Jeff, List, It will take me some time to mentally assimilate your post, but it is most impressive, and I believe that it contributes mightily to the discussion of cosmology we've been having. I sincerely hope that everyone here interested in Peirce's cosmology in relation to contemporary versions reads it closely and critically.
One thing I will say for now is it is helpful that you make the distinction between Peirce's *metaphysics* and the *physics* of current cosmological models. Best, Gary R On Mon, Oct 6, 2025 at 2:21 PM Jeffrey Brian Downard <[email protected]> wrote: > List, > > I am interested in exploring the various ways Peirce might offer fruitful > strategies for framing questions and hypotheses about the evolution of the > cosmos. Given the shift in focus from interpreting Peirce to developing the > ideas in the context of contemporary lines of inquiry, I have given a new > name for this thread. Here is a short overview of how the issues might be > framed: > > I. What the Competing Hypotheses Seek to Explain > The first second of cosmic history is the most intensively modeled and > least directly observed interval in all of physics. Every cosmological > hypothesis—standard or alternative—attempts to answer the same deep > question: how did stable, law-governed order emerge from the primal > condition of the early universe? > Empirically, we can observe the cosmic microwave background and infer > conditions back to roughly 10⁻³⁶ s after the putative “beginning.” But > beyond that frontier, our equations lose coherence. When we attempt to wind > the clock backward, general relativity (GR) predicts an initial > singularity—an infinitesimal point of infinite density—while quantum > mechanics (QM) insists that such a point cannot exist, because uncertainty > forbids precise localization of both energy and position. The result is a > conceptual fissure at the very threshold of time. > The challenge is twofold. First, to reconcile the gravitational curvature > of spacetime (the language of GR) with the probabilistic field dynamics of > quantum theory (the language of QM). Second, to explain the apparent > emergence of regularities—space, time, fields, and forces from the initial > conditions—whatever those are presumed to be. > The standard cosmological model assumes a hot, dense quantum vacuum that > undergoes rapid inflation, cooling into particles, forces, and atomic > matter through a series of symmetry-breaking transitions. Our family of > hypotheses, following C. S. Peirce’s metaphysical principle of > “habit-taking,” interprets these same transitions not as the enforcement of > pre-existing laws but as the evolutionary crystallization of *habits*—stable > relational patterns that become laws through repetition and > self-reinforcement. The contrast, therefore, is not merely physical but > ontological: one treats laws as *given*, the other as *grown*. > My general strategy is to question the assumption that so much happened, > so fast, from what was initially a very small space. Instead of supposing > the cosmos was initially very small and then, in a “Big Bang” dramatically > inflated in a very short amount of time, I'd like to explore the hypothesis > that the timeframe and size of the universe was, in the very, very early > period, indeterminate. > II. The Standard Cosmological Account of the Very, Very Early Universe: > The Six Early Epochs within the First Second > > 1. Planck Era (0 – 10⁻⁴³ s) > Physics as we know it breaks down. The universe’s density exceeds 10⁹⁴ > g cm⁻³ and the temperature surpasses 10³² K. GR predicts a curvature > singularity, but quantum gravitational effects should dominate. No > consistent theory yet unites them. > 2. Grand-Unification Era (10⁻⁴³ – 10⁻³⁶ s) > Gravity decouples from the other fundamental interactions. The strong, > weak, and electromagnetic forces remain unified under speculative > grand-unified theories (GUTs). Vacuum fluctuations drive exponential > inflation. > 3. Inflationary Epoch (≈10⁻³⁶ – 10⁻³² s) > The universe expands by a factor of ~10⁵⁰ in a tiny fraction of a > second, smoothing out inhomogeneities. Quantum fluctuations are stretched > to cosmic scales, seeding later galaxy formation. When inflation ends, > latent vacuum energy converts into matter and radiation—a process called > “reheating.” > 4. Electroweak Epoch (10⁻¹² – 10⁻⁶ s) > The strong force separates from the electroweak. The Higgs field > acquires a nonzero vacuum expectation value, giving mass to particles. W > and Z bosons and leptons acquire distinct identities. > 5. Quark Epoch (10⁻⁶ – 10⁻⁴ s) > The universe is a hot plasma of quarks, antiquarks, and gluons. As it > cools below ~10¹² K, quarks begin to bind into hadrons (protons and > neutrons). > 6. Hadron