1936 On Computable Numbers · 1939 Systems of Logic Based on Ordinals · 1950 Computing Machinery and Intelligence · 1952 The Chemical Basis of Morphogenesis
1936 On Computable Numbers · 1939 Systems of Logic Based on Ordinals · 1950 Computing Machinery and Intelligence · 1952 The Chemical Basis of Morphogenesis
Chinese content v1.3｜method version v1.3｜2026-10-24
Archival statement: the evidence of this archive rests on the listed texts of the author and formal text databases;
each card states clearly the range of verified text and of missing evidence awaiting checking. Judgement grades express the strength of interpretation and do not replace the original.
One-line placement: ④ Explaining the world (B); ③ Questioning the ground as an important competing direction (C); ① is a D-level stress test. He gave a formal model of effective computation and proved the limits of particular decision tasks, then brought the universality of machines and the possibility of learning into the discussion of intelligence, and explained the generation of biological form by reaction—diffusion.
Most distinctive point: he proposed that a machine can not only execute a single algorithm but also read in descriptions of other machines; at the same time he did not directly equate “being able to run a program” with all mental experience or human understanding.
Final load-bearing point: rules, discrete symbolic states, encoding and the relation of simulation, conditions of proof, the evaluation of learning, and reaction—diffusion dynamics bear the load; each is an analysable function, not an ultimate substantial knower.
Most subtle point: does formalizing the process of computation and letting a universal machine simulate formal activity already positively place thought itself? This is local self-inclusion, but it cannot be inferred from it that all semantic understanding and biological mind have been finally explained in a closed way.
This archive strictly distinguishes the reliability of the text (T1—T4) from the strength of structural judgement (A—D). T1 = the author’s own core papers / works or early core texts of strong attribution; T2 = reliably confirmed material whose genre, co-authorship, transmission or attribution needs further definition; T3 = texts whose edition, attribution or representativeness is substantively disputed; T4 = later commentary, research and extension in tradition, serving only as background and not passed off as the author’s own words. Differences among figures must be marked clearly in each card.
A = a textual fact stated directly by the original; B = a strong structural inference supported by several directly verified texts of the author, with clearly weaker alternative readings; C = grounded in the original, but with an equally reasonable structural reading;
D = a stress test / a hypothesis awaiting verification. A reliable translation can serve as a basis for B; not every item must be checked against the full text in the author’s original language; where only a library description, table of contents, abstract or later survey has been checked, these materials alone cannot bear B. The so-called “original language checked”, “translation checked” and “evidence missing, awaiting checking” are recorded separately as verification status; T1 attribution, A-level textual fact and B-level structural inference do not automatically imply one another. That an E card is B does not mean that the figure’s competing six-position placement reaches B: it must still be shown that it belongs to the main task of the thought.
Direction of evidence: supporting = supports the present six-position placement; limiting = shows a load-bearing function or a boundary of explanation; disputed = the original allows different readings; neutral = does not form a core limit for the present six-position criteria. ① must satisfy at once that cognition (including the proposing, utterance and understanding of thought itself) is positively built into a more basic whole, and that the complete final structure still holds once the function of “right cognition of the ground” is deleted. Local methodological reflection, psychological explanation or formal self-encoding cannot alone complete the first condition;
strong local evidence for ③ / ② does not automatically change a placement whose task of thought is primarily ④.
Main texts: “On Computable Numbers, with an Application to the Entscheidungsproblem” (1936/1937); “Systems of Logic Based on Ordinals” (1939); “Intelligent Machinery” (1948 report); “Computing Machinery and Intelligence” (1950); “The Chemical Basis of Morphogenesis” (1952)
Sources and scope of verification: §1, §6 and §8—11 of the original 1936 English paper, the text of the 1950 Mind paper and the specified arguments of the original 1952 reaction—diffusion publication constitute the main basis for ④ B; the proofs of the 1939 ordinal logics and the 1948 NPL report still keep a boundary of full-text verification; E-07 and E-08 are both C and are not necessary pillars of ④ B. The 1948 report may not be written as a journal article published in that year.
Methodological boundary: T1 decides authorship and core representativeness, and does not presuppose that the original language has been checked; each card separately lists original language / reliable translation / table of contents or abstract / missing-evidence status. B must be supported by verified direct texts of the author;
library descriptions or surveys alone do not constitute independent B evidence. Scientific explicability, predictability and confirmation are not the ultimate completion of cognition in the sense of ②; nor are the two conditions of ① automatically satisfied because a theory can explain the observer or the researcher. The main class is decided by the overall task of the thought, not by the number of quotations or the strength of a single card.
