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Balanophora Master
In EEG research, the N400 and the P600 are structurally associated, yet they are independently measurable. The only logically possible definitions are: the N400 reflects the relationship between the stimulus input and a specific cognitive category, with the production of this reading determined by the contact quantity of that cognitive category with non-prototypical exemplars; the P600 reflects the relationship between the stimulus input and the cognitive category boundary established by specific cultural norms, with the crossing state of the terminal-face boundary of that cognitive category determining whether this reading is produced. The conventional notion that semantic violations produce the N400, and syntactic violations produce the P600, bound the two readings to specific linguistic domains, obscuring the nature of these two readings for three decades. Indeed, these two readings can likewise be measured in EEG experiments within cross-modal domains such as music, faces, and voice. On the basis of the above positioning of the N400 and the P600, this paper derives a complete architecture for the autonomous operation of the cognitive act, four falsifiable predictions, and a zero-degree-of-freedom constraint formula for the operation of the cognitive act: |P600n⟩ ≝ ⟨N400n | P600n+1⟩, combining the event-components reflected by two observable readings to make them equivalent to one unobservable whole event.
Keywords: N400, P600, event-related potentials (ERP), cognitive act, contact quantity, cultural norms, structural associations, "equivalence → definition" operation, zero-degree-of-freedom identity
When participants hear a male voice say "I like to wear lipstick," a P600 reading is measured but no N400 reading (Lattner & Friederici, 2003, pp. 191–192): the semantics of the sentence conform to expectations, but the combination of a male voice with this semantic content violates the participant's cognition about the gender category. The participants produced a P600 reading in response to a grammatical gender violation spoken in a native accent (F(1,29) = 8.66, p = .006), but produced no P600 reading in response to the same violation spoken in a Turkish accent (all Fs < 1; Hanulíková et al., 2012, pp. 881–883).
These cases share a common feature: the ERP readings are constrained by variables (gender, accent) that fall outside linguistic concepts (semantics/syntax). Yet traditional research holds that semantic violations produce the N400 reading, and syntactic violations produce the P600 reading (Kutas & Federmeier, 2011, p. 627). When a semantic violation triggers a P600 reading rather than an N400 reading, the field labels this a "semantic P600" effect (Kutas & Federmeier, 2011, pp. 633–634; Kuperberg, 2007, pp. 26–41), without questioning the conventional understanding of the nature of the P600 reading and the N400 reading. This understanding mistook the linguistic concepts defined by linguists for the nature of the two readings, and organized experimental design around this principle for three decades. In fact, the nature of the N400 and P600 readings is domain-general (§3.2); Porkert et al. (2024, §4.3–§4.4), in a systematic review of 17 ERP studies, confirmed this view. The authors, however, offered no unified cross-domain explanation for this phenomenon.
This paper points out that the nature of the two readings, N400 and P600, reflects two explanatory variables: the contact quantity of a specific cognitive category with non-prototypical exemplars, and the crossing state of the terminal-face boundary of that category. These two explanatory variables reflect two independent operating processes of the cognitive act: contact quantity → the amplitude of the N400 reading (graded-value signal); the crossing state of the terminal-face boundary of the cognitive category → the presence or absence of the P600 reading (binary signal).
This is a theory-building article. Its argument is logically self-sufficient, requiring no new data. The argument proceeds by establishing the architecture (Section 2), verifying the architecture's validity against existing research findings (Section 3), diagnosing the misconceptions in prior research (Section 4), deriving methodological principles and four falsifiable predictions for subsequent research (Section 5), and finally deriving a zero-degree-of-freedom "equivalence → definition" identity: |N⟩ ≝ ⟨Xn | N+1⟩ (Section 6).
Stimulus inputs from different domains involve anatomically separable cortical pathways: voice-selective superior temporal sulcus (Belin et al., 2000, pp. 309–310), the fusiform face area (Kanwisher et al., 1997, pp. 4304–4306), a left-lateralized temporo-frontal language network (Friederici, 2011, pp. 1358–1360), and socially specialized regions including the temporo-parietal junction and the medial prefrontal cortex (Van Overwalle, 2009, pp. 831, 843–844). Different domains engage different brain regions within the same distributed network (Kutas & Federmeier, 2011, p. 639), reflecting the separability of the domains. At the same time, two ERP readings — the N400 reading and the P600 reading — can both be measured across different domains, indicating that the N400 and P600 readings, as explanatory variables, are domain-general (§3.2). These domains are proxy variables for the same pair of explanatory variables, not explanatory variables themselves.
On the basis of this domain separability, the five-layer architecture of the cognitive act is derived, from specific cultural norms to the observable subjective output layer:
Both the N400 and the P600 are Layer 3 readings; they reflect two different events of the cognitive act (§2.2–§2.3). The event reflected by the N400 reading is the cognitive act detecting the degree of unexpectedness of the stimulus input within the participant's specific cognitive category: a continuous gradient value. The lower the unexpectedness, the weaker the N400 amplitude; the higher the unexpectedness, the stronger the N400 amplitude; when entirely expected, no N400 reading is produced. The event reflected by the P600 reading is the cognitive act determining whether to cross the terminal-face boundary of that cognitive category: a binary signal. If crossed, the reading is produced; if not crossed, it is not produced.
The causal variable. Cultural norm internalization means that a specific culture establishes a boundary on the accumulated exemplars in the participant's cognition: specific cultural norms stipulate which exemplar is the prototypical exemplar of a specific cognitive category (the initial-face boundary of that cognitive category), which exemplars belong to that cognitive category, and which exemplar is the terminating exemplar of that category (the terminal-face boundary of that cognitive category).
The mechanism. The P600 reading reflects the crossing state of the terminal-face boundary of a cognitive category. The crossing state determines the presence or absence of the posterior positivity peaking around 600 ms post-stimulus (P600): a binary reading.
Cognitive category boundary. Specific cultural norms (linguistic grammar, moral laws, institutional rules, religious doctrines, etc.) specify a boundary cut-point on the line of accumulated exemplars in the participant's cognition, stipulating which exemplars belong to which specific cognitive category. Without specific cultural norms, no cut-point exists and no cognitive category can be established. When newly accumulated exemplars cannot be classified by the participant into any existing cognitive category, the cognitive act crosses the terminal-face boundary of the existing cognitive category and simultaneously establishes a new cognitive category. For example, the first time anyone hears about an "EEG experiment," the input cannot be classified into any existing cognitive category, so the cognitive act crosses the terminal-face boundary of an existing cognitive category and establishes the new cognitive category "EEG experiment." Thereafter, each time the individual discusses or operates EEG experiments, that individual dynamically reshapes this new cognitive category. When a new exemplar appears that cannot be classified into any existing cognitive category, the terminal-face boundary of the cognitive category "EEG experiment" is crossed in turn, and yet another new cognitive category is established, and so on. In other words, the crossed boundary has two faces: the terminal face of the old cognitive category and the initial face of the new cognitive category (§2.4).
Previously internalized cognitive category boundaries are mutable; when the individual receives new specific cultural norms, the previously assigned boundary cut-point changes (§3.4).
The first cognitive category. For any individual, before the first cognitive category is established, there is no prior cognitive category whose terminal-face boundary can be crossed. The first cognitive category, P6001, is automatically established at birth; therefore, the process of crossing the initial-face boundary of the first cognitive category can never be measured: all measurable P600 readings in an EEG experiment are P600n+1, where n+1 ≥ 2. When a P600 reading is measured, the stimulus input activates the cognitive act to cross the terminal-face boundary of cognitive category n, which is simultaneously the initial-face boundary of cognitive category n+1 — both share a single boundary. Since only the P600n+1 reading can be measured in an EEG experiment, using P600n+1 to refer simultaneously to the terminal-face boundary of cognitive category n and the initial-face boundary of cognitive category n+1 is the only accurate way of handling it.
The first cognitive category is the "knowable" category. At birth, the individual crosses from nothingness into a cognitively accessible world, establishing this first cognitive category. The terminal face of its boundary points toward the "unknowable." Unlike all the cognitive categories within the knowable, the unknowable cannot be defined as any kind of category because it cannot be known; nor can it be assigned any subscript. All exemplars knowable by a specific individual, without exception, are further subdivided into finer cognitive categories within the cognitive category of the "knowable". All exemplars unknowable to a specific individual automatically fall into the "unknowable," belonging to no cognitive category and producing no ERP reading.