and Lepton Epochs (10⁻⁴ – 1 s) > Matter–antimatter annihilation occurs, leaving a slight excess of > baryons. Neutrinos decouple. By ~1 s, the universe is filled with photons, > neutrinos, electrons, protons, and neutrons in near-thermal equilibrium. > > 2. The Theoretical Foundations > The standard model of cosmology (ΛCDM + inflation) joins: > > - General Relativity, governing the dynamics of spacetime and cosmic > expansion (via Einstein’s field equations). > - The Standard Model of Particle Physics, governing matter and fields > via quantum gauge theories. > > Each works remarkably well in its proper domain. GR predicts large-scale > structure and gravitational lensing; quantum field theory predicts particle > behaviors confirmed to 1 part in 10¹¹. Yet their conceptual languages > conflict. > 3. The Central Tension: GR vs QM > > - Background independence vs. fixed background: > GR treats spacetime geometry as dynamic; quantum theory presupposes a > fixed spacetime background. > - Deterministic vs. probabilistic law: > GR evolves smoothly and deterministically; quantum evolution is > probabilistic and discontinuous upon measurement. > - Continuum vs. discreteness: > GR’s continuum manifolds clash with QM’s quantized fields and > operators. > > Attempting to merge them yields contradictions. Quantizing gravity by > standard techniques leads to non-renormalizable infinities. String theory > replaces point particles with one-dimensional objects to tame those > divergences, while loop quantum gravity discretizes space itself into spin > networks. Both remain mathematically elegant yet empirically unconfirmed. > The deeper problem is conceptual: both assume laws are fixed and > pre-existent. Time, in both frameworks, is treated as a parameter that > orders events, not as something that itself *evolves*. When we > extrapolate back to t → 0, these assumptions collapse. The singularity is > not a physical object but a signal that the framework itself has reached > its limit. > Thus, the standard model offers a magnificent but incomplete chronicle. It > describes *how* the cosmos evolves from 10⁻³⁶ s onward, but not *why* > laws themselves appear, why symmetries break as they do, or why certain > constants take the values that make structure possible. > III. The Peircean Family of Hypotheses > 1. Philosophical Premise: Law as Evolving Habit > C. S. Peirce proposed in his 1891 essay “The Architecture of Theories” > that “the only possible way of accounting for the laws of nature and for > uniformity in general is to suppose them results of evolution.” The > universe, on this view, begins not in order but in pure spontaneity, a > chaos of ungoverned possibilities. Through repetition and reinforcement of > relations that persist, habits form; habits stabilize into laws. > 2. Ontological Ingredients: > > 1. Firstness — Pure Potentiality as Quality: The primordial condition > is a field of highly vague, undifferentiated potential having a continuum > of qualities, comparable to a pre-metric manifold. Temporal relations are > not well ordered. Spatial relations have very high degrees of freedom, > approximating an infinitude of vague topological dimensions. > 2. Secondness — Reaction: Initially, there are no actual objects > having a substantial character of individuals that perdue over time. > Rather, highly random encounters among continuous potentials yield > constraints—proto-events analogous to quantum fluctuations. > 3. Thirdness — Mediation/Habit: Stable patterns emerge that mediate > between possibilities and facts; these are the early ordered habits that > evolve into laws having symmetries. > > This triadic cycle repeats iteratively, giving rise to more complex, > self-referential systems of law. Order grows as natural habits. In time, > these natural habits take the character of natural laws having nested > levels of necessity and contingency, woven together into an evolving system > of regularities. > 3. Cosmological Reformulation > In mathematical terms, the Peircean hypothesis treats the evolution of > order as a process of constraint accumulation in an initially unconstrained > relational manifold. Instead of assuming pre-existing spacetime, we posit > networks of relations—logical and topological—whose persistent interactions > generate the effective metric structure. > > - Temporal Order: Time is not a fixed metrical parameter but an > emergent order parameter expressing the persistence of relation. > - Metric Emergence: As habits of relation stabilize, equivalence > classes of relational paths become metrically consistent; curvature arises > from deviations in those habits. > - Quantum Indeterminacy: Rather than randomness being primitive, > indeterminacy reflects ongoing openness of the