"The world is rationally comprehensible because it has structure" (Plato).
"What kind of things do I know? The answer is 'structure'" (Arthur S. Eddington).
"What is innate is not the ideas themselves, but the structure to achieve their knowledge" (Antonio Colino López).
Realism
Realism, in its simplest and most general conception, is that entities of a certain kind have an existence independent of our perceptions, conceptual schemes, linguistic practices, beliefs, and so on.
Realism is a way of referring to something deep, basic or absolute, the foundation of everything. In this sense, there is general consensus that there must be an ultimate reality, but there is no consensus about the nature of that ultimate reality.
Realism is opposed by anti-realism, which denies the objective reality of the entities under consideration.
There are many conceptions or variants of realism, among them:
Material realism (or materialism). Only physical reality exists.
Idealism. The mind is all that exists. The external world is an illusion created by the mind.
Nominalism. General, universal, or abstract concepts have no independent existence. They exist only as names.
Platonic realism (or Platonism). It is Plato's view that universals exist in a higher realm, the realm of Forms or Ideas. This realm is perfect and immutable, outside of space and time. A Form is a pattern or archetype of which objects are instances or copies. Forms are the most fundamental kind of reality and are only accessible by intuition.
Mathematical realism. Mathematical entities and truths exist in a higher realm, eternal and independent of the human mind. This realm we discovered and did not invent.
Conceptualism. Universals exist only in our mind.
Modal realism. Possible worlds are as real as the real world we live in.
Epistemological realism. Our knowledge exists independently of our mind.
Indirect realism (or representationalism). The world we perceive is not the real world, but internal or virtual representation.
Constructive realism. It is to construct new meanings from basic structures of knowledge.
Scientific realism and structural scientific realism. We comment it below.
Scientific Realism and Anti-Scientific Realism
Scientific Realism
Scientific realism is the conception that our most successful scientific theories correctly describe unobservable entities (subatomic particles, force fields, electromagnetic radiations, etc.).
The most powerful argument in favor is the so-called "no miracle argument", formulated by J.J.C. Smart, Hilary Putnam and Richard Boyd: if the most successful scientific theories were not true approximations to the real world, then their success would be truly miraculous. Therefore, the best explanation for the success of science is that scientific theories reflect unobservable reality.
Forms or variants of scientific realism are:
Semantic realism. Scientific theories must be interpreted literally. Their statements have their truth values, by virtue of their correspondence with reality.
Epistemic realism. Knowledge of unobservable reality is an attainable goal and its truth can be known.
The most powerful argument against scientific realism scientific anti-realism is based on the continual changes in scientific theories, and that our current best theories will someday be abandoned, so we should not rely on any of them. The history of science is a succession of incompatible theories, so that every theory is refutable. This is what is called "pessimistic meta-induction" [Laudan, 1981.
One form of scientific anti-realism is instrumentalism (sometimes identified with scientific anti-realism): theoretical statements and technical terms are not to be interpreted as referring to anything external and real, but as mere mental tools of assistance, disguised ways of referring to observable phenomena.
For the logical positivism of the Vienna Circle, scientific realism is only experimental. The only thing that is valid is experimental facts. In fact, scientific realism emerged in the 20th century as a reaction to logical positivism.
According to Popper, for a theory to be truly scientific it must be falsifiable, that is, it must be disprovable by experience. Therefore, we can never be sure of the veracity of scientific theories for unobservable entities.
Structural Scientific Realism
Structural scientific realism −usually referred to simply as "structural realism"− as an epistemological postulate goes back to Poincaré, Russell and Carnap. But it was the English philosopher John Worrall who formally introduced it into modern philosophy of science in 1989, as a way to overcome scientific realism and anti-scientific realism [Worrall, 1989]. According to Worrall, we should not accept scientific realism, nor should we be anti-realists in science:
We should accept only structural realism, that is, the structural or mathematical content of our scientific theories. Only the structure of the world is knowable, not the nature of the things whose relations define the structures. Scientific theories reveal to us, by means of their mathematical structure, the structure of reality. The mathematical structure of a theory can be identified as the set of equations that establish the relationships.
Scientific theories must be interpreted as structures and not as a set of sentences. The physical domain of a theory is an instance of a mathematical structure. Scientific theories make the structures, the underlying deep elements, reify.
Throughout successive scientific theories there is structural continuity. While the names of the entities that are part of scientific theories change, the mathematical structures remain.
"When our empirical theories change over time, what is retained is the structural content of our theories. The mathematical structure of our theories is what is retained and what is continuous, even in cases of radical theoretical change" [Worrall, 1989].
