01 The problem: knowing a reality that thought does not produce

Knowing a society requires more than listing events, recording opinions, or accumulating indicators. A wage, a law, an investment decision, and a protest belong to the same historical reality, but their coexistence does not yet explain the relations connecting them. The problem of knowledge consists in reconstructing those relations: identifying what makes a process possible, how it reproduces itself, what it depends on, and under what conditions it can be transformed.

The materialist starting point is the priority of reality over our knowledge of it. A social relation can exist and produce effects without those participating in it understanding its structure. Scientific thought works on representations, concepts, and evidence to develop an explanation; its constructive activity has an object that is not identical with that construction. The objectivity of the object is compatible with the elaborated character of knowledge.

Three questions should be distinguished. The ontological question concerns the relations and processes that exist; the epistemological question concerns how we know them and justify our claims about them; and the logical question concerns the articulation, consistency, and development of conceptual determinations. Their connection allows the same object to be investigated through complementary dimensions. No correspondence among them guarantees in advance that a category adequately describes reality.

Within this framework, historical materialism provides a historiographical and sociological theory of social formations, whose methodological grounding is developed in the philosophy of dialectical materialism. This relationship does not replace historical inquiry with deduction from general principles. It requires studying how the material production and reproduction of life are organized through determinate social relations, and how these are articulated with institutions, conflicts, practices, and forms of consciousness.

The position adopted in this essay is a materialist reconstruction of essence. It engages with Hegel, Marx, Dussel, Rosental, and Zubiri while distinguishing their problems and vocabularies. Its operational formulations are interpretive proposals whose usefulness depends on what they make it possible to explain and on their capacity to address objections.

02 Abstraction, ascent, and the return journey

2.1. The difference between the real concrete and the concrete in thought

The 1857 introduction to the Grundrisse distinguishes social reality from the way thought appropriates it. A population may seem to provide a sufficiently concrete starting point; naming it without determining its divisions, activities, and relations, however, yields a representation that remains inadequate. Inquiry must analyze that totality and reconstruct its mediations. The conceptual result is not society generated by thought, but its intellectual appropriation (Marx, 1973, introduction, section 3).

The real concrete is the actually existing process, with both known and unknown determinations. The concrete in thought is a conceptual reconstruction of its relations. It may be richer and more precise than an initial representation, but it remains partial and revisable. Its degree of concreteness is measured by the relevant mediations it articulates, rather than by the number of details it accumulates.

2.2. Abstraction as determinate separation

To abstract is to consider a determination under certain conditions while provisionally setting others aside. Studying real wages may require distinguishing nominal wages from the price level; studying the wage relation additionally requires considering property, hiring, the reproduction of labor power, and the organization of the labor process. Each operation addresses a question and establishes a scope.

An abstraction becomes impoverished when it forgets the conditions of its construction and presents itself as a sufficient explanation of the entire object. It can also fail by omitting a constitutive relation. If ownership of the means of production is relevant to the problem, excluding it to simplify the exposition changes what we are trying to know. Exclusions and the reasons justifying them must therefore be made explicit.

2.3. To ascend is to reconstruct mediations

The ascent from the abstract to the concrete articulates progressively richer determinations. An isolated category acquires content through its connection with others: wage labor, capital, competition, credit, and the state cannot be treated as independent pieces that can be added without changing the explanation. Introducing a new mediation may transform the meaning of previously established determinations.

Dussel systematizes this problem by distinguishing levels of representation, abstraction, and explained totality. His schema allows an initially constructed totality to be distinguished from a more determinate historical reconstruction. The attribution matters: this organization of levels belongs to an interpretation of Marx developed by Dussel, rather than to a universal protocol exhaustively formulated in the 1857 manuscript (Dussel, 2010, chap. 2).

2.4. Return and revision

In Marx’s passage, the return journey toward an enriched totality is connected with the ascent from abstract determinations. Interpretations that distinguish an ascent from a subsequent descent must specify what they mean by each movement. Operationally, it is useful to distinguish analyzing determinations, reconstructing their articulation, and evaluating the explanation in historical situations. These tasks recur and correct one another.