habit-formation process—what > Peirce called *tychism*. > > 4. Physical Analogues > In practice, these ideas correspond to several contemporary research > directions. Here are a few: > > - Causal-set theory, which builds spacetime from ordered relations. > - Process physics (Cahill, Kauffman), in which information networks > self-organize into geometry. > - Relational quantum mechanics, treating states as relations rather > than substances. > > The models I am developing seek to formalize these insights through > iterative mapping functions on networks of relations—analogous to > topological and projective transformations that, through self-consistency > constraints, converge toward a stable metric manifold. > 5. Epochal Reconstruction > In this framework, the first “second” is not a moment after a singularity > but a phase transition from ungoverned potential to emergent order: > > 1. Pre-habit phase (Peircean Firstness): Random relation fields > without duration or extent. > 2. Formation of stable triads (Secondness → Thirdness): > Self-consistent relational loops persist; these become the seeds of > temporal and spatial continuity. > 3. Emergent metrics: Statistical regularities among triads define > curvature; gravitational attraction is a large-scale manifestation of this > tendency of relations to cohere. > 4. Law consolidation: Repeated patterns establish stable > transformation rules—analogues of conservation laws and field equations. > > Thus, what the standard model describes as inflation and symmetry breaking > are interpreted as episodes of accelerated habit formation, in which local > relational networks reach new equilibria. > 6. Testable and Mathematical Implications > > - Variable constants: If laws evolve, coupling constants may vary > slowly over cosmic time—a testable prediction. > - Self-organizing field equations: Einstein’s equations appear as > late-stage equilibria of evolving relational space/time constraints that > co-evolve with the natural habits that evolve into the laws governing > strong, weak, and EM forces. > - No initial singularity: The vague highly random potential fields in > which space and time are not yet ordered are posited as kind of limiting > case from which order grows as a self-limiting process. > > This metaphysical framework can be made exact by representing evolving > relational networks through categorical or topological formalisms, such as > spin networks or iterative projective geometries, providing a unified > schema that naturally bridges quantum discreteness and gravitational > continuity. > IV. Comparative Evaluation > The standard cosmological model stands as one of the great triumphs of > modern science. It quantitatively predicts nucleosynthesis, cosmic > microwave background anisotropies, and large-scale structure. Its weakness > lies not in what it explains, but in what it must assume: fixed laws, fixed > constants, and a spacetime framework that pre-exists the very universe it > describes. It is operationally powerful yet ontologically incomplete. When > traced back to the first instants, its equations give rise to tensions > bordering on contradictions--singularities and unexplained initial > conditions. > The Peircean family of hypotheses inverts the order of explanation. It > begins with chaos, not law; with relation, not substance; with habit > formation, not imposed rule. Its strength is conceptual coherence across > scales: the same logic of iterative habit formation that explains the > emergence of atomic stability or biological order also accounts for cosmic > law. It offers a genuinely evolutionary metaphysics of law, potentially > unifying physical and logical modes of order. > Yet it faces formidable challenges. It lacks a single, empirically > confirmed mathematical formalism equivalent to GR or quantum field theory. > Its language of “habits” and “relations” must be rigorously specified to > make testable predictions. It risks drifting toward philosophical > generality if not anchored in quantitative models. > In sum: > *Criterion* > *Standard Model* > *Peircean Habit Hypothesis* > Predictive Power > High (CMB, nucleosynthesis, structure) > Moderate (conceptual; testable via variable constants) > Ontological Coherence > Fragmented (QM vs GR) > Unified (laws evolve from habits) > Empirical Confirmation > Extensive > Emerging / indirect > Explanatory Depth > Assumes laws > Explains laws > Mathematical Formalism > Mature > Developing (categorical/topological) > > For those who, like me, would like to develop and apply Peirce's methods > and explanatory strategies to contemporary questions in cosmology, our work > is cut out for us. How might we move from informal diagrams and toy models > (e.g. a spot of ink on a page, a