Core research question: can “effectively computable” be strictly defined by finite rules? Can the performance and learning of machines form a researchable standard of intelligence; and what non-deletable boundaries does the mathematical mechanism itself have?
1. In 1936 he first defines computable numbers through machines and configurations that execute rules (E-01—E-03).
2. The universal machine takes descriptions of machines as input, forming a local self-inclusion of computation (E-04).
3. He establishes formal limits for properties that cannot be generally decided and for the decision problem (E-05—E-06).
4. In 1939 he opens a direction of research into further rules beyond formal systems (E-07).
5. In 1948 he proposes unorganized machines and training, and in 1950 re-examines the question of intelligence through the imitation game and learning machines (E-08—E-11).
6. In 1952 he explains, by the coupling of reaction and diffusion, how uniform tissue can produce form (E-12).
Each E card below states separately the text level, the specific scope of verification, the gist of the text, its role in the six-position judgement, the overreaching readings that cannot be inferred, and the source. A checked short phrase indicates only the textual fact of the quotation; the certainty of interpretation is given separately by B / C / D. Direction terms are defined in Chapter 2; sentences not compared item by item are not passed off as quotations in the original language. This evidence base continues to distinguish strictly two sets of grades: T1 is a core text of the figure, of strong authorship and representative; T2 is reliable material whose edition, transmission or attribution must be qualified; T3 is a text whose attribution or representativeness is substantively disputed; T4 is later interpretation, serving only as background. A marks only what the text states directly;
B is a strong structural inference supported by several reliable texts of the author, with clearly weaker alternative readings; C is grounded but with a reasonable alternative reading at the same time; D is a stress test awaiting verification. Checked reliable translations can support B, but abstracts, bibliographies and library descriptions cannot alone prove B. An A-level textual fact does not automatically raise a complex interpretation to A. Supporting = supports the present six-position judgement; limiting = shows structural load-bearing or a boundary; disputed = the reading is not unique; neutral = does not form a key limit for the present judgement.
Verified short phrase in the English original / English translation (by verification status): According to my definition, a number is computable if its decimal can be written down by a machine.
Gist of the original (this archive’s restatement, not a verbatim quotation): Computable numbers are restricted to numbers whose decimal expansion can be produced by finite machine steps; the author explains that similar questions can be extended to functions and predicates.
Structural role here: Supporting｜positively specifies ④’s object of research; ③’s competition comes from “what are the limits of effective method”, not from a metaphysical theory of substance.
What it does not prove: Defining computable numbers does not declare that mathematical truth can be fully decided mechanically.
Gist of the original (this archive’s restatement, not a verbatim quotation): The machine reads, writes, moves and changes state according to rules, with finite symbols, tape positions and internal configurations, simulating a computer who proceeds by finite steps.
Structural role here: Supporting｜remove reading, writing and state transitions, and the later definition of computability loses its operable load-bearing point (structural layer).
What it does not prove: The abstract tape is not an empirical measurement of the actual organizational structure of the human brain.
Gist of the original (this archive’s restatement, not a verbatim quotation): Computable sequences are defined through the distinctions of automatic machines, circle-free running and continuing output.
Structural role here: Supporting｜confines the theoretical thesis to strict kinds of machine and properties of sequences, preventing the overreach that “any machine that runs will complete a computation”.
What it does not prove: That the running properties of particular machines cannot be uniformly decided does not mean that every actual computation is unpredictable.
Gist of the original (this archive’s restatement, not a verbatim quotation): The standard description of a machine is provided as data to be read by another machine, so as to simulate the steps the former executes.
Structural role here: Disputed｜the strongest local candidate for self-inclusion: the rules of computation themselves become objects that can be encoded and processed.
What it does not prove: Universal simulation does not automatically include all the judgements of meaning of the interpreter, still less is it a machine that creates every world.
Gist of the original (this archive’s restatement, not a verbatim quotation): By the diagonal method it proves that a general process for deciding a certain property of the unending output of computing machines cannot exist.
Structural role here: Limiting｜evidence for ③ on the limits of formal completeness, preventing the universal machine from being miswritten as “able to solve all problems”.
What it does not prove: The circle-free property in the 1936 original must be distinguished from the later common formulation of the halting problem;
they cannot be mechanically treated as the same theorem sentence.
Gist of the original (this archive’s restatement, not a verbatim quotation): Connects the limits of machine decision with the general decision problem of formal logic, obtaining the result that the general mechanical procedure sought cannot exist.
