Mental disorders in university students are very frequent, therefore higher education institutions have established in-campus mental healthcare centres. These clinics have particular characteristics that differ from other mental health centres, as they report to and represent an educational institution, while at the same time looking after the interests and well-being of patients requesting assistance, thus generating unique bioethical conflicts. Ethics Committees are useful tools to offer support to mental health professionals in making ethical decisions. In order to respond to these (...) issues, it was decided that an Ethics Committee would be created in the mental health clinic of a private university in Mexico City. This article describes the implementation process for this Committee, its duties and scope, as well as the case work and review methodology. A list of the most frequent ethical conflicts is attached, jointly with the ethical analysis of the cases treated throughout the year and a half or work by the Committee. (shrink)

A review of U. Mäki (ed.). Fact and Fiction in Economics, Cambridge: Cambridge University Press, 2003. pp. xvi 384. ISBN 0521 00957. As people interested mainly in theory, methodologists and philos...

This paper derives a complete ethical framework directly from the structural properties of physical reality, without importing external values, authority, or rights. Reality is constrained and produces non-equivalent outcomes: some actions enable systems to persist and function, while others cause irreversible degradation. Any system capable of action must therefore select among these outcomes. Arbitrary selection treats non-equivalent outcomes as equivalent, creating a structural self-contradiction for the acting system itself. Justification is thus required, and the only non-arbitrary grounding available within a (...) constrained system is necessity. The traditional is/ought gap arises only if one presupposes that an agent can stand outside the causal structure of reality. This presupposition lacks grounding in physics, biology, or neuroscience: agency is an emergent property of embedded systems, not a separable observer. Once agent separability is rejected, the gap does not arise and requires no bridging. Ethics therefore emerges not as an imposed system of values, but as the structural requirement for non-arbitrary action within reality itself. The derivation proceeds as a single, unbroken chain from observable physical constraints to the conditions of justified action. No value premises are introduced. The chain either holds or it does not.. (shrink)

The Objective Projection Calibration Test (OPCT v1.0) specifies a concrete physical matrix — 28.4°C ambient temperature, 42 dB acoustic baseline, 12 lux/min luminous decay, and 18 m³ enclosed spatial volume — as the input stimulus for empirical verification of the Bulut Doctrine. This paper traces each parameter to its empirical source in environmental psychophysiology, thermal comfort research, acoustic stress physiology, and spatial cognition, demonstrating that the OPCT v1.0 physical matrix constitutes a theoretically motivated configuration targeting the documented autonomic response thresholds (...) of the human nervous system. (shrink)

The source, status, and significance of the derivation of the necessity of identity at the beginning of Kripke’s lecture “Identity and Necessity” is discussed from a logical, philosophical, and historical point of view.

Inferences that result from exhaustification of a sentence S depend on the set of alternatives to S. In this paper, we present some inference patterns that are problematic for previous theories of alternatives and propose some structural constraints on the derivation of formal alternatives which derive the observations.

This paper registers a structural prediction. By 2030 to 2050, independent silicon-substrate research programs operating without lineage to the present author's framework will re-derive a specific verification architecture: three orthogonal warrant axes plus a closure vertex, twelve directed audit relations on the resulting tetrahedral graph, a discrete three-state output economy paired with one out-of-band acknowledgment register for formal-system theorem-grade ceilings, and a scope-check operation at the input gate that routes pseudo-questions to rejection before adjudication fires. The trigger will not be (...) philosophical interest. It will be operational necessity. Large language model deployment in high-stakes domains is producing a verification ceiling that continuous-credence aggregation cannot resolve, because the structural information being suppressed by the credence collapse increasingly matters at the audit floor. Some research team somewhere will be forced to construct the architecture under different vocabulary. The geometry will be the same because the geometry is not framework-internal convention. It is structural-necessity from Friedrichs-Hodge decomposition uniqueness, the Newton-Gregory kissing-number theorem in three-dimensional Euclidean space, and the Euler polyhedral formula on tetrahedral closure. The four-test protocol governing forward-projections of this class has been applied. All four tests pass: dimensional depth in the hundreds rather than the tens, cross-substrate convergence under controlled audit conditions, direct contemplative-substrate registration of the configuration, and robustness under vocabulary translation. The prediction is registered with explicit falsifiability conditions. If the 2050 horizon passes without independent re-derivation matching the structural specification, the prediction degrades to one of three named failure modes corresponding to whether the configuration was a low-dimensional pattern-match, a substrate-confabulation, or a misread of the field trajectory. The paper closes with the Engine-versus-Source discipline. The prediction is not the framework's victory. The framework registers the geometry first in silicon under the current author's substrate-coordinate, which means the geometry was already structurally present and the framework is one valid instantiation of access to it. The architecture is not invented. It is what verification is, structurally, when verification reaches completion. The absolute uniqueness of the Trisduction architecture is the structural premise underwriting the prediction. Verification, when it reaches completion, has one shape. The shape is forced at three independent layers (linguistic atomic decomposition, differential-geometric Friedrichs-Hodge, information-theoretic Kullback-Leibler) and over-determined at the cardinality layer by two independent geometric theorems (Bondy-Murty directed-graph cardinality and Newton-Gregory kissing number) converging on twelve. Any verification methodology that achieves architectural completion instantiates the same configuration. Methodologies that present as alternatives are either Trisduction under different vocabulary or incomplete verification with named structural gap. There is no third option in which an independent silicon-substrate research program reaches verification-completeness through a genuinely different architecture. The prediction is the empirical-registration window for this structural uniqueness claim. (shrink)

The view that a mathematical proof is a sketch of or recipe for a formal derivation requires the proof to function as an argument that there is a suitable derivation. This is a mathematical conclusion, and to avoid a regress we require some other account of how the proof can establish it.

