain the best statements and theories from the standpoint of truth, providing the best descriptions of the world of facts, or what we call 'reality'.

Emergence from reduction

Physics and chemistry, which deal with physical things and states, are closely related. Chemistry’s inapplicability at extreme temperatures suggests it may be reducible to physics—a significant scientific achievement, fostering unity and understanding. Assuming chemistry is fully reduced to physics, we might hope to similarly reduce biology to physics. However, living organisms differ fundamentally from non-living things, making this reduction more challenging. While progress in understanding the origin of life and creating primitive organisms may occur, true reduction requires more than control over processes. It demands theoretical integration, comprehending the new field through the principles of the old one.

The reduction of chemistry to physics, seemingly progressing well, can be seen as a prime example of a true scientific reduction that meets all the criteria for a robust scientific explanation. A 'good' or 'scientific' reduction is a process through which we gain significant insights: we come to understand and explain the theories of the field being reduced (chemistry in this case) and we also learn about the capabilities of the theories from the reducing field (physics in this instance).

I term "bad reduction" or "ad hoc reduction" as the method of reducing concepts through mere linguistic maneuvers. For instance, physicalism, which proposes the ad hoc existence of physiological states to explain behavior previously explained by mental states (without such ad hoc postulation), is an example. Another example is the linguistic device of claiming to describe a physiological state when stating that one understands the Schrödinger equation. This second type of reduction, or misuse of Ockham's razor, is problematic because it obscures the real issue. As Imre Lakatos vividly describes, it is a "degenerating problem shift" that can hinder either a good reduction or the study of emergence, or both.

Thought process and understanding

Supporting the emergent nature of theories or knowledge in an objective sense. I'll mention a few arguments against the naive and popular view that theories can be reduced to the mental states of those who create or understand them. (We won't discuss whether these mental states can, in turn, be reduced to physical states.) The notion that a theory in its objective or logical sense can be reduced to the mental states of those who hold it is typically framed as the theory simply being a thought. However, this is a fundamental mistake: it fails to distinguish between two meanings of the word 'thought'. Subjectively, 'thought' refers to a mental experience or process. But two mental experiences or processes, while possibly causally related, cannot be logically related. 

For example, if I say that certain ideas of the Buddha align with those of Schopenhauer or contradict those of Nietzsche, I'm not referring to the mental thought processes of these individuals or their interactions. Conversely, if I say Nietzsche was influenced by Schopenhauer's ideas, I mean that Nietzsche's thought processes were causally affected by his reading of Schopenhauer. Therefore, we have two distinct realms: the realm of thought processes and the realm of the products of thought processes. The former may be causally related, while the latter are logically related. The incompatibility of certain theories is a logical fact, independent of whether anyone has recognized or understood this incompatibility. These objective logical relationships define the entities I call theories or knowledge in the objective sense. 

This distinction is evident when considering that the creators of theories often do not fully understand them. For instance, it could be argued that Erwin Schrödinger did not fully understand his own equation until Max Born provided a statistical interpretation; or that Kepler did not fully comprehend his own area law, which he reportedly disliked. Understanding a theory is akin to an infinite task, suggesting that a theory is never completely understood, although some may grasp certain theories very well. 

Understanding a theory is similar to understanding a human personality: we may predict a person's behavior in various situations but cannot fully understand all their possible responses due to the infinite variety of potential situations. Similarly, a full understanding of a theory would require grasping all its logical consequences, which are infinite. Thus, no one, not even its creator, can fully comprehend all the possibilities within a theory, highlighting that theories, in their logical sense, are objective entities that we can study and attempt to understand. It is no more paradoxical to say that theories or ideas are our creations yet not fully understood by us than to say that our children are our creations yet not fully understood by us, or that honey is a product of bees yet not fully understood by any bee.

Realism and physics

In modern physics, subjectivism has become integral in two key areas: Boltzmann's theory of entropy (the arrow of time) and Heisenberg's uncertainty principle, which define a minimum limit on the observer's influence over the observed object. Einstein also introduced subjectivity when he included the observer in various thought experiments aimed at elucidating relativity, but he subsequently removed the observer from this domain over time.

The Heisenberg formula for energy is independent of both wave mechanics and Heisenberg's matrix mechanics. It also does not rely on commutation relations. Surprisingly, it does not stem from the revolutionary quantum mechanics of 1925-1926 but directly derives from Planck's earlier quantum postulate from 1900.

The interpretation proposed here suggests viewing Heisenberg's uncertainty principles as statistical scatter relations rather than indicators of the precision of measurements or limits to our knowledge. In this view, the principles don't speak directly to the precision of measurements but rather to the limits of homogeneity in quantum-physical states, indirectly addressing predictability. 