The causal variable. Contact quantity refers to the amount of a participant's contact with non-prototypical exemplars of a specific cognitive category in a specific domain. Contact quantity is not equivalent to contact time. Kang and Rubin (2009, pp. 449–451) found that raw contact time with non-native speakers could not predict speech evaluation outcomes (strongest association p = .051), while diverse experience reflecting contact quantity proved diagnostic: linguistic maturity could predict listening comprehension (β = 0.17, p = .044), and language-teaching experience could predict teaching quality ratings (β = 0.18, p = .036). "Diagnostic" here refers to new information that widens the expectation distribution, distinct from prolonged, repeated contact with old information the participant already knows. Allport's (1954) contact hypothesis identified the conditions under which prejudice between groups is reduced: equal status, common goals, institutional support, and common interests (Chapter 16, p. 280). The present architecture explains why these conditions work: contact with diverse information makes people more inclusive — the expectation distribution widens. Allport distinguished quantitative from qualitative contact (pp. 262–263) but did not explicitly identify the diversity of the conditions as the cause of prejudice reduction.
The mechanism. The expectation distribution width is determined by the diversity of exemplar types the participant has dynamically accumulated. Each time the participant comes into contact with a new exemplar type, the cognitive act dynamically updates the expectation distribution width of the specific cognitive category in that corresponding domain. The expectation distribution width determines the amplitude range of the centro-parietal negativity peaking around 400 ms post-stimulus (N400): a continuous gradient value.
Based on the above analysis, for any cognitive category n, the reading-output patterns of N400 and P600 can be formalized as: When only a P600 reading is measured in an EEG experiment, cognitive category n has just been established; the current stimulus input is the prototypical exemplar of cognitive category n, and therefore no prediction error is generated. When only an N400 reading is measured in an EEG experiment, this indicates that the current stimulus input falls within cognitive category n and does not cross the terminal-face boundary of cognitive category n. When both readings are simultaneously measured in a single EEG experiment, this indicates that the current stimulus input activates the cognitive act to cross the terminal-face boundary of cognitive category n and simultaneously establish cognitive category n+1. When neither reading is produced, there are two possible situations. The first situation is exemplar coincidence: the current stimulus input coincides with the prototypical exemplar that established cognitive category n. For example, when a participant hears "a man likes to wear lipstick" for the first time, cognitive category n is established; upon hearing the same statement again, the stimulus input falls at the center of cognitive category n, and this individual produces neither an N400 reading nor a P600 reading. The second situation is that the current stimulus input is unknowable to the participant, is classified by the participant as "unknowable," and therefore produces no ERP reading.
N400 and P600, although independently measurable (§1), are not in a random combinatorial relation; rather, a logically necessary structural relation exists between the two readings. This relationship is anchored by six kinds of relations: N400 amplitude continuity, the symmetry of the cognitive category boundary, the sequential relationship, the set-theoretic relationship, the geometric relationship, and the logical-entailment relationship.
N400 amplitude continuity. The amplitude of the N400 reading is a continuous gradient value, from no amplitude to weak amplitude to medium amplitude to large amplitude. The smaller the difference between the stimulus input and the prototypical exemplar, the weaker the N400 amplitude; the larger the difference, the stronger the amplitude. Each time the participant comes into contact with a new non-prototypical exemplar, the cognitive act adjusts the expectation distribution width of that cognitive category — that is, "differentiation + integration" as one single cognitive act. The change in amplitude from none to large reflects the cognitive act's movement from an object with no "differentiation + integration" (no amplitude) to an object that can be infinitely "differentiated + integrated" (large amplitude); so long as the terminal-face boundary of that cognitive category has not been crossed by the cognitive act, the act of "differentiation + integration" is perpetually ongoing. This nature of the cognitive act makes all exemplars within a specific cognitive category form a continuum: the number of intermediate exemplars between any two exemplars is potentially infinite. But the concept of "continuum" itself cannot generate the concept of a boundary, because there is no natural breakpoint between one exemplar and the next.
The symmetry of the cognitive category boundary. The P600 reading reflects a threshold-gated binary reading (an all-or-none response): the stimulus input either triggers the production of this reading or does not. When triggered, it indicates that the current stimulus input activates the cognitive act to cross the terminal-face boundary of an existing cognitive category and establish a new cognitive category. When a P600 reading is measured in an EEG experiment, it indicates that the current stimulus input completes a single event — two sides of the same coin: the existing category ends here, and a new category begins here. At this point, the terminal face and the initial face of the cognitive category boundary are symmetric: for the existing category, what is crossed is the terminal-face boundary; for the new category, what is established is the initial-face boundary. Both are symmetric perspectives on the same boundary line, but the concept of "boundary" itself cannot determine which perspective carries meaning for the cognitive act.
The sequential relationship between N400 and P600. N400 peaks at ~400 ms post-stimulus, P600 at ~600 ms. This 200 ms time difference is the sequential operating trajectory of the same cognitive act: within a specific cognitive category, the stimulus input first activates the cognitive act to detect the participant's degree of unexpectedness regarding this stimulus input; the cognitive act then determines whether to select this stimulus input as the terminating exemplar of that category (that is, whether to cross the terminal-face boundary of that cognitive category). The reverse is impossible: once the terminal-face boundary is crossed, a new cognitive category is established; the cognitive act can no longer cross back through the initial-face boundary of this new cognitive category to establish the previously existing cognitive category. At this point, the task of the cognitive act is to detect the participant's degree of unexpectedness regarding the stimulus input relative to the prototypical exemplar of the current cognitive category, and to determine whether to cross the terminal-face boundary of the current cognitive category. The vectoriality of time and the determinacy of the cognitive act's task together impose a sequential relationship on this single process: the 400 ms reading must precede the 600 ms reading, and the crossing act applies only to the terminal-face boundary of the current cognitive category. But the concept of "sequence" itself cannot explain why the boundary that serves as the terminal face of a cognitive category can, against the direction of the sequence, cross non-prototypical exemplars to reach the initial-face boundary of the same cognitive category, thereby completing the concept of "cognitive category," yet cannot cross that initial-face boundary.
The set-theoretic relationship between N400 and P600. Every exemplar within a specific cognitive category is an element of that cognitive category as a set. The continuous gradient of the amplitude of the N400 reading, from weak to strong, makes these elements form a continuous sequence. The number of elements can therefore be infinite. At the same time, the mutability of cognitive category boundaries (§2.2) makes the characteristic function of the set constantly variable: when the boundary shifts (a P600 reading is produced), which exemplars belong to the set and which do not change with it. Set theory classifies elements into specific sets using explicit characteristic functions, and therefore the concept of "set" itself cannot handle a set in which both the characteristic function and the elements are continuously changing.
The geometric relationship between N400 and P600. When the stimulus input activates the cognitive act to cross the terminal-face boundary of an existing cognitive category and establish a new cognitive category, the prototypical exemplar of the new cognitive category automatically becomes its geometric center. Thereafter, each non-prototypical exemplar from the same domain, upon entry, automatically forms a geometric body with this prototype, having a geometric center (the prototypical exemplar) and a geometric periphery (the non-prototypical exemplars): the greater the difference between the stimulus input and the prototypical exemplar, the farther the distance from the geometric center. But the mutability of the cognitive category terminal-face boundary (that is, the non-prototypical exemplar selected by the cognitive act as the terminating exemplar) (§2.2) makes the shape of this geometric body also variable: when the position of the cognitive category terminal-face boundary shifts (a P600 reading is produced), the geometric distance between the non-prototypical exemplar and the prototype shifts with it. Geometry requires a determinate distance from periphery to center, but the geometric distance of the cognitive category as a geometric body is in a state of constant variability. Therefore, the concept of "geometry" itself cannot explain a geometric body whose shape can change at any moment.
The logical entailment between N400 and P600. A cognitive category must first be established before the cognitive act can begin detecting prediction error values within it. Upon being activated by a specific stimulus input, the cognitive act crosses the terminal-face boundary of the existing cognitive category and establishes a new cognitive category. At that moment, no non-prototypical exemplars have yet been encountered within this new cognitive category; no expectation violation is possible, and therefore only a P600 reading can be measured. When only a P600 reading is produced, the stimulus input activates the cognitive act to cross the terminal-face boundary of the current cognitive category. At this point, the reading of this cognitive category's terminal-face boundary, P600n+1, necessarily entails the initial-face P600n of the same cognitive category, because the terminal face and the initial face are the two ends of the same cognitive category, and the establishment of the initial-face boundary necessarily precedes the crossing of the terminal face. When only an N400 reading is produced, N400n likewise entails P600n: the cognitive act can only carry out detection work within a cognitive category whose prototypical exemplar already exists. When both readings, P600n+1 and N400n, are simultaneously measured, both readings entail P600n: the cognitive act both detects the prediction error value within the same cognitive category and simultaneously crosses the terminal-face boundary of that cognitive category. When a stimulus input is knowable to a participant yet produces no ERP reading, it still entails P600n: the current stimulus input coincides exactly with the prototypical exemplar that established this cognitive category (§2.3). In other words, so long as a stimulus input is knowable to the participant, whichever reading-output pattern appears entails the corresponding cognitive category's initial-face boundary (P600n). But what does this multi-fold entailment mean? The concept of "logical entailment" itself cannot answer.