Structural role here: Supporting｜brings the model of computation back to questions of the foundations of mathematics, without treating formal computation as an all-powerful engine of discovery.
What it does not prove: It does not mean that all logical propositions cannot be proved, still less that no special class has an effective algorithm.
Gist of the original (this archive’s restatement, not a verbatim quotation): Through formal hierarchies and ordinal notations it discusses the extension of certain capacities of proof, studying how effective method changes in strengthened systems.
Structural role here: Disputed｜shows that ③’s continued questioning goes beyond the single result of 1936; the scientific task cannot be understood merely as the construction of a single machine.
What it does not prove: The theoretical use of an oracle in 1939 cannot be equated with actual hypercomputing hardware having been built.
Gist of the original (this archive’s restatement, not a verbatim quotation): Attempts to explain how certain intelligent behaviour can gradually form from the states of simple networks and processes of training.
Structural role here: Supporting｜④’s functional explanation extends to the organization of learning; intelligence is seen as a process of change rather than a single right awakening.
What it does not prove: The report was written in 1948 but first published after 1968; it cannot be written as “published in a public journal in 1948”.
Verified short phrase in the English original / English translation (by verification status): I propose to consider the question, ‘Can machines think?’
Gist of the original (this archive’s restatement, not a verbatim quotation): Proposes turning from the abstract verbal dispute over “whether machines can think” to a definite situation of judgement through written exchange.
Structural role here: Supporting｜evidence of the transformation of the research question: the game organizes the dispute by a behavioural standard, still within the task domain of explaining intelligence.
What it does not prove: The imitation game is not a complete philosophical definition of all questions of consciousness and intelligence, still less a historical report that some machine has already passed the test.
Gist of the original (this archive’s restatement, not a verbatim quotation): Distinguishes the digital computers under discussion from the form of physical devices, and uses universality to explain the functional range of the machine.
Structural role here: Supporting｜separates hardware implementation, representation of rules and evaluation of performance, establishing a reflexive structure of scientific argument.
What it does not prove: Universality refers to formal simulability; it does not mean that every physical process can be reproduced in real time with finite resources.
Gist of the original (this archive’s restatement, not a verbatim quotation): Brings the child machine, training and experiential feedback into the conception of the development of intelligence, distinguishing the initial program from behaviour after training.
Structural role here: Supporting｜an internal correction of the model “intelligence = rules written out in full in advance”, and also a return to education and interactive experience.
What it does not prove: This is a research programme, not a mature machine-learning system already verified in 1950.
Gist of the original (this archive’s restatement, not a verbatim quotation): Discusses how chemical substances react with one another and diffuse within tissue, so that a uniform equilibrium, when disturbed, can generate spatial form.
Structural role here: Supporting｜the strongest cross-domain return: a dynamic mechanism explains how visible differences arise, clearly belonging to ④ explaining the world.
What it does not prove: The author proposes a feasible mathematical mechanism, not a confirmation that all biological patterns are fully explained by the model given.
computable number｜Computable number: a strict object whose representation is generated by effective steps.
a-machine｜Automatic machine: an ideal device that changes state according to a determinate table.
universal machine｜Universal machine: a formal structure that simulates other machines through symbolic descriptions.
Entscheidungsproblem｜Decision problem: whether there is a general mechanical procedure for logical decision.
imitation game｜Imitation game: a framework of discussion for behavioural judgement.
learning machine｜Learning machine: a direction of research allowing training and the formation of behaviour.
reaction–diffusion｜Reaction—diffusion: a mechanism coupling chemical kinetics with spatial diffusion.
Positive evidence: the ground is which processes can be expressed by rules and produce analysable behaviour in real and mathematical problems; from 1936 to 1952 there is continuous cross-domain explanation (E-01, E-12).
Limiting evidence: the undecidability results limit the exaggerated interpretation that “computation can exhaust all problems”; nor did 1950 claim that intelligence equals the whole of human consciousness.
Disputed reading: ③’s E-05 and E-06 have B-level local arguments on the limits of decidability and are not “missing evidence”; but the combination of the formal definition of 1936, the framework of intelligent behaviour of 1950 and the morphological dynamics of 1952 shows that the theoretical task lies mainly in modelling and explaining bounded phenomena, so ③ as a competing main class is C. The 1939 E-07 still awaits formula-by-formula checking and cannot serve as an additional B pillar.
Most secure present conclusion: at present ④ explaining the world (B); ③ questioning the ground (C) is real, but it is not the whole final task of this thought.