"Equations express relations, and if equations remain true, it is because relations preserve reality" [Worrall, 1989].
Worrall justifies structural continuity by giving as an example the case of optics, where Fresnel's theory was changed to Maxwell's, but the equations of diffraction and reflection were still maintained. On the other hand, the term "ether" that appeared in Fresnel's theory does not appear in Maxwell's theory, where the concept of electromagnetic field was introduced.
Ontic and epistemic structural realism
James Ladyman [1998] distinguishes between ontic structural realism and epistemic structural realism.
According to ontic, ontological or metaphysical structural realism, there are no "things", but only structures (properties and relations). The basic ontological entities are structures.
According to epistemic structural realism, scientific theories refer only to the structure of relations between things and not to the things themselves. In this sense there are 3 positions:
We cannot know the elements that constitute the nature of the world, but we can know their properties and relations.
We cannot know the elements that constitute the nature of the world nor their intrinsic (non-relational) properties, but we can know their first-order relational properties.
We can know neither the elements that constitute the nature of the world nor their intrinsic (non-relational) properties nor their first-order relational properties, but we can know their second-order relational properties: those associated with sensible experience, with perceptions.
Worrall's structural realism is of epistemological cut: we can only know the structure of the world, its ontology remaining unknowable.
According to the empiricist structuralism of Bas van Fraason [1980], theories are true if they are empirically adequate, that is, if they explain phenomena. There is no justification for assuming a structure to the world. It is sufficient to consider the external structure of phenomena. Ontological structural realism is unnecessary.
The current structural realism is that proposed by Steven French and James Ladyman [2003]: All there is is structure; Our scientific theories are able to capture the existing structures of reality. Structures are the ontological primitives. The structural knowledge provided by scientific theories exhaust all that can be known about the world, for structures are the ultimate element of reality.
This position reconciles ontic and epistemic structural realism by considering that the only thing there is is structure, that the structural content is the only thing that exists and, therefore, the only thing we can know.
Poincaré's structural realism
Henri Poincaré is considered the main precursor of structural realism:
Cognizable structures.
The unobservable entities postulated by scientific theories are Kantian noúmenos, i.e., things in themselves. But he qualifies Kant by saying that the noúmenos can be known indirectly through the relations between them.
We have direct epistemic access to our perceptions, which are private in nature and cannot be transmitted. But we can communicate relations between sensory experiences, such as that one color is darker than another (we can only transmit the structure or relation "darker than"). Cognizable reality is not the things themselves, but only the relations between things, i.e., the structures.
"Classifying things into natural classes is not what science can achieve, as naive dogmatists think, but only the relations between things; outside of these relations there is no cognizable reality" [Poincaré, 2002].
Mathematical objectivity.
Objective reality is that which is common to everything, which is the harmony of mathematical laws. The history of science is the history of the evolution of the conceptions of these relations and not of the conceptions of the objects.
Structural continuity.
Throughout the change of scientific theories there is continuity, but that continuity is not of ontology, but of structure. New mathematical theories retain the mathematical structure of old theories because the mathematical structures of scientific theories represent the structures of the world.
Poincaré identified the mathematical structure of a theory (even the theory itself) with the equations of the theory. About Maxwell's electromagnetic theory he said, "Maxwell's theory is Maxwell's equations."
Worrall took from Poincaré this concept of structural continuity and also identified structure with equations.
According to Javier de Lorenzo [2008], Poincaré was a "structural constructivist", a position that is beyond structural realism and structural empiricism.
Russell's structural realism
Bertrand Russell made an early defense of structural realism in "The Problems of Philosophy" (1912). In his 1927 work "Analysis of Matter" [Russell, 1976] he presents a detailed defense. The central argument of this defense is a causal theory of perception based on two principles:
The Helmholtz-Weyl principle: different percepts (or percepts, the basic units of perception) imply different causes.
The principle of specular relations: relations between percepts correspond to relations between non-perceptual causes, so that logical-mathematical properties are preserved.
From these principles, Russell argues:
Perception does not produce direct knowledge of external objects. It yields only direct knowledge of the intrinsic or qualitative character of percepts, but not of objects in the external world. However, percepts encode information about the external world. Therefore, the only way to gain knowledge of the external world is to make inferences from our percepts. And all that we can infer is of a structural kind.
The structure of our perceptions is isomorphic to the structure of the world. This structure is of a logical-mathematical type.
The only thing we can know is the second-order structure and relations of the world, the world of empirical phenomena, not the first-order physical properties (the ontological or intrinsic ones).