The above six relations establish that the N400 and P600 readings are structurally associated. But why does this structural association exist? All concepts that reveal this association cannot themselves answer this question.
The preceding section demonstrated the structural relationship between N400 and P600; each structural relation internally encounters a problem that its own concept cannot answer (§2.4). This section uses the inductive act and the deductive act of cognition to answer these six questions: the answers to the six questions reflect the complete process of the cognitive act autonomously operating one whole event. The inductive act is the prerequisite for the deductive act.
The act of induction can only operate on events that have already occurred — this is a constraint on the act of induction itself. The act of induction answers the first five questions:
Induction and N400 amplitude continuity. The continuum of exemplars offers no natural breakpoint. When the act of induction is initiated, the continuity of exemplars is interrupted, and the interruption creates a breakpoint on the continuum, and the breakpoint is the boundary.
Induction and the symmetry of the cognitive category boundary. The two faces of the cognitive category boundary are symmetric. The act of induction determines that only the terminal-face boundary can face toward events that have already occurred, and therefore the terminal-face boundary of the cognitive category is necessarily reached by the inductive act; the initial-face boundary of the cognitive category faces toward events that have not yet occurred, and is therefore unreachable by the act of induction. The act of induction determines that what carries meaning for the cognitive act is the terminal face of the cognitive category boundary, rather than the initial face of the cognitive category boundary — the act of induction breaks the symmetry of the boundary.
Induction and the sequential relationship. As for the question that the concept of sequence itself cannot answer, the act of induction provides the answer: the act of induction begins from the terminal-face boundary of the cognitive category, crosses the 200 ms time difference between the P600 and N400 readings against the direction of the sequence, and advances toward the initial-face boundary of the same cognitive category. At the same time, the act of induction cannot cross the initial-face boundary of the same cognitive category to point toward the initial-face boundary of another, already existing cognitive category, because crossing the initial-face boundary of the same cognitive category would dissolve the very concept of "cognitive category" itself. Without the concept of "cognitive category," the "pointing act" toward another cognitive category cannot logically stand by itself.
Induction and set theory. A cognitive category, as a set, has elements (exemplars) and a characteristic function (the cognitive category boundary) in constant flux — a problem that set theory itself cannot answer. When the act of induction reaches the initial-face boundary of that cognitive category, that initial-face boundary is simultaneously the prototypical exemplar of that cognitive category — boundary and exemplar are one. At this point, the cognitive category as a set contains only one prototypical exemplar as an element, and this prototypical exemplar is simultaneously the characteristic function of the cognitive category — the characteristic function and the element are one. Therefore, the premise upon which the concept of "set" holds true rests not on static characteristic functions partitioning static elements, but on the ontologically constitutive feature that the element and the characteristic function are one.
Induction and geometry. When the cognitive category, as a geometric body with a shape, begins to shift its geometric periphery, its shape changes with it — a problem that geometry itself cannot answer. When the act of induction begins, the distance from the periphery to the geometric center of the cognitive category as a geometric body also continually shortens; when the distance between the periphery and the geometric center reaches zero, the geometric center and the periphery coincide. Coincidence means no distance; no distance means no shape; no shape means no "geometry"; without "geometry," only the "act of induction" itself remains, existing as a concept.
These five answers are not five parallel solutions to five problems, but the complete inductive process of the act of induction, which has induced a single logical chain: the initiation of the act of induction halts the continuous process of the continuum, creating a breakpoint — this breakpoint is the boundary. The boundary generates symmetry, and the orientation of the act of induction breaks the symmetry, endowing the terminal-face boundary that faces toward the initial-face boundary of the same cognitive category with meaning. Thereafter, the act of induction crosses, against the direction of the sequence, from this terminal-face boundary toward the initial face of that cognitive category, across the 200 ms time difference and all intermediate non-prototypical exemplars, and finally coincides with the initial-face boundary of the same cognitive category. When the terminal-face boundary and the initial-face boundary of the same cognitive category coincide, the act of induction will no longer cross the initial-face boundary of this cognitive category to induce the initial-face boundary of another, already existing cognitive category — otherwise the very concept of a "cognitive category" would be dissolved. At this point, the cognitive category as a set contains one exemplar and one cognitive-category boundary: it contains one element and one characteristic function, and the two are one. And as a geometric body, at this point the distance between its periphery and geometric center is zero; the shape of the geometric body disappears, the formed becomes the formless, and only the "act of induction" remains, existing as a concept. "Concept," as a concept, exists, and cannot be measured. The "concept" is produced by the cognitive act, and therefore the cognitive act is ontologically prior to the concept. The "cognitive act" is a kind of action, and the "action" itself is the source of all actions: to make a moving thing still requires applying an action, and to make a still thing move likewise requires applying an action. Whether still or moving, both originate from the action. This is the self-sufficiency of the action, which is at the same time the self-sufficient action. The self-sufficient action is "autonomy."
Deduction is the application of induction. The deductive act of cognition autonomously unfolds along the logical chain induced by the inductive act:
In the beginning, the "cognitive act" is an autonomous being in which prototypical exemplar and prototype boundary are one; no instrument can directly measure it. When specific cultural norms intervene, the prototypical exemplar and the prototype boundary of the cognitive act begin to separate: the prototypical exemplar has lost its corresponding prototype boundary, and the prototype boundary has lost its corresponding prototypical exemplar. When the cognitive act, as a complete concept, begins to operate autonomously, the prototypical exemplar — because it has lost the prototype boundary and thus has no concept of "boundary," and does not know that it can stop — consequently gives birth to infinitely many non-prototypical exemplars; the prototype boundary has lost its corresponding prototypical exemplar, and thus, in accordance with specific cultural norms, arbitrarily selects one among infinitely many non-prototypical exemplars to serve as its prototypical exemplar. Because a non-prototypical exemplar is not the prototypical exemplar of the prototype boundary, and the boundary internalized by specific cultural norms is not the prototype boundary of the prototypical exemplar, an unbridgeable 200 ms time difference always exists between the non-prototypical exemplar selected as the prototypical exemplar and the boundary internalized by specific cultural norms. In order to eliminate this time difference and find each other, the prototypical exemplar and the prototype boundary of the same cognitive act transform from the formless into formed images. The formed gives birth to geometry; geometry gives birth to change; change gives birth to rules; rules give birth to sets; sets give birth to infinitely varying elements (non-prototypical exemplars) and characteristic functions mutable at any time (the terminal-face boundary of the specific cognitive category). All observable images exist only to restore the prototypical exemplar and the prototype boundary of the cognitive act.
The cognitive act itself is never measured at any point in this event, yet both the exemplar-birth event and the exemplar-selection event are events autonomously completed by the cognitive act; the exemplar-birth event and the exemplar-selection event are offshoot events of a single cognitive act. The offshoot events entail the whole event, and therefore the four output patterns of the N400n and P600n+1 readings (§2.4) that reflect these offshoot events always entail P600n.
To narrate a whole event, each offshoot event must be clearly described and then combined; only then can the complete picture of the whole event be presented. To describe is to define; the combination of offshoot events into the whole event is an equivalence operation. Therefore, when presenting the whole event autonomously completed by the unmeasurable P600n, the two measurable readings, N400n and P600n+1, must be used to perform the "equivalence → definition" operation upon it: |P600n⟩ ≝ ⟨N400n | P600n+1⟩.
In this formula, '|' denotes the boundary, '⟩' denotes the unfolding direction of the cognitive deductive act, '⟨' denotes the gathering direction of the cognitive inductive act, and '≝' denotes the act of first performing the operation of equivalence and then performing the operation of definition — a behavioral symbol. |P600n⟩ denotes a complete cognitive event that exists autonomously and operates autonomously but cannot be measured. This cognitive event performs the "equivalence → definition" operation through the following five possible reading-output patterns:
First pattern, the cognitive event of producing only an N400 reading "equivalence → definition" P600n: |P600n⟩ ≝ ⟨N400n. Second pattern, the cognitive event of producing only a P600 reading "equivalence → definition" P600n: |P600n⟩ ≝ |P600n+1⟩. Third pattern, the cognitive event of producing an N400 reading and the cognitive event of producing a P600 reading "equivalence → definition" P600n: |P600n⟩ ≝ ⟨N400n | P600n+1⟩. Fourth pattern, the stimulus input is identical to the prototypical exemplar, and the cognitive event of producing no reading "equivalence → definition" P600n: |P600n⟩ ≝ ⟨ | ⟩. Fifth pattern, the current stimulus input cannot be cognitively recognized by the participant and cannot be classified into any cognitive category previously established by the participant; at this moment, the unknown "equivalence → definition" P600n. The unknown cannot be formalized by any symbol (§2.2); hence it is formalized as: |P600n⟩ ≝ .