Already withdrawn / de-substantialized: presuppositions such as that effective computation can rest on intuition without definition, that the universality of machines means every problem has an algorithm, and that intelligence can only be borne by the particular material of humans (E-01, E-05, E-09).
Core structural load-bearing points: finite configurations and symbolic rules, the encoding of machine descriptions, the conditions of logical proof, and operational definitions for models of learning and form.
Disputed functional load-bearing point: the 1950 evaluation needs human observers and written exchange, but this is an experimental criterion of judgement, and does not prove that the existence of the world or of intelligence takes some “right cognition of the ground” as its final condition.
Nature of the load-bearing points: formal structures, behavioural tests and dynamical mechanisms, all functional relations set according to specific problems, not static entities.
What still holds after deletion: different physical media can realize the same computing table;
delete an example in the narrative of the 1950 game, and the theory of the universal machine can still hold (expressive / teaching layer).
Where it breaks after deletion: remove finite states and the rules of reading and writing, and the definition of computation in 1936 §1 collapses; remove encoding and the rules of simulation, and the argument for the universal machine in §6 cannot run; remove the coupling of reaction and diffusion, and the chain of mathematical conditions for spontaneous patterning in 1952 cannot be derived by the original model. According to 1936 §1, the machine’s action is determined by “the scanned symbol + the machine configuration (m-configuration)”, and is put into effect in the concrete transition tables of §3; delete this state—symbol—action relation, and an algorithmic process cannot be defined by the rules in the text. The universal machine of §6 requires another machine to read the standard description; delete encoding, and the simulator has no way to choose the simulated transitions according to the description (E-02, E-04; S1). 1952 is limited to the model conclusions of the reaction—diffusion mechanism and does not directly assert that all biological form must be formed by that mechanism.
Layer of break: machine configurations, encoding and simulation are at the structural layer; training samples at the layer of practical path; the mathematical parameters of reaction—diffusion at the layer of model structure;
a particular test story at the teaching layer.
Place in the complete ultimate structure: the results of the relevant theories hold under given formal and experimental conditions; there is no relation of completion in which “the machine or the researcher finally realized the ground”.
Mode of existence after completion: a post-awakening subject does not apply; research results continue to be tested for computability, by experiment and for the domain of applicability of models.
The place of thought itself (reflexivity / self-inclusion): the universal machine can treat machine rules as data, forming a strong local formal self-inclusion; interpretation of meaning, rules of evaluation and biological processes are not thereby completely closed by a single model.
Return: questions of formal logic return to actual digital computation, the education of learning machines and the generation of biological form, showing an explanatory strategy that is transferable but not conflated.
Another reasonable reading: ③ takes “what is a mechanically effective method and what formal limits are there” as the main line, seen in 1936 and 1939; but it can hardly cover the main task of the 1952 study of mechanism.
Most secure present boundary: ④ (B), ③ (C), ① (D).
Local formal self-inclusion and total occurrence itself cannot be joined by the single phrase “universal machine”.
Judgement grade: the key formal tasks of 1936 and 1950 are B; the transmission layer of 1948 and part of the proofs of 1939 are C; ① is D.
Reflexivity: 1936 turns research on computation back to study the limits of the machine’s own capacity, an explicit methodological reflexivity.
Positive evidence of self-inclusion: E-04, within the object domain of computation, turns machine descriptions into machine input; formal rules can be operated on by another system of rules, and the local property can be confirmed at B. But this is only the limited domain of “objects of computation and syntactic expression”, and does not contain a positive overall account of the semantic truth values of this archive’s argument, all linguistic meaning and real understanding; so ①’s first condition, by its complete definition, is not satisfied; this local property does not change ①’s complete criterion.
Cognitive deletion test: delete some conscious subject’s right recognition, and the machine still runs according to its table; but the same structure cannot positively explain all meaning, consciousness, understanding and its own utterance, so ①’s first condition still does not hold.
Most secure present judgement: local self-inclusion can be acknowledged at B, and cannot be smuggled into the complete self-inclusion that ① requires; ② also has no independent right awakening as a final condition.
Positive evidence: one machine’s description becomes the input of another machine, giving “computation describing the conditions of its own computation” provable technical content (E-04).
Limiting evidence: the limits of §8—11 show that formal self-description cannot solve all semantic and decision problems.
Disputed reading: this result can be read as a deep reflexivity of ③, or placed in ④ as a cross-domain scientific product; neither is decided by degree of cleverness.
Most secure present conclusion: finally ④ (B); ③ (C), ① (D).
④: computable models, universal simulation, intelligent behaviour and chemical form receive rule-governed explanations (E-01—E-04, E-09—E-12; B).