blackboard, rolling of dice, drawing from > an urn, etc.) to formal models? What mathematical frameworks should we draw > on for the sake of developing models that will enable us to make the > hypotheses about the law of mind and the growth of order more exact? > > Yours, > > Jeff > > > > > ------------------------------ > *From:* [email protected] <[email protected]> on > behalf of Jon Alan Schmidt <[email protected]> > *Sent:* Sunday, October 5, 2025 5:55 PM > *To:* Peirce-L <[email protected]> > *Subject:* Re: [PEIRCE-L] An attempt at at dialogical integration of > Peirce's early and late cosmologies, was, Peirce's semeiotic holism > > Gary R., List: > > In accordance with my label of the first cosmological "layer" as the > constitution of *being*, you are correct that it would apply to *any > possible* universe. However, as I see it, there is no reason to suspect > that any other universes *exist* except our own; in fact, since such a > conception has no practical bearings, it is "meaningless gibberish" (CP > 5.423, EP 2:338, 1905). Put another way, the inexhaustible continuum (3ns) > of indefinite possibilities (1ns) indeed *transcends *our universe, but > those possibilities that have been actualized (2ns) *constitute *our > universe. After all, Peirce posits multiple "Platonic worlds" but only one > "actual universe of existence," which is the one "in which we happen to be" > (CP 6.208, 1898). > > My use of "complete chaos" to describe the initial state of things also > comes directly from Peirce. "The original chaos, therefore, where there was > no regularity, was in effect a state of mere indeterminacy, in which > nothing existed or really happened" (CP 1.411, EP 1:278, 1887-8). "The > state of things in the infinite past is chaos, tohu bohu, the nothingness > of which consists in the total absence of regularity" (CP 8.317, 1891). > "So, that primeval chaos in which there was no regularity was mere nothing, > from a physical aspect" (CP 6.265, EP 1:348, 1892). "In the original chaos, > where there was no regularity, there was no existence. ... This we may > suppose was in the infinitely distant past" (CP 1.175, c. 1897). > > I agree that the entire universe cannot possibly be a complex *adaptive > *system > without existing within an environment to which it is *adapting *itself, > and that 1ns encompasses not only qualities but also "Freedom, or Chance, > or Spontaneity" (CP 6.200, 1898). > > GR: Peirce’s grand semeiotic vision in which the universe itself is > conceived as a vast sign, a perfect sign, and a semiosic continuum from > which facts (and events?) are prescinded > > To clarify, Peirce explicitly describes the universe as "a vast > representamen," but he does not directly connect his remarks about a > "perfect sign" to the universe, and I am not aware of any writings where he > refers to a "semiosic continuum." That is why the subtitle of my "Semiosic > Synechism" paper is "A *Peircean *Argumentation," not "*Peirce's > *Argumentation"; > I believe that my synthesis is faithful to his insights, but I recognize > that he never spelled it out that way himself. > > As for your reference to "facts (and events?)," Peirce seems to maintain > that we *only *prescind facts, because he *defines *an event as "an > existential junction of incompossible facts ... The event is the > existential junction of *states *(that is, of that which in existence > corresponds to a *statement * about a given subject in representation) > whose combination in one subject would violate the logical law of > contradiction" (CP 1.492&494, c. 1896). This is consistent with his remark > a decade later, "A *fact *is so highly a prescissively abstract state of > things, that it can be wholly represented in a simple proposition" (CP > 5.549, EP 2:378, 1906). > > Peirce also takes exception with "the idea that a cause is an event of > such a kind as to be necessarily followed by another event which is the > effect" (CP 6.66, 1898). On the contrary, "So far as the conception of > cause has any validity ... the cause and its effect are two *facts*" (CP > 6.67). "Now it is the ineluctable blunder of a nominalist ... to talk of > the cause of an event. But it is not an existential event that has a cause. > It is the *fact*, which is the reference of the event to a general > relation, that has a *cause*" (CP 6.93, 1903). We prescind two *different > *facts and recognize that the earlier one is a cause, the later one is > its effect, and the *change *from one state of things to the other is an > event. > > Regards, > > Jon Alan Schmidt - Olathe, Kansas, USA > Structural Engineer, Synechist Philosopher, Lutheran Christian > www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt > > On Sat, Oct 4, 2025 at 11:00 PM Gary