Returning to the object means asking what the reconstruction explains, what it leaves unresolved, and what evidence might require changing it. Totality is a requirement to articulate relevant relations. Conceiving it as possession of every possible fact would turn a methodological orientation into a claim to omniscience.

03 Inquiry, exposition, and historical order

Inquiry requires examining materials, comparing situations, and developing hypotheses, often through advances, corrections, and unsuccessful paths. Exposition requires organizing results so that their connections can be understood and discussed. Marx distinguishes these tasks in the 1873 afterword to the second German edition of Capital. A well-articulated exposition may appear to be a deduction preceding experience, even though it presupposes prolonged research (Marx, 1873).

The order of exposition must be justified by the dependencies within the object and the results of inquiry. Chronology, by contrast, establishes when processes occurred. Explaining a present structure may usefully begin with relations that emerged relatively late in its history. This expository choice retains the obligation to explain their genesis and avoids projecting them backward as if they had always existed.

The treatment of merchant capital illustrates the problem: its historical existence before capitalist industry does not automatically determine the place it should occupy in an explanation of developed capitalism. Its function depends on the social formation under examination. Rosental devotes part of his analysis of Capital to this relationship between logical and historical order (Rosental, 1961, pp. 366–377). Temporal priority, explanatory priority, and causal importance are different determinations.

Another example is the relationship among value, average profit, and the price of production. Analyzing a more determinate category requires reconstructing mediations and recognizing the assumptions of the presentation. Marx defines the price of production in terms of cost-price and average profit; this does not warrant identifying it directly with the individual value of each commodity (Marx, 1894, chap. 9). A complete assessment of the transformation problem requires a separate study. Its methodological significance here is to show that adding mediations changes the quantitative and conceptual relations under consideration.

04 Essence as an articulation of relations

4.1. Shared properties and constitutive relations

That several objects share a property allows them to be classified, but does not establish that the property explains their constitution. Two institutions may use similar technologies while reproducing different labor relations. Conversely, the same relation of domination may be organized through different technical and legal arrangements. Observable similarity provides a starting point for inquiry; its explanatory importance must be established.

Here, essence is understood as the articulation of relations whose reproduction makes the determinate identity of a process intelligible, and whose transformations help explain changes in that identity. The definition refers to an object, a scale, and a question. A relation may be decisive in explaining the wage-based character of a productive organization yet insufficient to explain the distribution of occupational disease within it.

The tradition of Rosental and Iudin emphasizes the connection between essence, relatively stable relations, and variable manifestations. It also recognizes that essence changes. This approach is fruitful when stability is investigated as the reproduction of relations under determinate conditions, and when every attribution of essentiality is accompanied by an explanation of its scope (Rosental & Iudin, 1971, entries “Essence” and “Essence and Phenomenon”).

4.2. A unity with multiple determinations

The unity of a process can be investigated through several structural dimensions. The following complementary questions are developed here for use when the object calls for them. Their articulation concerns the same reality examined through different relations; their selection must be justified in each study.

Connections can be formalized as a network; a measurement may require a metric structure; continuous change may be studied through differential equations. Adopting each tool requires defining its objects and conditions of application. Sharing an essence or belonging to a totality does not establish an isomorphism among components. An exact structural correspondence requires specifying the operations or relations preserved and demonstrating that the mapping satisfies the relevant properties.

4.3. Identity, contradiction, and reproduction

The identity of a process can be sustained through transformations of its components. An organization replaces machinery and personnel while maintaining certain relations of property and command. Its continuity requires activities, rules, material flows, and decisions that reproduce it. Investigating these conditions makes both its stability and its vulnerability intelligible.

A dialectical contradiction here designates an opposition between tendencies or relations that require and place pressure on one another within the process being investigated. We must show what is opposed, through which mechanisms, and with what effects. The word “contradiction” loses explanatory force when applied indiscriminately to a verbal inconsistency, a disagreement, a negative correlation, and any social conflict.

The relative autonomy of an institution forms part of this inquiry. The reproduction of a social formation depends on legal, political, and ideological mediations that have material effects. Engels’s letter to Bloch warns against turning economic determination into an exclusive explanation of every event (Engels, 1890). Establishing which mediations are decisive requires studying their reciprocal action in concrete situations.