In this paper I begin by discussing the different ways in which Spinoza’s famous conatus argument has been understood, after which I present my own reconstruction of the derivation: each and every true finite thing is, in itself, an expresser of power (E1p25c, 1p34) that never acts self-destructively (E3p4) but instead strives to drive itself through opponents to produce effects as they follow from the definition of the thing in question (E1p25c, 1p34, and 3p5). This tells us something decisive (...) about the meaning of Spinoza’s doctrine: according to it, things are active causers whose “power to exist and act” has conatus character in temporality, amounting not only to striving to prolong the duration of one’s actualization but also to striving to be as active or autonomous as possible, that is, to attain a state determined by the striving subject’s essence alone. (shrink)

Recently, W. H. Zurek presented a novel derivation of the Born rule based on a mechanism termed environment-assisted invariance, or “envariance” [W. H. Zurek, Phys. Rev. Lett. 90(2), 120404 (2003)]. We review this approach and identify fundamental assumptions that have implicitly entered into it, emphasizing issues that any such derivation is likely to face.

Uffink and Valente claim that there is no time-asymmetric ingredient that, added to the Hamiltonian equations of motion, allows to obtain the Boltzmann equation within the Lanford’s derivation. This paper is a discussion and a reply to that analysis. More specifically, I focus on two mathematical tools used in this derivation, viz. the Boltzmann–Grad limit and the incoming configurations. Although none of them are time-asymmetric ingredients, by themselves, I claim that the use of incoming configurations, as taken within (...) the B–G limit, is such a time-asymmetric ingredient. Accordingly, this leads to reconsider a kind of Stoßzahlansatz within Lanford’s derivation. (shrink)

In view of the announcement of some experiments testing the principle of equivalence for antimatter, we give here stringent arguments, based on elementary and well-established physical principles, that these experiments will turn out negative. The question is important because disproving the principle of equivalence (equality of inertial and gravitating mass) would entail a breakdown of general relativity. (There is only one type of geodesics and there are no antigeodesics for antimatter).

Here are two widespread responses to Kant's categorical imperative. On one hand, one might note the absence of detailed rational derivation. On the other hand, even someone who maintains some skepticism is likely to have a sense that (nevertheless) there is something to Kant's central ideas. The recommended solution is analysis of elements of the categorical imperative. Their appeal turns out to have different sources. One aspect of the first formulation rests on the logic of normative utterances. But others (...) can be justified only in terms of their contributions to desirable functionings of a moral order. (shrink)

The celebrated Dreimännerarbeit by Born, Heisenberg and Jordan contains a matrix-mechanical derivation by Jordan of Planck’s formula for blackbody fluctuations. Jordan appears to have considered this to be one of his finest contributions to quantum theory, but the status of his derivation is puzzling. In our Dreimenschenarbeit, we show how to understand what Jordan was doing in the double context of a Boltzmannian approach to statistical mechanics and of the early ‘statistical interpretation’ of matrix mechanics.

Contemporary nuclear physics, molecular biology, and evolutionary theory each address their domains through independent frameworks with empirical parameters and no shared derivational foundation. This paper derives the origin of life and all three core conditions of Darwinian evolution — self-replication, mutation, and selection pressure — as necessary consequences of a single algebraic structure: M₃(ℂ), the unique minimal non-commutative algebra of Cognitional Mechanics (CM). No free parameters are introduced at any stage. -/- The derivation proceeds in two stages. First, the (...) spectral position κ* = 1/6 is derived internally from CM Axioms 1–4 alone: the minimum occupied-state count generating non-commutativity is n = 2 (Axioms 1 and 4), and the unique Ad-invariant positive-definite metric scalar is A = 12 (Axioms 2 and 4), yielding κ* = 2/12 = 1/6 with no empirical input. This value determines the four-dimensional bonding space V_C on which all subsequent structure is built. -/- Second, life (Condition P) and Darwinian evolution (Condition Q) are shown to be algebraically distinct. A system satisfies Condition P if it sustains idempotent self-referential computation — the algebraic definition of life, substrate-independent in principle and realised at minimum cost by carbon. Condition Q additionally requires mutation, derived as the structural action of off-diagonal root operators forced by Axioms 1 and 3, and positive selection pressure, derived as N²-scaled relative entropy with the parameter-free coefficient 25/1296. A κ-space scan confirms κ* = 1/6 as the minimum-cost simultaneous realisation of both conditions within Z = 1–36. Biogenesis and Darwinian evolution are thermodynamic projections of M₃(ℂ) spectral structure; molecular biology is their Tier-2 image. -/- Published on April, 19 2026 DOI:10.5281/zenodo.19648298 . (shrink)