Richmond <[email protected]> > wrote: > > Jon, List, > > We are clearly in agreement on one matter: that while Peirce initially > conceived the universe as beginning with 1ns (possibility, “boundless > freedom”), he later came to see 3ns (generality, continuity, habit-taking) > as primordial. Categorial involution—that is, that 3ns involves 2ns & 1ns, > and 2ns involves only 1ns—adds logical support to that later view. > Additional support comes from your arguing the cosmological integration of > these three as a continuum (3ns) of indefinite possibilities (1ns), only > some of which become actualized (2ns), with the sequence of events > unfolding as spontaneity (1ns), reaction (2ns), and habit (3ns). As you > argue, this reinforces an underlying evolutionary trajectory from chaos, > through process, toward regularity (ultimately, complete regularity in > Peirce’s view). > > JAS: My own attempt at integrating these two accounts or phases was to > suggest that the *constitution (or hierarchy) of being* is an > inexhaustible continuum (3ns) of indefinite possibilities (1ns), some of > which are actualized (2ns); while the *sequence of events* in each case > when this happens consists of spontaneity (1ns) followed by reaction (2ns) > and then habit-taking (3ns). The resulting overall *evolution of states *is > from complete chaos (1ns) in the infinite past, through this ongoing > process (3ns) at any assignable date, toward complete regularity (2ns) in > the infinite future. These three "layers" conform respectively to your > categorial vectors of representation, order, and process. (Emphasis added, > GR) > > You seem to be arguing that* your* three layers (italicized above)*: the > constitution of being*,* the sequence of events*, and *the overall > evolution of states* all apply to our existing universe. I don't agree. > As I've been arguing, the blackboard metaphor suggests to me that your > first layer, the constitution of being, does not apply only to our > universe, but to* any possible universe* that might come into existence. > Indeed, in my view 'being' is not 'constituted' in the proto-universe > represented by the blackboard at all -- that's why I refer to it as a > * proto*-universe. There is, no doubt, a *reality moving towards > existence*; but in my reading of the lecture in which the blackboard > analogy appears, out of the infinite number of 'Platonic ideas' any number > of different ones *migh*t have been 'selected' so that some other > universe different from ours might have come into existence (who knows? > *has* come into existence). > > I would also not call the proto-world foreshadowing our existent cosmos > "complete chaos". The ur-continuity of the blackboard already suggests that > there is something in the cosmic schema that has the capacity and > intelligence to select just those Platonic ideas which *can be* and * > will be realized *in an actual, existential, evolutionary cosmos such as > ours. What seems at all 'chaotic' to me is that infinite number of Platonic > 'ideas' (characters, qualities, dimensions, categories, etc.) But do those > possibilities actually represent chaos? > > But to return for a moment to a different cosmological disagreement, it > has been pointed out before by several on the List including both of us, > that the universe as a whole cannot qualify as a complex adaptive system > because it does not exist within a larger environment to which it must > constantly adapt. For example, in Peirce's cosmology 1ns corresponds not > essentially to qualities but to pure possibility and “boundless freedom.” > In his 1898 blackboard analogy Peirce explicitly *does not confine these > categories to the spatiotemporal universe*; instead, he refers to > “Platonic worlds” of infinite possibilities, some of which become the > characters of a universe which *will come into being*. He is clear that > this particular universe in which we live and breathe and have our being > came out of one such Platonic world, which may even suggest, as I and > others have noted, an early multi-universe model. > > The two later developments in Peirce’s thought which you say shaped your > own synthesis, Jon: (1) the topical conception of continuity which sees a > continuum as an undivided whole of indefinite parts, and (2) Peirce’s grand > semeiotic vision in which the universe itself is conceived as a vast sign, > a perfect sign, and a semiosic continuum from which facts (and events?) are > prescinded—further explicates and extends Peirce’s cosmology. > > Best, > > Gary R > > _ _ _ _ _ _ _ _ _ _ > ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] > . > ► <a href="mailto:[email protected]";>UNSUBSCRIBE FROM > PEIRCE-L</a> . 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