4.4. Hegel, Marx, and the dialogue with Zubiri

In the Science of Logic, Hegel develops essence through relations of reflection, negativity, and ground. Its identity includes mediation and difference; reducing it to the formal identity of an object with itself removes precisely the problem he seeks to develop (Hegel, n.d.-b, §§ 807–816). A materialist appropriation must distinguish that development from the status it assigns to the relationship between thought and reality.

Zubiri offers his own examination of essence and of different historical ways of understanding it (Zubiri, 1985). His vocabulary can serve as a point of dialogue, provided the relevant passages are identified and a Marxist philosophy is not attributed to him. Moving between authors requires reconstructing arguments and differences; the recurrence of a term does not guarantee that its concept is identical.

The proposal developed here locates objective essence in the relations of the object, and the conceptual elaboration of that essence in the activity of knowing. Inquiry transforms concepts; praxis can transform the relations being studied. Distinguishing these operations makes it possible to explain their connection without making the existence of a process depend on someone conceiving it.

05 Essence, content, form, phenomenon, and appearance

These categories intersect, but their differences should be preserved. The following table establishes their use in this essay. It functions as an analytical tool while recognizing that translations and philosophical traditions may employ the terms differently.¹

Form organizes and conditions content. A contract establishes obligations and possibilities for action; a form of property shapes decisions and appropriation. Calling a relation “formal” therefore does not establish that it is superficial or causally irrelevant. Forms can stabilize a process, open possibilities, or block transformations.

A phenomenon need not coincide with what is immediately visible to the naked eye. Instrumental records, archives, and statistical procedures allow mediated manifestations to be investigated. The distinction between observation and explanation recognizes the need to elaborate relations; it does not divide reality into an accessible exterior and an absolutely inaccessible interior.

Appearance can be sustained by objective relations. In Marx’s analysis of fetishism, the problem concerns how social relations present themselves through things and acquire practical efficacy in exchange (Marx, 1867, chap. 1, section 4). Understanding this presentation requires explaining its social conditions and reproduction, alongside examining individual representations.

An adequate explanation of essence must account for its forms of manifestation. Claiming that a datum is misleading requires showing how it was produced, which relation it expresses, and why it leads to an inadequate interpretation. Otherwise, invoking the essential would become a means of shielding theory from any test.

The depth of an explanation is expressed in its capacity to reconstruct what is observable, its mediations, and its conditions of transformation.

06 Determinate negation and dialectical sublation

The German verb aufheben combines the senses of abolishing and preserving that Hegel regards as philosophically decisive. What is sublated loses its immediate independence and is preserved as a moment of a transformed relation (Hegel, n.d.-a, §§ 184–187). The term requires specifying which determination ceases to hold, what is preserved, and within which new articulation it acquires meaning.

Consider a hypothesis that interprets an increase in nominal wages as an improvement in purchasing power. Incorporating prices may show that the conclusion was incorrect. The wage datum is preserved, its sufficiency as a measure of purchasing power is negated, and its relationship to inflation is reconstructed. The initial information acquires a different place within a more determinate explanation.

A nominal wage rising from 100 to 110 and a price index rising from 100 to 120 yield a real wage of 110/1.20 ≈ 91.67 in base-period units. The nominal increase of 10% coexists with an approximate decline of 8.33% in the real wage. The calculation illustrates reinterpretation through additional relations; it does not, by itself, demonstrate a universal philosophical logic.

In inquiry, the sublation of an explanation may preserve results that remain valid under more restricted conditions. It may also require abandoning a premise. Its assessment requires argument and evidence: the mere succession of theories or combination of two positions does not constitute dialectical sublation.

Determinate negation is incompatible with automatically discarding inconvenient facts. A discordant observation may reveal a measurement error, an omitted condition, an explicable exception, or a structural limit of the theory. Each possibility requires investigation. The category of appearance does not authorize making an interpretation immune to criticism.

07 Universality, singularity, and parsimony

7.1. Generalizing while preserving differences

The universal, the particular, and the singular express relations of generality and determination. A law with a defined scope may be realized differently under particular conditions, and each singular case may reveal combinations that require refining that scope. The singular enters inquiry through evidence, comparison, and the testing of limits.