External relations (between perceptions) have the same logical-mathematical structure as internal relations; and, therefore, science can only describe the world as a second-order isomorphism of the structure of the world.
"The only legitimate attitude about the physical world seems to be one of complete agnosticism with respect to everything except its mathematical properties" [Russell, 1976].
This position of Russell's is one of structural realism because to know the mathematical properties of relations without knowing their elements is tantamount to saying that we know only the structure of the world.
Carnap's structural empiricism
Carnap was an advocate and promoter of logical positivism, according to which the only valid thing is the experimental facts. It makes no sense to speculate about the deep (unobservable) nature of reality. It is necessary to stick to the phenomenal facts and their relations or structures.
Carnap's approach is based on structural empiricism, linguistics and formal logic:
Structural empiricism.
Every scientific statement can be transformed into a structural statement. Everything that does not belong to the structural but to the material is in the end subjective. The objective are the structural descriptions of reality. Science can only know the purely structural and logical characteristics of the empirical world, structures that are only accepted to organize, explain and predict empirical phenomena.
The linguistic problem.
In his essay "Methodological Character" −considered the culmination of the positivist program− states that it attempts to dissolve rather than resolve the dispute between realism and instrumentalism. The problem is linguistic and semantic rather than ontological. The discussion should not be approached in the form Are theoretical entities real, but in the form Do we prefer a language of physics (and of science in general) containing theoretical terms or a language without such terms? It is a matter of preference and practical decision [Carnap, 1974].
For Carnap, questions such as Are electrons real? and Can electrons be shown to be real? are meaningless questions, without cognitive content, because they are formulated outside the linguistic framework of science and involve metaphysics. Within the scientific framework physical entities (quantum particles, waves, etc.) have not only theoretical meaning but also practical utility for scientists.
Carnap developed a systematized language for integrating theory and empirical observation. He distinguished between observable and unobservable entities. But since language does not distinguish predicates on the basis of observational categorization, Carnap divided the vocabulary into two categories: observable terms (O) and unobservable or theoretical terms (T). And he used Ramsey sentences to capture the factual content of a theory. A Ramsey sentence is a logical proposition in which unobservable terms have been replaced by observable terms.
Structural realism and the various authors
Galileo.
The book of nature is written in the language of mathematics. Therefore, mathematics is the deep nature of reality. Reality is mathematical and, therefore, structural. Galileo reified the image of the world, establishing direct correspondence between scientific theory and reality.
Kant.
Deep reality, the noun, the thing-in-itself (ding-an-sich), is unknowable. We can only know the superficial (phenomenal) reality. That knowledge is conditioned and restricted by our mental structures.
Wittgenstein.
There is isomorphism between external reality, internal reality, and language. The structures are the same.
Ernst Cassirer.
Quantum particles have no substantiality and individuality, they exist only in relation to the field in which it is immersed. The field is not a" thing" but a system of effects.
Joseph D. Sneed.
"Structuralism is essentially a conception about the logical form of the assertions of empirical theories and about the nature of the predicates that are used to make these assertions" [Sneed, 1983].
Grover Maxwell [1971].
He defended the epistemic version of structural realism, echoing Russell's position: we cannot know the first-order (ontological) properties of physical objects, but we can know the higher-order properties: the structural properties.
Maxwell was the coiner of the term "structural realism" in 1968 [Maxwell, 1968] to refer to Russell's position.
David Lewis.
Everything that exists is an interconnected network of intrinsic properties and spatio-temporal relations. There are no abstract entities. All facts of the world are particular facts or combination of them. Intrinsic properties are those possessed by an entity, independent of all other entities. Extrinsic properties are non-intrinsic or relational.
The problems of structural realism
Structural realism presents several major problems or challenges:
Max Newman's problem [1928].
It is epistemic. It claims that whatever structural realism has to say about knowledge of reality is either trivial (it adds no knowledge) or false. For example, if a physical domain is a set of a certain cardinality, then what underlies the observable properties and relations of that domain will have a structure of the same cardinality.
Newman thus replied to Russell's arguments set forth in "Analysis of Matter" (1927).
The ontological problem.
It is of a metaphysical type. It states that structural realism does not clarify what is the ontology that is hidden behind the structures. Nor does it clearly separate structure and ontology, since structures can be considered ontology. In short, we are dealing with the problem (or dialectic) of relationism-substantialism.
The problem of pure structure (without substance).
A structure cannot be said to be real apart from the objects that make up that structure. Form is inseparable from matter (or substance). Structures cannot be separated from ontologies. "Does it make sense to conceive of a structure that is not structure something? A structure of nothing is nothing" [van Fraassen, 2007].