For instance, the formula Δ𝑝⋅Δ𝑞 ≈ ℎ implies that upon determining the coordinate 𝑥 of a system, such as an electron, the momentum 𝑝 will scatter upon repetition of the experiment. This assertion can be tested by conducting a series of experiments with a fixed shutter opening Δ𝑥, measuring the momentum 𝑝​ in each case. If the measured momenta scatter as predicted, the formula survives the test. Notably, these experiments require measuring 𝑝 with a precision greater than Δ𝑝, as otherwise, speaking of Δ𝑝 ​ as the scatter of 𝑝 ​ wouldn't make sense. Such experiments are routinely conducted in physical laboratories, challenging the interpretation of Heisenberg's indeterminacy principle. While Heisenberg acknowledged the possibility of such measurements, he deemed attaching meaning to them a matter of personal belief or taste, leading to their disregard as meaningless. 

However, they serve a specific purpose: testing the formulae themselves as scatter relations. This perspective argues against accepting Heisenberg's or Bohr's subjectivist interpretation of quantum mechanics, suggesting instead that quantum mechanics is a statistical theory suited to solving statistical problems, such as spectral intensities. As such, there's no philosophical need to defend its non-causal character.

There's no reason to doubt the realism and objectivity of physics. In modern physics, the observer's role remains similar to that in classical physics – primarily testing theories. This process involves evaluating competing and auxiliary theories, highlighting that we are not so much observers as thinkers.

Realism in logic

Logic, in essence, can be seen as the theory of deduction or derivability. It involves transmitting truth from premises to conclusions, as seen in proofs, and transmitting falsity from conclusions back to premises, as seen in disproofs or rebuttals. In critical discussions, logic is frequently used to challenge assertions by demonstrating their falsehood. If a conclusion is shown to be false, and the inference is assumed to be valid, it follows that at least one premise must be false. Thus, criticism becomes a vital methodological tool. Rejecting criticism by dismissing the logic used undermines the effectiveness of critical discussion. Logic serves two main purposes: in demonstrative sciences like mathematics, it's primarily used for proofs, while in empirical sciences, it's predominantly employed for critical analysis to uncover falsity. Although applied mathematics plays a role in empirical sciences, its significance is somewhat questionable in various aspects.

The rationalist view is characterized by its realist perspective on logic. Firstly, it associates logic with the methodology of the natural sciences, which the rationalist view considers to be grounded in realism. Secondly, it emphasizes logical inference as a process of transmitting truth or retransmitting falsity, thus highlighting the importance of truth in logical reasoning.

Theories of Truth

There are three main theories of truth. The oldest, the correspondence theory, posits that truth corresponds to the facts or accurately describes them, as Tarski emphasized. The coherence theory views truth as coherence with existing knowledge, while the pragmatic theory defines truth in terms of its practical utility or usefulness.

The coherence theory encompasses various interpretations, two of which are notable. The first posits truth as coherence with our beliefs, implying that a statement is true if it aligns with our existing beliefs. However, this approach raises concerns about integrating beliefs into logic due to potential logical constraints conflicting with individual beliefs. The second version suggests that an uncertain statement should be deemed true if it aligns with previously accepted statements, fostering a highly conservative approach to knowledge preservation. Contrastingly, the pragmatic utility theory focuses on the utility of theories in natural sciences, particularly physics. It suggests that a physical theory should be accepted as true if it proves pragmatically useful and successful in tests and applications.

Questions and interpretations???

Eliminating verbal or definitional questions, considering them as pseudo-questions. Questions like "What is life?", "What is matter?", "What is mind?", or "What is logic?" are viewed as unfruitful. They advocate discarding the question "What is truth?" for two main reasons. First, they reject essentialism, and second, they advise against discussing the meaning of words, likening it to a game that philosophers are addicted to but which they consider unimportant.

Incorporating the concept of verisimilitude or approximation to truth into logic enhances its realism by enabling discussion of how one theory aligns better with real-world facts than another. From a realist perspective, logic serves as the tool for criticism rather than proof in our quest for true and highly informative theories. Criticism becomes the primary instrument for advancing our knowledge about the factual world, aiming to promote the growth of our understanding by refining and improving upon existing theories.

This article is inspired from the works of Sir Karl Popper, Wolfgang Yourgrau, Allen D Breck

This is a distant part of model theory - https://jjohnpaul.blogspot.com/2022/01/mt1-model-theory-how-does-our-brain.html   and https://jjohnpaul.blogspot.com/2022/05/empiricism-and-rationalism.html .

Hope this article inspires you. 

Contact me through my blog or https://www.instagram.com/phy.sci/?hl=en.

- J John Paul