The problem of universals is likewise not resolved by declaring concepts less real than things. A conceptual formulation has a different mode of existence from a machine or a property relation. It can adequately represent objective relations, prove mistaken, and exercise material effects by guiding practices. The epistemological question concerns its adequacy and justification; the ontological question requires identifying the kind of entity and relation being discussed.

A critique of nominalism must address specific historical positions and be distinguished from a general critique of any use of names or classifications. Economy of assumptions, for its part, can be useful from different philosophical perspectives. Its use does not, by itself, establish that a scientific procedure belongs to a particular ontological school.

7.2. Simplicity, fit, and explanation

Parsimony counsels avoiding complexity that is unjustified relative to the purpose of a study. A compact model may be inadequate if it omits a relevant mechanism. A more extensive model may improve fit to observed data while impairing generalization. Moreover, predicting a response, identifying a causal effect, and explaining a historical formation are different tasks.

A general modeling schema can be written as follows:

The definition of each term depends on the problem. Counting coefficients can provide a measure of complexity, but constraints and regularization modify effective complexity. Nor is there a general equivalence between fewer coefficients and fewer variables: a categorical variable, a transformation, or an interaction may introduce several terms.

Comparing explanations requires establishing what is held constant: available information, task, evaluation conditions, and scope. A compact formula may conceal strong assumptions; a more detailed representation may make them explicit. Simplicity must be assessed together with empirical adequacy, coherence, and the proposed mechanism.

7.3. Transforming data while retaining the problem

Logarithms can help stabilize increasing variance or express multiplicative relations when the conditions permit. Choosing a transformation requires knowledge of the process and diagnosis of the data; the adequacy of the resulting model must then be checked (National Institute of Standards and Technology [NIST], n.d.).

If Y = exp(Xβ + ε) is proposed, taking logarithms gives log Y = Xβ + ε for positive responses. The variation under study now belongs to the logarithmic scale. Returning to the original scale requires attending to the estimation target, because exponentiating a mean on the logarithmic scale does not generally yield the original arithmetic mean.²

The useful methodological analogy consists in making operations explicit and assessing what they preserve or modify. Transforming data does not automatically eliminate historical contingencies, nor does it demonstrate that the object follows a particular dialectical structure.

08 Necessity, contingency, and transformation

Explaining a process requires distinguishing what is necessary under established conditions from what can vary within them. A structural relation delimits possibilities and exerts pressures, but reconstructing an outcome requires considering mediations and actions. A historical result cannot simply be deduced from the identification of a contradiction.

The oak example helps clarify the problem. An acorn contains material conditions for a possible biological development; germination requires specific circumstances and may fail. Continuity among seed, tree, and fruit must be investigated through organization, metabolism, reproduction, and environment. The future tree does not already exist fully realized within the seed.

In social processes, agents’ purposes form part of causality: a policy may pursue a goal and produce consequences different from those intended. Identifying that purpose requires evidence about decisions and practices. Attributing a goal to the historical process as a whole is an additional thesis requiring independent justification.

Metaphors of a spiral, center of gravitation, attractor, or fixed point can help formulate questions, but their technical meanings must be preserved. In a discrete system x_t+1 = F(x_t), a fixed point satisfies F(x*) = x*; its stability requires additional conditions. An attractor may be a more complex set and requires specifying both the dynamics and a notion of approach.

The reproduction of a social relation does not, by itself, demonstrate the existence of a mathematical attractor. Establishing one would require constructing the state space, dynamic rules, and stability criterion, and assessing their adequacy. Without such a formalization, it is preferable to speak of reproduction, tendency, or relative stability, according to what the evidence supports.

09 El Salvador, 2020–2022: hypotheses and mediations

Tensions between the United States and El Salvador offer a useful case for examining the difference between recording events and explaining their articulation. The period considered runs from 2020 through March 21, 2022. The analysis uses information from that period and assesses hypotheses without using later outcomes as retrospective proof.

9.1. Constructing the object and ordering the evidence

“Diplomatic tension” requires observable indicators: official statements, changes in cooperation, sanctions, financial conditions, and shifts in institutional exchanges. These phenomena involve different actors and mechanisms. An IMF decision should not automatically be attributed to the U.S. government or confused with a bilateral diplomatic statement.