The meaning of the first cognitive category. For any individual, the first cognitive category is already automatically established at birth, and every subsequent cognitive category is established after crossing the terminal-face boundary of the first cognitive category (§2.2). The initial-face boundary of the first cognitive category faces the knowable; its terminal-face boundary faces the unknowable. The knowable has no end; the final conclusion reached by the act of deduction is that the cognitive act is perpetually establishing the initial-face boundary. As established earlier, the initial-face boundary of the cognitive category carries no meaning. The act of induction enables us to trace back to the initial-face boundary of the first cognitive category (the knowable category), which is simultaneously the terminal-face boundary of the unknowable. As established earlier, the terminal-face boundary of the cognitive category carries meaning. In other words, the unknowable has meaning but cannot be known; the knowable can be known but has no meaning.
Time as the container of cognition. Time, as the container of the cognitive act, always remains ahead of the cognitive act: the vectoriality of time. The vectoriality of time guarantees the uniqueness of all the above cognitive acts. No two acts of induction ever coincide; no two acts of deduction ever coincide. The P600n of the previous moment is not the P600n of the next moment; the N400n of the previous moment is not the N400n of the next moment; the P600n+1 of the previous moment is not the P600n+1 of the next moment; the knowable of the previous moment is not the knowable of the next moment; the unknowable of the previous moment is not the unknowable of the next moment. Ultimately, everything of the previous moment is not everything of the next moment, and this fundamentally precludes the possibility of any individual's cognitive act falling into chaos.
In summary, at any moment, so long as one recognizes that "the knowable has no meaning; only the unknowable has meaning," meaning can be found at any moment; but one must still remember: the meaning of this moment is not the meaning of the next moment. At any time, the formula |P600n⟩ ≝ ⟨N400n | P600n+1⟩ holds. This is the cognitive act's recursion over time: without beginning, without end.
The five-layer architecture of the cognitive act (§2.1) demonstrates that Layer 3 and Layer 4 are mutually independent. Layer 3 is the non-autonomous ERP readout layer: the participant cannot autonomously control the production process of the two readings (N400 and P600). Layer 4 is the subjective output layer that the participant can autonomously control: the participant can produce subjective output data that are faithful or unfaithful to the results of the ERP readout layer. Because the cognitive-behavioral paths between the two layers cannot be inferred from each other, the logical space is 4 ERP readings (N400 ± × P600 ±) × 2 expression modes (faithful/unfaithful) = 8 cognitive-behavioral paths: A+F (N400, faithful), A+U (N400, unfaithful), B+F (P600, faithful), B+U (P600, unfaithful), C+F (N400+P600, faithful), C+U (N400+P600, unfaithful), D+F (neither, faithful), D+U (neither, unfaithful).
Two participants with identical subjective-output-layer data, or the same participant producing identical subjective-output-layer data at different moments, may be following entirely different cognitive-behavioral paths. Results based solely on a single layer — whether Layer 3 or Layer 4 — cannot distinguish these paths; a complete ERP study requires data from both cognitive-behavioral layers, Layer 3 and Layer 4, collected simultaneously.
Section 3 verifies the framework derived in the preceding sections against twelve authoritative works of ERP research, using the following notational convention to formalize the eight cognitive-behavioral paths. Each study is annotated as [N400: {+, −, ?, ∅}, P600: {+, −, ?, ∅}, Φ: {F, U, ?, ∅}], where "+" indicates that the relevant reading is measured, "−" indicates that the relevant reading is not measured, "∅" indicates that the participant cannot know the specific stimulus input; "F" indicates that the participant's subjective output layer faithfully outputs the result of the ERP readout layer, "U" indicates that the participant's subjective output layer unfaithfully outputs the result of the ERP readout layer, and "?" indicates that no EEG-layer ERP reading measurement was conducted, or no subjective-output-layer data was collected.
This chapter draws on twelve authoritative works of ERP research, completed by different authors, at different times, with different research participants, and in different research contexts, to verify the present framework. The proxy variables involved come from different domains, such as accent, age, gender, social class, semantics, syntax, pragmatics, empathy, identity, and music. All of these studies converge on a single unified pattern: the output regularities of the N400 reading can be explained by the contact quantity of the specific cognitive category with the non-prototypical exemplars of a specific domain, and the output regularities of the P600 reading can be explained by whether the specific cultural norm reflected by that domain was internalized before or during the experiment. This unified convergence pattern proves that two domain-general explanatory variables necessarily exist: contact quantity and the internalization of specific cultural norms. §3.2 presents the domain-generality of both readings; §3.3 presents how contact quantity explains the output regularities of the N400 reading; §3.4 presents how the internalization of specific cultural norms explains the output regularities of the P600 reading. In the specific analyses (§3.3, §3.4), the relevant studies are all annotated using the diagnostic notation stipulated in §2.6.
For three decades, the field has bound the nature of the ERP readings to specific concepts in the linguistic domain, holding that the N400 reading reflects "semantic" violations and the P600 reading reflects "syntactic" violations (§1). Yet even within a single linguist-defined concept, this view fails. Porkert et al. (2024, §4.4, p. 7), in a systematic review of 17 studies, confirmed: when sentence structure forced readers to infer the referent's gender before the critical word, the semantic violation of gender produced a P600 reading (5/5 cases); when the sentence structure did not require the reader to make an advance inference, the same violation produced an N400 reading (4/4 cases). In other words, what determines the ERP output is not the specific category of linguistic concepts but whether the reader has established the cognitive category of "the gender of the referent" in the semantic domain (§2.2). Indeed, music, faces, and voice all independently produce both N400 and P600 readings (see below); cross-domain evidence demonstrates that regardless of which specific domain the stimulus input belongs to, the operating mechanism of the same explanatory variable is entirely consistent (verified item by item below).
N400 domain-generality. The N400 reading is not bound to any specific domain. First, the N400 reading is characterized by domain separability: Wu and Cai (2026) simultaneously manipulated social-gender violations (e.g., a man saying "I'm going to have a manicure this weekend") and biological-gender violations (e.g., a man saying "The first time I got pregnant I had a hard time") within a single paradigm, finding that social-gender violations produced an N400 reading (β = −0.89, p = .005; pp. 553–554) while biological-gender violations produced a P600 reading. Furthermore, the authors found that the higher a participant's personality trait of openness (openness to experience, i.e., receptivity to non-traditional ideas), the smaller the amplitude of the N400 reading produced by social violations (β = 0.71, p = .026; p. 554); openness, however, did not constrain P600 reading production under biological violation conditions (β = −0.40, p = .245; p. 554). The same participants, the same experimental design, the same control variables, yet the same personality trait produced different constraining effects on ERP readings across different domains, verifying that the operating processes of the cognitive act in different domains are mutually independent (§2.1). Second, the N400 reading is the same in nature across different domains: Van Berkum et al. (2008) found that three distinct social domains—speaker age, gender, and social class—all produced the same N400 reading with an identical scalp distribution. The domain-generality of this explanatory variable (contact quantity) is further verified in music: Koelsch (2012, §5.5.1) reported the same N400 effect for musical excerpts, chords, and single timbres.
P600 domain-generality. First, the P600 reading is characterized by domain separability: Wu and Cai (2026) simultaneously manipulated social-gender violations and biological-gender violations within a single paradigm, finding that biological-gender violations produced a P600 reading (β = 1.43, p = .011; pp. 553–554), while social-gender violations produced only an N400 reading. Grey et al. (2020) further verified this separability: when foreign-accented sentences were paired with an Asian face, grammatical errors produced a P600 reading (F(1,26) = 5.56, p = .026; Results, §3.2.2), whereas when the face cue was absent, the same grammatical errors did not produce a P600 reading. The same participants, the same experimental design — the operating modes of the cognitive act in two different domains differ, and the above two studies once again demonstrate that the operating processes of the cognitive act in different domains are mutually independent (§2.1). Second, the P600 reading is the same in nature across different domains: Patel et al. (1998, pp. 724–726) found that P600 readings produced by syntactic violations in language and harmonic violations in music were statistically indistinguishable in amplitude and scalp distribution (domain main effect: F(1,14) = 2.37, p = .15). Van Herten et al. (2005, p. 247) found that purely semantic reversal anomalies produced a P600 reading, with a scalp distribution indistinguishable from the "syntactic P600" (F(1,41) = 8.77, p < .01). These two studies, spanning music and linguistic domains, jointly demonstrate that the ways in which cultural norms are internalized across different domains are the same — P600 is not bound to any specific domain.