③: the limits of decision of 1936 and the ordinal logics of 1939 keep real questions about the foundations of mathematics (E-05—E-07; C).
②: assessment by written exchange or training does not mean that the universe must finally be rightly recognized.
①: the universal machine of 1936 realizes a formal self-encoding within the domain of computation (E-04, local B), but does not positively build in all utterance, semantic understanding and their more basic relations of occurrence; ①’s complete first condition does not hold, and it does not become ① C because of a local B (D).
Final placement: ④ Explaining the world (B); ③ Questioning the ground as an important competing direction (C); ① is a D-level stress test
He rewrote effective computation from an intuitive mental capacity into a mathematically analysable process of states, showed the universality and formal limits of this process, and at the same time made machine learning and the spontaneous generation of form into researchable problems.
Strongest counter-reading: The universal machine describes itself and can execute any computation, so the whole of existence and thought is also within it.
Adjudicated reply: Universality is limited to the computable processes as defined, and does not contain a complete positive placement of all meaning and existence.
Strongest counter-reading: Since there are problems that cannot be generally decided, computational methods cannot be trusted.
Adjudicated reply: The original theorem specifies the type of general algorithm that cannot exist; it does not deny that a great many specific algorithms can run.
Strongest counter-reading: As long as written answers are humanlike, subjective consciousness has been proved.
Adjudicated reply: 1950 is a test framework replacing the question in dispute; it does not deductively prove the inner nature of phenomenal consciousness.
Strongest counter-reading: Humans are needed to judge training, so the completion of intelligence depends on a final knower.
Adjudicated reply: The evaluation of training is an engineering arrangement, variable and not an ultimate ontological condition of the universe or of intelligence.
Strongest counter-reading: The self-reference of 1931 and of 1936 are different ways of writing one theorem.
Adjudicated reply: Their formal systems and aims of argument differ; undecidability within a system must be distinguished from the non-existence of a general effective procedure.
Strongest counter-reading: Having the reaction—diffusion equations already explains all the causes of the forms of natural life.
Adjudicated reply: The paper establishes the possibility of a mechanism and gives illustrations; biological empirical verification and the domain of parameters remain limited.
Compared with Gödel (No.62), both are concerned with the limits of formalization, while Turing stresses effective steps and algorithmic decision; compared with Bohr (No.61), both keep conditions of observation / formulation, but the description of quantum experiments and machine rules are different domains; compared with Darwin (No.63), the morphogenesis of 1952 is a mechanism of developmental dynamics and does not replace natural selection and genealogical explanation.
Summary: Turing used computability, universality and undecidability to form a bounded account of rule-governed computation, and advanced learning and the generation of form into model research; his self-inclusion is an explicit local formal structure, not the total occurrence of ①.
Final placement: ④ Explaining the world (B); ③ Questioning the ground as an important competing direction (C); ① is a D-level stress test
Scope limits: the degree of verification of the evidence is listed card by card; where there are reasonable alternative interpretations it is kept at C; originals not yet verified are not used as direct quotations.
④ B is formed independently by the specified originals of 1936, 1950 and 1952; the 1939 and 1948 materials are still treated as missing evidence or locally verified, and are not claimed as checked in full text.
Source 01｜S1｜Turing 1936, “On Computable Numbers”, checkable English text by section: https://www.abelard.org/turpap2/tp2-ie.asp
Source 02｜S2｜Mind 1950, “Computing Machinery and Intelligence”, full text of the original publication: https://doi.org/10.1093/mind/LIX.236.433
Source 03｜S3｜London Mathematical Society collection of Turing’s original papers, including the 1939 ordinal logics: https://londmathsoc.onlinelibrary.wiley.com/doi/toc/10.1112/%28ISSN%291460-244x.alan_turing_collection
Source 04｜S4｜Turing scientific bibliography: the 1948 NPL report and its later publication history: https://www.turing.org.uk/sources/biblio1.html
Source 05｜S5｜PDF of the original 1952 “The Chemical Basis of Morphogenesis”, held at the University of Cambridge: https://www.damtp.cam.ac.uk/user/gold/pdfs/teaching/old_literature/Turing1952.pdf
Source 06｜S6｜The Turing Digital Archive, Cambridge: typescript of the 1950 Mind paper: https://turingarchive.kings.cam.ac.uk/publications-lectures-and-talks-amtb/amt-b-9
Note on the text version: where quotations involve English translation, they are understood according to the translation noted in the card and not passed off as the original language; this archive does not treat later modern research as the author’s own text; the present limits of verification are stated item by item within the cards.