According to van Fraassen [2006], if there is nothing but structures, then it makes no sense for us to speak of structures. The distinction between structure and non-structure disappears.
The problem of the concept of structure.
Structural realism does not specify which types of relations exist in a structure. It refers to the concept of mathematical structure: a formal axiomatic system based on set theory and predicate logic. This definition of structure is ambiguous, since it is not precisely defined. Nor does it clarify whether there are primary or fundamental relations with which structures can be built.
The problem of representation.
According to structural realism, scientific theories represent - by means of mathematical structures - the structure of reality. But it does not explain what exactly this mechanism of representation consists of.
The problem of interpretations.
A structure can have more than one interpretation. In other words, given a formal structure, it is not possible to identify a unique physical referent.
Moreover, a mathematical structure is not compatible with different ontologies, since every mathematical structure carries with it an ontological load. No language, not even mathematical language is free of ontology.
Ladyman proposes to consider only ontic structural realism, for the way to refrain from making different interpretations of a given structure.
The problem of different formalizations.
A theory may have several empirically equivalent formalizations. The problem arises when different formulations of a theory involve different mathematical structures. Moreover, the formalism conditions (and sometimes determines) the interpretation.
A representative example of this problem are the two mathematical theories of quantum physics: Heisenberg's matrix theory (of 1925) and Schrödinger's wave theory (of 1926). In 1932, Von Neumann proved in 1932 that the two theories were equivalent. However, the two theories describe different physical realities. The first is a theory of discrete physics, and the second is a theory of continuous physics. But structural realism should have expected the underlying mathematical structure to be the same, which is not the case. It fails the structural realist inference that the theory captures the structure of reality because different formalizations refer to different structures.
The problem of the continuity of mathematical structures.
The history of science provides episodes in which the mathematical structures of scientific theories do not seem to have survived.
The problem of idealization.
Scientific theories cannot be considered literal descriptions of reality because theoretical descriptions are idealized.
The problem of the mind.
Is the mind part of structural realism? If the mind is considered to be part of nature and to have structure, then we have to consider structural realism as universal.
Universal structural realism
According to structural realism, the physical domain of a theory is an instance of a mathematical structure. It follows that if the domain of a theory extends to the entire universe, then the entire universe is an instance of a mathematical structure of a certain class or category. In other words, the physical universe is isomorphic to a mathematical structure. This philosophy is called "universal structural realism," which also has its epistemic and ontic conceptions:
According to the ontic version, the whole universe is nothing but a mathematical structure, and that the notion of "substance" is meaningless. The mathematical structure is the only thing that exists. This is the theory of the Mathematical Universe Hypothesis (MUH) of Max Tegmark [2008]. [see Addendum].
According to the epistemic version, we can only know the mathematical structure of the universe.
If it is claimed that the physical universe is an instance of a mathematical structure, it can be assumed that there may be other physical universes that are instances of the same mathematical structure or instances of other, different mathematical structures.
Informational structural realism
According to Luciano Floridi [2007], ontic and epistemic structural realism are reconcilable through informational structural realism. The world is the totality of informational objects interacting dynamically with each other.
MENTAL and Structural Realism
With the universal paradigm of primary archetypes and MENTAL as the universal language relating those primary archetypes, the concept of structural realism is clarified:
Universal structural realism.
Mind and nature share the same primary archetypes. Therefore, the domain of ontology and epistemology is the same. There is structural isomorphism between internal world, external world and language.
MENTAL is a universal structural realism in the sense that it contemplates and unifies inner world and outer world through the primary archetypes, which are the foundation of consciousness. The structures are relations between the manifestations of the primary archetypes.
Ontic and epistemic structural realism are reconcilable, not at the informational level (as Floridi holds), but at the level of primary archetypes. Information cannot serve as a foundation because it is an indefinable concept, like consciousness.
Types of relationships.
With MENTAL the types of relations that can exist to form structures are clarified: those defined by the primary archetypes (qualitative, quantitative, generic, conditional, etc.). In addition to these relations, their "substance" (to create concrete structures) consists basically of atoms, which are digits and letters. These relations can be operational and descriptive.
MENTAL transcends mathematics. The structures of MENTAL are much richer than conventional mathematical structures. The structures are not just logical forms (as Seed says) nor just equations (as Worrall says), but the relationships defined by the primary archetypes.
MENTAL allows to express the strange relations of the microscopic or quantum world (entanglement, tunnel effect, etc.) and also the relations of the macroscopic world.
Structures.