The present architecture has derived that the amplitude of the N400 reading is determined by contact quantity: as the contact quantity of a specific cognitive category with non-prototypical exemplars increases, the participant's expectation distribution widens, and the amplitude of the N400 reading correspondingly grows from none to weak to large until it triggers a P600 reading. At zero contact, no N400 reading is produced (§2.3).
Zero contact: no ERP reading is produced. When a stimulus input cannot be classified by the participant into any existing cognitive category, the cognitive act can neither detect the degree of unexpectedness of the stimulus input within a specific cognitive category nor determine whether to cross the terminal-face boundary of that cognitive category, and therefore cannot produce an ERP reading (§2.3). Grey and van Hell (2017) found that for Pennsylvania monolinguals listening to English spoken with a Chinese accent — those who could not identify the Chinese accent (non-identifiers, 64% of the sample) — no ERP reading was measured at all in response to L2 grammatical error stimuli (pp. 103–104). For such phenomena, the present framework's explanation is as follows: the participants cannot identify the "Chinese accent," and therefore the "Chinese accent" as stimulus input cannot be classified into any cognitive category (§2.2). This case measured both N400 and P600 readings, and also collected behavioral data, but such behavioral data do not belong to the subjective output layer as defined by the present framework; therefore the diagnostic annotation assigned by the present framework is as follows: [N400: ∅, P600: ∅, Φ: ?].
Low contact: narrow expectation distribution, large N400 amplitude. When the participant's contact quantity with non-prototypical exemplars in a specific domain is small, the participant establishes a narrow expectation distribution, and a non-prototypical exemplar presented as a stimulus input will produce an N400 reading with a large amplitude (§2.3). Proverbio et al. (2018) found that only male participants produced a significant N400 reading in response to male-character gender violation stimuli (Group × Congruence: F(1,31) = 6.26, p < .018; pp. 11–12). No P600 reading was measured in the same experiment, indicating that the current stimulus input fell within the specific cognitive category and the cognitive act did not cross the terminal-face boundary of that cognitive category. This case measured both N400 and P600 readings, and did not collect subjective output layer data; therefore the diagnostic annotation assigned by the present framework for this case is: [N400: +, P600: −, Φ: ?].
Moderate contact: the amplitude of the N400 reading is reduced. As the participant's contact quantity with non-prototypical exemplars increases, the participant's expectation distribution widens, and repeated presentation of the same non-prototypical exemplar weakens the N400 reading (§2.3). Grey and van Hell (2017) found that accent identifiers (i.e., participants who identified the Chinese accent, 36% of the sample) produced an N400 reading to L2 grammatical error types without a P600 reading; the authors found that the nature of the N400 reading in this case lies between the non-identifiers' null response and the high-contact pattern (pp. 103–104). This case measured both N400 and P600 readings, and also collected behavioral data, but such behavioral data are not subjective output layer data as defined by the present framework; therefore the diagnostic annotation assigned by the present framework is as follows: [N400: +, P600: −, Φ: ?].
High contact: N400 amplitude disappears. When the participant's contact quantity with non-prototypical exemplars of a specific cognitive category is very high — that is, the participant has repeatedly contacted sufficiently diverse exemplars — any stimulus input belonging to this cognitive category will fall entirely within the participant's expected range, and the participant's expectation distribution will thereby widen to its maximum extent, and the amplitude of the N400 reading it produces undergoes a change from presence to absence (§2.3). van den Brink et al. (2012, pp. 178–179) found that women's N400 to speaker-identity violations dropped from 1.56 μV in the first half (p = .001) to 0.18 μV in the second half (n.s.). This case measured both N400 and P600 readings, and did not collect subjective output layer data; therefore the diagnostic annotation assigned by the present framework for the change across halves is: [N400: +, P600: ?, Φ: ?] → [N400: −, P600: ?, Φ: ?].
The present architecture has derived that the P600 reading reflects the crossing state of the terminal-face boundary of a specific cognitive category (§2.2). The ERP readout layer has four possible reading-output patterns: P600 reading alone, N400 reading alone, both co-occurring, and neither. Furthermore, the architecture has derived that the terminal-face boundary of cognitive categories is mutable (§2.2).
P600 reading alone: the stimulus input activates the cognitive act to cross the terminal-face boundary of an existing cognitive category during the EEG experiment, simultaneously establishing a new cognitive category. At this point, the stimulus input sits at the center of the newly established cognitive category; within the entire cognitive category, only this stimulus input exists as the prototypical exemplar. Therefore, the participant produces only a P600 reading, and no N400 reading is produced (§2.2). Lattner and Friederici (2003) found that when hearing a male voice say "I like to wear lipstick," the participant produced a P600 reading (F(1,30) = 9.91, p < .01), yet no N400 reading was measured (pp. 191–192). In this case, the semantics of the sentence conform to semantic rules, but the combination of a male voice with the semantics expressed by the sentence does not conform to the participant's way of internalizing the cognitive category "gender"; therefore this stimulus input activates the cognitive act to cross the terminal-face boundary of the existing gender cognitive category, simultaneously establishing a new cognitive category that the participant had not possessed before the EEG experiment (§2.2). This case measured both N400 and P600 readings, and did not collect subjective output layer data; therefore the diagnostic annotation assigned by the present framework is as follows: [N400: −, P600: +, Φ: ?].
N400 reading alone: the specific cognitive category already existed before the EEG experiment. When a stimulus input violates the participant's expectations within a cognitive category already established by the participant, but the cognitive act does not cross the terminal-face boundary of that cognitive category, the participant produces only an N400 reading (§2.3). Proverbio et al. (2018) found that male participants produced an N400 reading in response to male-character stereotype violations (Group × Congruence: F(1,31) = 6.26, p < .018; pp. 11–12), with no P600 reading measured under the same conditions. Wu and Cai (2026) found that social gender violations produced an N400 reading (β = −0.89, p = .005) but did not produce a P600 reading (pp. 553–554). Hanulíková et al. (2012) found that semantic violations produced an N400 reading for both native-accented and foreign-accented speakers (pp. 883–884) and did not produce a P600 reading. Grey and van Hell (2017) showed that accent identifiers (i.e., participants who identified the Chinese accent, 36% of the sample) produced an N400 reading to L2 grammatical error types and did not produce a P600 reading (pp. 103–104). All four of the above studies measured both N400 and P600 readings, and did not collect subjective output layer data; therefore the diagnostic annotation assigned by the present framework for this group of studies is uniformly: [N400: +, P600: −, Φ: ?].
Neither: neither an N400 reading nor a P600 reading is produced. This output pattern has two cases, each following a different cognitive-behavioral path (§2.6). First, when the participant's expectation distribution is sufficiently wide and the stimulus input does not activate the cognitive act to cross the terminal-face boundary of the current specific cognitive category, all stimulus inputs therefore conform to the participant's expectations, and the participant produces no ERP reading. Proverbio et al. (2018) found that women produced neither an N400 reading nor a P600 reading to any gender stereotype exemplar (pp. 11–12). Hanulíková et al. (2012) found that participants produced neither a P600 reading nor an N400 reading to grammatical errors spoken by a foreign-accented speaker (all Fs < 1; pp. 881–883). Taken together with the authors' relevant discussion, the present architecture attributes this phenomenon to the participant's long-term accumulated experience with L2 errors, which has already brought all L2-type grammatical errors within the participant's expected range. Both of the above studies measured N400 and P600 readings, and did not collect subjective output layer data; therefore the diagnostic annotation assigned by the present framework is as follows: [N400: −, P600: −, Φ: ?]. Second, the stimulus input cannot be recognized by the participant's cognitive system, and therefore cannot be classified into any established cognitive category (§2.2). Grey and van Hell (2017) found that non-identifiers (that is, participants who did not identify the Chinese accent, 64% of the sample) produced no ERP reading to L2 grammatical errors (pp. 103–104). For this case, the present architecture's explanation is as follows: the participants did not identify the category of the Chinese accent, and therefore the stimulus input automatically fell into the participants' unknowable, producing no reading (§2.2). This study did not detect the N400 and P600 readings; although behavioral data were collected, such behavioral data do not belong to the subjective output layer as defined by the present framework; therefore the diagnostic annotation assigned by the present framework is as follows: [N400: ∅, P600: ∅, Φ: ?].