The chronology establishes that documented diplomatic objections preceded the legislative decision on Bitcoin. This observation limits an explanation attributing the exclusive origin of all tensions to the cryptocurrency. It remains possible to investigate whether its adoption intensified existing conflicts or opened a specific front of financial negotiation.

9.2. Comparing hypotheses and mechanisms

Hypotheses can coexist and carry different weights depending on the outcome being explained. Identifying material interests requires reconstructing actors, resources, positions, and decisions. Expressions such as “Washington” or “international capital” can be useful shorthand, but they must be disaggregated when a concrete action is attributed.

U.S. support for authoritarian regimes in other periods can ground a critique of the consistency of its discourse. To explain this episode, that critique must be connected to evidence about the relevant decision-making mechanisms. Selective application of a declared principle and its possible causal efficacy in a particular conjuncture are different questions. Assuming that an institution never acts for a reason because it disregarded that reason in other cases introduces a conclusion that historical comparison alone does not establish.

9.3. Financial dependence and institutional influence

The IMF’s January 2022 statement identifies financial, fiscal, and consumer-protection risks and recommends removing Bitcoin’s legal tender status. It is a primary source for the institution’s stated position. Assessing the sufficiency of those reasons requires additional studies; inferring an exclusively geopolitical intention likewise requires specific evidence (IMF, 2022b).

U.S. influence within the IMF must be examined through quotas, votes, rules, and blocking power. The institutional handbook explains the effect of special 85% majorities and the U.S. capacity to block those decisions (Ramlogan & Fritz-Krockow, 2007, chap. 9). This position confers power, but it is not equivalent to exclusive ownership and does not establish a U.S. order behind every decision of the institution.

Bitcoin’s legal tender status coexisted with that of the dollar during the period studied. The thesis of a break with the dollar system therefore requires additional indicators: actual payment use, contract denomination, saving, credit, reserves, and external financing. Legal innovation and a substantial change in monetary dependence are distinct outcomes that must be measured.

9.4. What can be concluded

The documentation examined identifies several fronts of tension and situates Bitcoin within a specific financial conflict. It does not establish that this conflict is the sole or fundamental cause of all bilateral tensions. The most productive materialist interpretation frames an inquiry into the relations among financial dependence, institutional reorganization, and political interests, specifying mechanisms and evidence that can discriminate among explanations.

In this case, abstraction preserves relevant facts and reconstructs their relations. Declaring an institutional decision secondary requires specifying the outcome, period, and grounds of that judgment. Causal hierarchy is a revisable result of inquiry.

10 Algebra and physics: the scope of analogies

Interdisciplinary connections are fruitful when they respect the definitions of each domain. It is useful to distinguish analogy, which guides a comparison; formalization, which constructs a mathematical representation; and proof, which derives a conclusion from defined assumptions. A verbal coincidence between disciplines does not, by itself, establish any of these relations.

10.1. Rings and ideals

A ring has an additive abelian-group structure and an associative multiplication that distributes over addition; conventions concerning a multiplicative identity must be stated. A field is a commutative ring with an identity distinct from zero in which every nonzero element has a multiplicative inverse. A two-sided ideal I of a ring R must be an additive subgroup satisfying:

Absorption asserts membership in the ideal and does not imply the equality rx = xr. An example developed here is 2M₂(ℤ), the set of 2-by-2 integer matrices with even entries, within M₂(ℤ): evenness of the entries is preserved under multiplication by integer matrices, without imposing commutativity.

10.2. Annihilators: two constructions

For a left module M over a commutative ring R and a subset S ⊆ M, the annihilator is:

The condition must hold for every element of S. For example, in the ℤ-module ℤ/6ℤ, the element 2̅ has annihilator 3ℤ, because 2r is divisible by 6 exactly when r is divisible by 3. This is an exact algebraic condition, independent of a philosophical interpretation of the word “annihilation.”

In linear algebra, if W is a subspace of a vector space V over a field K, its annihilator in the dual is:

If V = ℝ² and W is the horizontal axis, the functionals φ(x,y) = by form W^∘. They retain information about the transverse direction while vanishing on W. This construction differs from the ideal of scalars annihilating elements of a module. Definitions of ideals and modules can be found in Altman and Kleiman (2013, chaps. 1 and 4).