Apparently there are 4 types of structures, but they are the same: 1) external, empirical or phenomenal structures; 2) ontic (unobservable) structures of reality; 3) mental or internal structures; 4) linguistic structures.
MENTAL unites linguistics and structures. They are the same thing. Every structure is linguistic and every linguistic expression is structural.
Primitives are not structures, as French and Ladyman claim. Structures are second order. The primary archetypes are the ontological and epistemological primitives (with which the internal and external structures are built) are first order.
And the structures are not the only thing: there are third order elements, which are the models, the interpretations of the structures.
Archetypes.
The objection raised against structural realism that it makes no sense to establish structures without reference to the elements that make them up is easily resolved: The primary archetypes are the deep structures, inexpressible and manifesting themselves in particular structures. It makes full sense to speak of abstract structures, independently of their concrete content. Form is separable from matter. "Archetypes are forms without content" (Jung). Reality, in the last analysis, is constituted by abstract structures.
Universal language.
MENTAL is the universal grammar and universal language (structural semantics is the same as lexical semantics) that allows to express the structures, the relations between all things by means of the primary archetypes.
The concept of structural realism is motivated by quantum physics. But in MENTAL structural realism is universal, valid for all reality (internal and external), for the microscopic and macroscopic world. It is an archetypal language valid for all things and phenomena, for the static and the dynamic. It follows the principle of hermeticism: "As above so below, as within so without" (The Kybalion).
Scientific theories.
A theory is all the more accurate the closer the epistemic structural reality is to the ontic structural reality. Ideally, both structures should coincide.
The "structural continuity" referred to by Poincaré and Worrall are not the concrete mathematical structures, but are the primary archetypes, which are always present in all scientific theories.
Objective and subjective knowledge.
The subjective is the superficial, concrete and particular. The objective is the deep, the abstract and the generic or universal. In this sense, MENTAL is a totally objective language, free of subjectivity.
Limits of knowledge.
Deep reality is not that it is unknowable (as Poincaré said), but that it belongs to another mode of consciousness: the one associated with the mode of the right hemisphere of the brain (intuitive consciousness). It is unknowable from the point of view of the left mode (rational consciousness). The limit of our knowledge is set by the primary archetypes that connect the deep with the superficial, the intuitive with the rational.
Philosophy.
There is no philosophy of science, for MENTAL is born of philosophical principles (the primary archetypes, which are at the same time philosophical categories). MENTAL is a scientific metaphysics. It is a naturalized or reified metaphysics.
Simplicity.
MENTAL is the simplest possible theory. It follows the principle of Occam's razor: the simplest theory is the one most likely to be true.
In short, MENTAL is not just another scientific theory. It is a universalistic and falsifiable theory. It is the language of the deep structure of reality and possible worlds.
Moreover, there is a connection with Wigner's question. The world is comprehensible because mind and nature have the same structure because they share the same principles: the primary archetypes.
Addenda
Group theory, structures and invariants
Group theory plays an important role in the structural ontology and epistemology of physics.
"What kinds of things do I know? The answer is 'structure.' To be precise, it is structure of the kind defined and investigated by mathematical group theory" [Eddington, 1939].
A very important type of relations are those of symmetry, which are described by group theory. A symmetry is a transformation of a structure or object that leaves it invariant in some respect. A symmetry group is a set of symmetries that has group structure. Mathematical objects can be characterized in terms of symmetry transformations that leave them invariant.
The idea of invariance is the key to the relational concept of reality, not only in physics, but in any science. The idea is that we can have several representations of a physical structure that can transform into each other. Invariants are the foundation of objectivity, because reality is a kind of invariance of a structure.
According to Max Born, invariants are the concepts of science, just as ordinary language speaks of "things". For Ernst Cassirer objects are individual invariants. For Weyl, objectivity means invariance with respect to the group of automorphisms.
The bootstrap theory
According to Geoffrey Chew's bootstrap conception (presented in the 1960s), all quantum particles are held together by the relationships between them. There are no independent physical entities. Everything is interrelated. Nature is a dynamic network of interrelated events. Things exist as a function of their mutually consistent relationships.
The Mathematical Universe Hypothesis (MUH), by Max Tegmark
The universe is isomorphic to a mathematical structure. Our external physical reality is a mathematical structure. That is, the physical universe is mathematical, but the self-conscious substructures it contains cause us to have conscious experiences and subjectively perceive it as a real physical world. All universes corresponding to different mathematical structures can be considered equally real. The MUH theory is elaborated within the Computable Universe Hypothesis (CUH), which states that all computable mathematical structures exist. The MUH is a radical mathematical platonism.
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