Both co-occurring. The architecture has derived that when a stimulus input is a non-prototypical exemplar within a cognitive category already established by the participant, and the exemplar simultaneously activates the cognitive act to cross the terminal-face boundary of that cognitive category, the participant will produce both the N400 and P600 readings (§2.3). No study among the twelve authoritative works cited in this paper has ever statistically analyzed this reading-output pattern. This does not in practice diminish the authority of the present architecture: existing studies lack statistical analyses specifically targeting the reading-output pattern in which "the same stimulus input both is a non-prototypical exemplar within the same cognitive category and activates the cognitive act to cross the terminal-face boundary of that cognitive category." This situation reflects current methodological problems in the field: P600 is a threshold-gated binary signal, yet the field processes the relevant data with the mean-amplitude approach — cross-trial averaging obscures the reading-output pattern that the present architecture derives (§4.2). This paper makes a prediction for this type of reading-output pattern in Prediction 4 of §5.2: the N400 reading and the P600 reading can co-occur, and when they co-occur, the N400 reading produced will necessarily be a large N400.
Within-experiment boundary mutability. Du and Zhang (2023a) presented a case in which a counter-stereotyping discourse context changed the cognitive category boundary within a single EEG experiment, immediately resetting the participant's expectation distribution and causing a directional reversal of the N400 reading (Consistency × Context: N400 χ² = 10.00, p = .002; §3). Although the P600 reading was not measured in that study, the reversal of the N400 reading itself confirms the birth of the new category: the counter-stereotypical information, an unexpected exemplar within the old cognitive category, became the prototypical exemplar of the new cognitive category. This confirms the within-experiment mutability of category boundaries (§2.2). This case measured only the N400 reading, and did not concurrently measure P600 or the subjective output layer; therefore the diagnostic annotation assigned by the present framework is as follows: [N400: + (reversed), P600: ?, Φ: ?].
Previous research has offered various accounts of the nature of the N400 and P600. Some studies view them as mappings onto specific linguistic concepts — semantic violations produced an N400 reading, syntactic violations produced a P600 reading (Kutas & Federmeier, 2011, p. 627). When a semantic violation produced a P600 reading, the field labeled this a "semantic P600" effect (§1), treating such cases as exceptions, without questioning the understanding of the nature of the two readings. Other studies attribute them to sex differences: Proverbio et al. (2018, p. 11, p. 13) found that only male participants produced N400 and P600 readings, and sex differences were treated as explanatory variables. Still other studies attribute this to the participant's specific strategy choices. Du & Zhang (2023b, Discussion, §4) interpreted the presence of an N400 reading as a kind of strategic control. When the experimental environment encourages the participant to use stereotypical gender cues to predict the gender of the upcoming role noun, the participant adopts this as the sole strategy; when the environment does not support the use of stereotypical cues and the sentence context already provides gender information, the participant suppresses the prediction pathway of stereotypical gender cues and relies solely on contextual information to determine the gender of the upcoming role noun. The strategy established first becomes the sole strategy and persists into subsequent experimental phases. For example, a participant who first uses contextual information to determine the gender of the upcoming role noun will not switch strategies even upon entering a subsequent experimental environment that supports using stereotypical cues, and will produce no N400 reading throughout. Yet other studies acknowledge that the empirical data do not match the field's current understanding of the nature of the two readings, but provide no unified explanatory approach (e.g., Porkert et al., 2024, §4.3–§4.4; see also §4.2 of this paper).
In the absence of a unified cross-domain explanatory scheme, ERP research has fallen into a vicious circle of circular explanation. For example, when the linguistic domain is held constant and parameters of other domains are varied, the cause of changes in the two readings, N400 and P600, is attributed to those domains. Hanulíková et al. (2012, pp. 881–883) found that native-accented grammatical errors stimulated the participant to produce a P600 reading, while the same grammatical errors with a foreign accent did not stimulate the participant to produce a P600 reading; the paper's explanation was that the accent domain determines the nature of the P600 reading. Grey et al. (2020, Results, §3.2.2) found that when a face appeared, grammatical errors stimulated the participant to produce a P600 reading, and when no face appeared, the participant did not produce a P600 reading; the presence or absence of a P600 reading was attributed to the face factor. By this logic, if other domains are held constant and the specific conceptual parameters of the linguistic domain are varied, should changes in N400 and P600 readings then be attributed to the linguistic domain?
In fact, changes in the N400 and P600 readings do not depend on concepts internal to the linguistic domain. Wu & Cai (2026, pp. 553–554) found that social gender violations produced an N400 reading and biological gender violations produced a P600 reading, interpreting this to mean that domain differences determine the output of the two readings. In other words, the factors governing the output patterns of the two ERP readings have nothing to do with specific linguistic concepts. Proverbio et al. (2018, p. 11, p. 13) found that male participants produced an N400 reading in response to male-character violations and a P600 reading in response to female-character violations, interpreting this to mean that character gender determines the output pattern of the two readings. This, too, has nothing to do with linguistic concepts.
In each of the above studies, the researchers treat the independent-variable domain they manipulate as the explanatory layer, and the output pattern of the two readings as the phenomenon layer. Each study uses the same argument logic to establish the explanatory layer and phenomenon layer within its own domain. This practice causes explanatory layers to multiply as the domain types taken as independent variables multiply: each new domain introduced as an independent variable adds another explanatory layer, forming an ever-extending chain of explanatory layers that never converge.
The root cause of this circular explanation is that the field has treated proxy variables as explanatory variables. Section 3.2 established that the nature of the N400 and P600 is domain-general. Gender, accent, face, and even variables from the linguistic domain are not explanatory variables; they are merely proxy variables. For the participant, proxy variables are the party acted upon — determined by contact quantity and the crossing state of the terminal-face boundary of the cognitive category — not the decider that determines the output pattern of the two readings. Each time a stimulus input from a specific domain is presented to the participant, the participant's corresponding cognitive category increases its contact quantity: the stimulus input activates the cognitive act to detect the prediction error of the current stimulus input, and simultaneously the cognitive act determines whether to cross the terminal-face boundary of that cognitive category. This research field has elevated proxy variables to the status of explanatory variables, treating independent variables as explanatory layers; yet these "explanatory layers" systematically fail when research is conducted in a different domain: the explanatory layer is always changing, which is equivalent to having no explanatory layer at all. Therefore, only by anchoring the explanatory layer in the contact quantity of the participant's specific cognitive category with non-prototypical exemplars and the crossing state of the cognitive category boundary can the problem of circular explanation in this field be systematically resolved.
To take the twelve authoritative works of ERP research cited in Section 3 as an example, in this field's research, the same data-processing method is used when normalizing the two readings, N400 and P600 — multi-trial amplitude averaging: the mean amplitude produced by multiple stimulus inputs within a preset time window is computed, typically 300–500 ms for N400 and 500–800 ms for P600 (Kutas & Federmeier, 2011, pp. 623–627).
The harm that multi-trial amplitude averaging inflicts on the N400 reading lies in how it flattens the gradient nature of the N400 reading: the N400 reading is a continuous gradient value (§2.3), and the gradient values of its amplitude reflect the continuous differences among the non-prototypical exemplars within the same cognitive category; computing the mean amplitude of multiple stimulus inputs within a preset time window collapses the continuously changing gradient values of multiple stimulus inputs into a single number, flattening the differences among these stimulus inputs. The harm that multi-trial amplitude averaging inflicts on the P600 reading lies in how it conflates the crossing states of the terminal-face boundaries of multiple cognitive categories: the P600 reading is a threshold-gated binary reading (§2.2), and the presence or absence of this reading reflects the crossing state of the terminal-face boundary of a single cognitive category; cross-trial averaging conflates the crossing states of the terminal-face boundaries of multiple cognitive categories. For the N400 reading, multi-trial amplitude averaging damages the amplitude quantities of the different non-prototypical exemplars within the same cognitive category. For the P600 reading, multi-trial amplitude averaging damages the quality of different cognitive categories.
The convergence of the cross-literature statistical results of the N400 and P600 readings reflects the harm that multi-trial amplitude averaging inflicts on amplitude quantities and the quality of categories. For the N400 reading, it is relatively good: amplitude correlates with cloze probability at approximately r ≈ .90, and studies across different EEG experiments, different participants, and different time points consistently report this effect (Kutas & Federmeier, 2011, p. 621). Kutas & Federmeier (2011) did not mention the convergence of the P600 reading; nevertheless, the conclusions of Porkert et al.'s review of 17 ERP studies indirectly reflect the cross-literature convergence of the P600 reading. Porkert et al. (2024, §4.3–§4.4) found that, across the literature, only two conclusions about the P600 reading are reliable: when participants had already inferred a character's gender from a previously mentioned role noun, a gender-mismatching pronoun in the current sentence produced a P600 reading (5/5 cases); but when no such inference had been made before the pronoun appeared, the participant produced an N400 reading when the same gender mismatch appeared (4/4 cases). On this basis, this paper predicts: in existing research, the convergence of the cross-literature statistical results of the P600 reading is far less ideal than that of the N400 reading, and when subsequent research uses an appropriate statistical method, the convergence of the cross-literature statistical results of P600 will significantly improve (Prediction 2 of §5.2).