Unique factorization of ideals requires assumptions. In a Dedekind domain, every nonzero proper ideal factors uniquely, up to order, into nonzero prime ideals; this claim does not hold for an arbitrary ring (Altman & Kleiman, 2013, chaps. 24–25). Uniqueness is a property relative to a defined structure and operation. It does not, by itself, establish a unique historical genesis of the object.⁴

10.3. Creation and annihilation operators

For the quantum harmonic oscillator, with dimensionless operators and normalized states, the relevant relations are (Meunier, n.d., chap. 7):

The commutator expresses the difference between two compositions of operators. Lowering by one quantum corresponds to the action of a on a state; the commutator’s result 𝕀 does not mean neutralization through the multiplicative identity. Moreover, a|0⟩ = 0 yields the zero vector, which must be distinguished from the vacuum state.

In quantum field theory, operators describe excitations of modes, and interaction processes require a specific dynamical description. Electron–positron annihilation can yield photons, with energy, momentum, and charge conserved in the process (Tong, n.d., section 6). Photons are physical entities carrying energy and momentum; the process does not convert matter into an immaterial substance called energy.

These examples let us ask what is preserved and what changes under precise operations. Comparison with dialectical sublation has heuristic value when its differences are delimited. Algebraic theorems and physical equations must be justified within their respective domains; their philosophical interpretation is a further task.

11 A research procedure

The usefulness of these categories becomes apparent when they are translated into research decisions. The following procedure is an operational proposal that can be revised according to the object. Its tasks feed back into one another and accommodate qualitative, quantitative, and mixed methods when relevant.

1. Delimit the process. Specify the object, unit of analysis, period, scale, and outcome to be explained. “The state,” “the economy,” and “artificial intelligence” require further determinations to become researchable objects.
2. Build the empirical record. Identify documents, observations, measurements, and gaps. Distinguish data, actors’ claims, and the researcher’s inferences.
3. Propose constitutive relations. Explain why certain relations would be necessary to the identity or reproduction of the process and which conditions allow them to operate.
4. Compare mechanisms and hypotheses. Establish alternative explanations, interactions, and evidence capable of supporting or weakening them.
5. Reconstruct mediations. Articulate institutions, practices, magnitudes, conflicts, and temporalities while preserving relevant differences.
6. Return to the cases. Assess chronologies, counterexamples, variation across situations, and observable consequences.
7. Revise the explanation. Specify its limits, modify categories, and document the uncertainties that remain.

Praxis connects knowledge and social intervention. In the Theses on Feuerbach, Marx places the question of truth in relation to practical activity (Marx, 2002, thesis II). This orientation requires investigating what is done, under which conditions, and with what results. The immediate success of an intervention may depend on mechanisms other than those assumed by its proponents; its analysis requires comparison and revision.

Objectivity is a social task: making operations explicit, allowing criticism, and testing results independently of the political convenience of the conclusions. Class position and interests can influence the questions asked and the uses of knowledge. Identifying them allows those conditions to be examined; justifying a claim additionally requires relevant argument and evidence.

12 Knowing essence to understand transformation

A materialist theory of knowledge studies how a socially situated subject reconstructs relations within a reality that precedes it and of which it is part. Abstraction makes it possible to determine relations; synthesis articulates their mediations; returning to historical situations allows the explanation to be assessed and revised.

Essence thus acquires a researchable content: constitutive relations, modes of reproduction, contradictions, and conditions of transformation. Knowledge of essence advances by explaining why a process manifests itself in certain ways, what it preserves through its variations, and under what circumstances it ceases to reproduce its identity.

The link between essence and phenomenon requires preserving evidence; the relationship between logic and history requires explaining mediations and genesis; and the connection between theory and praxis exposes knowledge to material consequences that must themselves be interpreted critically. The strength of the method lies in sustaining these requirements throughout concrete research.

Understanding a historical relation makes it possible to recognize both the conditions of its persistence and its possibilities of transformation. Such knowledge requires precise concepts, testable explanations, and a continuing readiness to revise what the analysis itself regards as fundamental.