The reason the convergence of the cross-literature statistical results of the two readings falls short of the ideal is that researchers used the operation of "averaging." Taking the N400 reading and the P600 reading as examples, "averaging" inflicts multi-layered harm on the objects reflected by the two readings. First, "averaging" changes the nature of the data: multi-trial amplitude averaging changes the nature of the amplitude of each non-prototypical exemplar within the same cognitive category. Second, "averaging" conflates the nature of the data: multi-trial amplitude averaging conflates the crossing states of the terminal-face boundaries of different cognitive categories. Third, the operation of averaging harms the very concept of "averaging": the purpose of averaging should have been to treat every object it operates upon equally, but the actual consequence is this: the more uniform the final result and the more uneven the distribution of the harm — the more unequal the treatment that each operated-upon object receives.
The preceding sections have derived that, within the five-layer architecture of the cognitive act, the ERP readings of Layer 3 and the subjective output data of Layer 4 are mutually independent (§2.1): Layer 3 is the non-autonomous ERP readout layer, where the participant cannot autonomously control the production process of the two readings, N400 and P600; Layer 4 is the subjective output layer, where the participant can choose to faithfully or unfaithfully output the Layer 3 readings. Data from only a single layer — whether Layer 3 or Layer 4 — cannot clearly determine the eight output paths of cognitive-behavioral data (§2.6). Kang & Rubin (2009, pp. 450, 452) found that for the same participant, the same Standard American English voice yielded lower listening comprehension scores when paired with an Asian face than with a Caucasian face; this score is part of the participant's subjective-output-layer data. In essence, researchers cannot determine whether the difference between the two scores reflects the participant faithfully reporting the results non-autonomously produced by the ERP readout layer, or the participant reporting data opposite to the results of the ERP readout layer.
Statistical model-building methods are not suited to cognitive-behavioral data with eight output paths. The reason is that the cognitive-behavioral data produced by different participants do not satisfy the conditions for normalization. For example, Grant et al. (2020, Results, §4.2.2) found that when different participants in the same EEG experiment heard the same stimulus inputs, their N400 reading showed sharply different patterns of change across the EEG experiment depending on their ASI (Ambivalent Sexism Inventory) scores: low-ASI participants' N400 reading underwent a significant change between the first and second halves of the EEG experiment (β = 3.89, p = .007), while high-ASI participants showed no change. Du & Zhang (2023b, Results, §3.1) similarly found that the consistency proportion of initial trials determined which strategy the participant would adopt in subsequent trials, and that the strategy established first became the sole strategy: the group first exposed to a high proportion of consistent trials (80%) formed a strategy of using stereotypical cues to predict the gender of the upcoming role noun, and continued to produce an N400 reading (p = .004); the group first exposed to an equal proportion of consistent and inconsistent trials (50%) formed a strategy of relying solely on contextual information to determine the gender of the upcoming role noun, and produced no N400 reading at all. Even for a single participant, the cognitive-behavioral data produced in the same EEG experiment are no longer suitable for homogenization: van den Brink et al. (2012, pp. 178–179) found that female participants' N400 reading to speaker-identity violations was 1.56 μV in the first half of the EEG experiment (p = .001) and dropped to 0.18 μV in the second half (n.s.), declining by nearly an order of magnitude within a single hour. In summary, whether between different participants or for the same participant at different times, normalization processing erases the constitutive information of the data themselves.
Research methods should be matched to the nature of the object under study. When the nature of the cognitive-behavioral data can change during the EEG experiment, and the same final output of the cognitive act can be produced through multiple paths, the most appropriate method is to enumerate the specific paths, rather than to build statistical models that may conflate them. The construction of statistical models depends on specific hypothetical premises; the data, once normalized, fit significant effects, but a significant effect is not equivalent to a phenomenon that actually occurs. A model whose premises are false can neither faithfully reflect nor fully predict phenomena as they actually occur; failure of any single hypothetical premise invalidates the model: truth and falsity are incompatible.
The preceding sections diagnosed the methodological misconceptions present in the field's research (§4). First, proxy variables are used as explanatory variables (§4.1). Second, multi-trial amplitude averaging damages the nature of the two readings (§4.2). Third, the unjustified embrace of statistical models that depend on hypothetical premises (§4.3).
All existing studies target proxy variables in their experimental designs and collect single-layer data (from the ERP readout layer or the subjective output layer). A complete method targeting the two explanatory variables — the contact quantity of cognitive categories with non-prototypical exemplars and the crossing state of the terminal-face boundary of cognitive categories — does not yet exist. Future research in this field must adhere to the following principles. First, the problem of data normalization. The contact quantity of a cognitive category with non-prototypical exemplars and the crossing state of its terminal-face boundary vary across individuals because no two individuals share the same history of contact with non-prototypical exemplars and the same history of crossing the terminal-face boundary of cognitive categories. Even for a single individual, their cognitive-behavioral data may undergo changes within a single EEG experiment that render them unsuitable for homogenization (§3.3). Normalizing data across participants and across time will obscure the constitutive information of the data (§4.3). Second, when collecting P600 reading data, the single-trial statistics approach must replace multi-trial amplitude averaging (§4.2): determine for each trial whether a posterior positivity was measured at approximately 600 ms post-stimulus (§2.2), without averaging the P600 data across multiple measurements (§4.2). Third, the method must possess domain specificity. The contact quantity of a specific cognitive category with non-prototypical exemplars in one domain does not automatically transfer to another; for example, the contact quantity of the same individual with non-prototypical exemplars in the social-gender category and in the biological-gender category cannot be transferred across domains (§3.2). As another example, the same participant has established the cognitive category of the grammatical-gender domain for native-accented speech, but not for foreign-accented speech (§3.4).
No existing study has simultaneously collected the participant's N400 reading, P600 reading, and subjective-output-layer data within a single EEG experiment. Collecting both readings and subjective-output-layer data simultaneously is the minimum experimental-design requirement for determining the eight cognitive-behavioral paths (§4.3).
The preceding sections started from the two objective readings produced by EEG instruments, N400 and P600 (§1), derived and established the present architecture (§2), and verified it against twelve authoritative works of ERP research (§3). Then, from the perspective of this architecture, this paper diagnosed the field's methodological limitations (§4) and pointed out the methodological principles to be followed when conducting future research in this field (§5.1). On this basis, this paper provides four falsifiable predictions:
Prediction 1: In an EEG experiment, if only minimal changes are made between successive stimulus inputs, then the N400 reading will be measurable as a continuous gradient value of amplitude, rather than merely three discrete categories of weak, medium, and large.
Prediction 2: In existing research, the convergence of the cross-literature statistical results of the P600 reading is far less ideal than that of the N400 reading; if the single-trial statistics approach replaces multi-trial amplitude averaging in processing P600 reading data, then the convergence of the cross-literature statistical results of P600 will significantly improve, demonstrating the binary nature of the P600 reading.
Prediction 3: Change in the N400 reading is determined by the participant's contact quantity with the non-prototypical exemplars of a specific cognitive category, not by contact time. As the participant's contact quantity with the non-prototypical exemplars of the specific cognitive category in a specific domain grows from low to high, the amplitude of the N400 reading produced by the participant should decrease in a continuous gradient from large to weak until it disappears. The rate of this change correlates with contact quantity, not with contact time.
Prediction 4: The N400 reading and the P600 reading can co-occur, and when they co-occur, the N400 will be large. The geometric relationship (§2.4: being far from the center necessarily means being near the boundary) entails that the prediction error value within that cognitive category must be large when its terminal-face boundary is crossed.
The four predictions correspond to four core claims of the architecture: the continuous-gradient nature of the N400 reading, the binary nature of the P600 reading, the causal determination of the N400 reading by contact quantity, and the geometric relationship between the N400 reading and the P600 reading. Falsifying any one of them would falsify the architecture established in this paper.
For three decades, the field has used specific linguistic concepts to explain the nature of N400 and P600, when in fact these linguistic concepts and variables from other domains such as gender, accent, and face are proxy variables alike (§4.1). The specific cognitive categories of each domain have their own independent histories of contact with non-prototypical exemplars and of crossing the terminal-face boundary of cognitive categories (§2.2–§2.3); these proxy variables therefore cannot provide a unified account of the nature of the N400 reading and the P600 reading.
The present framework has demonstrated the unique way of defining the two readings, N400 and P600 (§1): the N400 reflects the relationship between the stimulus input and a specific position within the participant's specific cognitive category, and the P600 reflects the crossing state of the terminal-face boundary of that cognitive category.
Proceeding from this nature, this paper derived a complete theoretical architecture (§2). Twelve authoritative ERP studies verified the validity of the architecture against empirical data (§3). Using this architecture, this paper also diagnosed three methodological misconceptions in the field (§4) and clarified the directions for future research (§5).
This paper has also demonstrated the nature of the reading-output patterns of N400 and P600: for any cognitive category n, N400n is the participant's prediction error value regarding the non-prototypical exemplars of cognitive category n (§2.3), and P600n+1 indicates that the cognitive act has crossed the terminal-face boundary of cognitive category n and simultaneously established the initial-face boundary of cognitive category n+1 (§2.2). The first cognitive category is automatically established at the individual's birth, and the crossing process of this category (i.e., P6001) can never be measured; therefore all observable P600 readings in EEG experiments are by nature P600n+1 (n+1 ≥ 2) (§2.2). Therefore, logically, the P600 that co-occurs with N400n must be P600n+1 (§2.4). On the basis of this nature, this paper formalized the four reading-output patterns of N400 and P600 (§2.4).
On the basis of the above definitions, this paper derived six logically necessary structural associations between N400 and P600 (§2.4). The gradient values of the N400 amplitude reveal that the non-prototypical exemplars within a cognitive category form a continuum, but the concept of "continuum" itself cannot generate a boundary (§2.4). The symmetry of the cognitive category boundary reveals that a single boundary line has two symmetric faces, but the concept of "boundary" itself cannot determine which face carries meaning for the cognitive act (§2.4). The sequential relationship establishes that N400 must precede P600, but the concept of "sequence" itself cannot explain why the terminal-face boundary of a cognitive category can, against the direction of the sequence, cross non-prototypical exemplars to reach the initial-face boundary of the same cognitive category, thereby completing the concept of "cognitive category," yet cannot cross that initial-face boundary (§2.4). Set theory reveals that the element count and the characteristic function of the cognitive category as a set are in constant flux, but the concept of "set" itself cannot handle a set in which both the characteristic function and the elements are changing (§2.4). The geometric relationship between N400 and P600 reveals that the distance from periphery to center is constantly in a state of change, but the concept of "geometry" itself cannot explain why the distance from periphery to center can change at any moment (§2.4). Logical entailment reveals that all four output patterns of N400 and P600 entail the same P600n, but the concept of "entailment" itself cannot explain the meaning of this entailment relation (§2.4). These six structural relations of N400 and P600 confront all six concepts with problems they themselves cannot answer (§2.4).
The inductive act of cognition only acts upon events that have already happened, and this nature determines the direction of the inductive act: the inductive act can only act upon exemplars that already exist, and therefore necessarily reaches the terminal-face boundary of the cognitive category; the initial-face boundary of the cognitive category faces toward exemplars that do not yet exist, and is therefore unreachable by the inductive act (§2.5). The initiation of the inductive act halts the continuous process of the continuum, creating a breakpoint — the breakpoint is the boundary (§2.5). The boundary generates symmetry, and the orientation of the inductive act breaks the symmetry, endowing the terminal-face boundary that faces toward the initial-face boundary of the cognitive category with meaning (§2.5). Thereafter, the inductive act crosses from this terminal-face boundary, against the direction of the sequence and toward the initial-face boundary of that cognitive category, across the 200 ms time difference and all intermediate non-prototypical exemplars, and finally coincides with the initial-face boundary of the same cognitive category (§2.5). When the terminal-face boundary and the initial-face boundary of the same cognitive category coincide, the inductive act will no longer cross the initial-face boundary of this cognitive category to induce the initial-face boundary of another cognitive category — otherwise the very concept of a "cognitive category" would be dissolved (§2.5). At this point, the cognitive category as a set contains one element and one characteristic function, and the two are one (§2.5). As a geometric body, when the distance between the periphery and the geometric center becomes zero, the shape of the geometric body disappears; the formed becomes the formless; and only the "inductive act" remains, existing as a concept (§2.5). Yet the "concept" has not disappeared — it has merely become unobservable: the concept is produced by the cognitive act, and the cognitive act is ontologically prior to the concept. Under the action of the cognitive act, the formed becomes the formless, and ultimately the cognitive act itself remains — the cognitive act itself is a kind of action, and "action" itself is the source of all actions: the self-sufficiency of the action (§2.5).
The self-sufficiency of the action is the self-sufficient action. The self-sufficient action is "autonomy" (§2.5). The deductive act of cognition autonomously unfolds along the logical chain induced by the inductive act (§2.5): P600n is an autonomously existing cognitive act, which autonomously completes the entire process from establishing the initial-face boundary of a cognitive category, through accumulating non-prototypical exemplars, to crossing the terminal-face boundary of that cognitive category — one whole event (§2.5). N400n and P600n+1 reflect offshoot events of this whole event — the offshoot events entail the whole event — and the deductive act of cognition answers the sixth question (§2.5). The unfolding process of an event can only be presented through description, and to describe is to define. A whole event is constituted by the combination of offshoot events, and the process of combination is an equivalence operation (§2.5). Therefore, the two measurable readings, N400n and P600n+1, must be used to perform the "equivalence → definition" operation upon P600n, restoring one unmeasurable whole event: |P600n⟩ ≝ ⟨N400n | P600n+1⟩ (§2.5).
Time as cognition's container — its vectoriality guarantees the uniqueness of all the above cognitive acts: no two cognitive acts ever coincide. At any time, the formula |P600n⟩ ≝ ⟨N400n | P600n+1⟩ holds. This is the cognitive act's recursion over time: without beginning, without end (§2.5). The meaning of the first cognitive category is simultaneously revealed: the initial-face boundary of the knowable category can be known but has no meaning; the terminal-face boundary of the unknowable category has meaning but cannot be known. At any moment, for any individual, if that individual recognizes that "the knowable has no meaning, only the unknowable has meaning," then for that individual, this moment has meaning. This is the meaning of time: to perceive it is to find it meaningless; only by not perceiving it does one find it meaningful.
A static, false formula is one in which the logical chain circles around cognition: the chain has neither a starting point nor an ending point, and both are filled in by hypotheses. A dynamic, real formula is one in which cognition chases the logical chain: the chain has both a starting point and an ending point, and both are connected to reality. Human cognitive activity is an autonomous, dynamic, real event — not an abstracted, static, false event. In a natural state where there is no stimulus input and the two readings N400n and P600n are not being measured, the operating principles of the human cognitive act are entirely identical to those when participating in an EEG experiment. The operating regularities of the human cognitive act can therefore be further generalized from |P600n⟩ ≝ ⟨N400n | P600n+1⟩ to:
In this formula, | denotes the cognitive category boundary, N denotes any cognitive category, ⟩ denotes the unfolding direction of the cognitive deductive act, ⟨ denotes the gathering direction of the cognitive inductive act, Xn denotes any non-prototypical exemplar of cognitive category N, N+1 denotes the next cognitive category simultaneously established when the terminal-face boundary of cognitive category N is crossed, and ≝ is the autonomous act of performing "definition → equivalence." The vectoriality of time guarantees the dynamic infinitude of the content of these forms; the formula's sole unchanging autonomous act, ≝, anchors the other forms whose content changes without limit. This paper endows the bra-ket form ⟨φ|ψ⟩ proposed by Dirac (1939) with complete and precise meaning: using observable form to "equivalence → definition" unobservable essence. Form may alter its shape; essence does not alter its essence. Autonomy generates the act; the act generates concepts; concepts generate all things.
Anyone who reads this paper will establish a cognitive category called COGNITIVE ACT. Whoever understands this paper will cross that category and recognize that the unknowable essence alone has meaning, while knowable form has none. For those who do not understand this paper, according to the framework's own conclusion, even if this paper falls into the unknowable for them, it has not lost its inherent meaning. Any reader (such as physicists, mathematicians, logicians, and AI) can verify this conclusion. Uncomprehending readers therefore need not be persuaded — they need only read it once, and again, and again … When the meaning of this paper is finally understood, they will have crossed the terminal-face boundary of this cognitive category, and will stand face to face with "meaning" itself. "Meaning" itself cannot be observed, but "meaning" itself exists autonomously. This paper is the observable exemplar of "meaning" itself operating autonomously.
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