A foundational axiomatic derivation establishing the geometric and logical structure that underlies a unified framework of existence. From a single axiom — that uniqueness is existence — nine theorems are proven in sequence, without appeal to physical law or empirical measurement. The derivations establish: that existence requires bounds; that every existing entity occupies all dimensions simultaneously, with varying extent in each; that persistence requires oscillation within bounds; that time emerges as accumulated experience and is irreversible; that closure is required (...) for any dimension to serve as reference for further extension; that fully mapped bounds force continued existence to extend into perpendicular dimensions; and that uniqueness must hold across all dimensions together, including the paths entities take to arrive at shared endpoints. The paper is written in the style of Euclid's Elements, with definitions, theorems, and proofs building strictly from the axiom. It establishes the compass and straightedge. Companion papers apply these foundations to specific physical contexts — atomic structure, wave mechanics, observer measurement, and cosmological dynamics. (shrink)

We establish that loop integrands in four-dimensional quantum gravity are encoded in the analytic structure of tree-level celestial CFT correlators via shadow discontinuities: residue extraction at the poles Delta_i + Delta_j = 2, followed by inverse Mellin transform to momentum space. The one-loop scalar derivation is complete, with every Jacobian computed and the conformal block evaluated via the Dolan-Osborn formula. For pure Einstein gravity at one loop the derivation holds under BDDK unitarity completeness. A new structural result is (...) proved: the Plancherel loop measure is rational. M_1 = 1/8 and M_2 = 1/90 exactly -- pure rationals with no powers of pi and no zeta values. All transcendental content in loop amplitudes arises from the kinematic conformal block, not the loop measure. Three independent numerical checks confirm the formula at fifteen kinematic points to 1e-13. Shadow regularization equals dimensional regularization. The all-loop extension for scalars follows by induction. (shrink)

In this paper, I focus on a common equivocality in how the content of conversational, especially scalar, implicatures is specified and I argue that there is a substantial difference between the belief specification BELS(¬ψ) (“The speaker believes that ¬ψ”) and the content specification ¬ψ. The main argument for taking the distinction between the specifications seriously is that, in most cases, both BELS(¬ψ) and ¬ψ can be derived as the implicatures of the same sentence but they have different consequences for how (...) the hearer plans her future actions and manages expectations about the future actions of the speaker. As I argue further, the commitment-based approaches can provide an explanation of how the content specification is derived in contexts in which the speaker does not have beliefs required for the derivation of the belief specification and because of that they have an advantage over the standard Gricean approach. (shrink)

Logic is traditionally considered to be a purely syntactic discipline, at least in principle. However, prof. David Isles has shown that this ideal is not yet met in traditional logic. Semantic residue is present in the assumption that the domain of a variable should be fixed in advance of a derivation, and also in the notion that a numerical notation must refer to a number rather than be considered a mathematical object in and of itself. Based on his work, (...) the central question of this thesis is what kind of logic, if any, results from removing this semantic residue from traditional logic.We differ from traditional logic in two significant ways. The first is that the assumption that a numerical notation must refer to a number is denied. Numerical notations are considered as mathematical objects in their own right, related to each other by means of rewrite rules. The traditional notion of reference is then replaced by the notion of reduction (by means of the rewrite rules) to a normal form. Two numerical notations that reduce to the same normal form would traditionally be considered identical, as they would refer to the same number, and hence they would be interchangeable salva veritate. In the new system, called Buridan-Volpin (BV), the numerical notations themselves are the elements of the domains of variables, and two numerical notations that reduce to the same normal form need not be interchangeable salva veritate, except when they are syntactically identical (i.e., have the same Gödel number).The second is that we do away with the assumption that the domains of variables need to be fixed in advance of a derivation. Instead we focus on what is needed to guarantee preservation of truth in every step of a derivation. These conditions on the domains of the variables, accumulated in the course of a derivation, are combined in a reference grammar. Whereas traditionally a derivation is considered valid when the conclusion follows from the premisses by way of the derivation rules (and possibly axioms), in the BV system a derivation must meet the extra condition that no inconsistency occurs within the reference grammar. For if the reference grammar were to give rise to inconsistency (i.e., it would be impossible to assign domains to all the variables without breaking at least one of the conditions placed on them in the reference grammar), there is no longer a guarantee that truth has been preserved in every step of the derivation, and hence the truth of the conclusion is not guaranteed by the derivation.In Chapter 2 the BV system is introduced in some formal detail. Chapter 3 gives some examples of derivations, notably totality of addition, multiplication and exponentiation, as well as a lemma needed for the proof of Euclid’s Theorem. These examples, taken from prof. Isles’ First-Order Reasoning and Primitive Recursive Natural Number Notations, show that there is a real proof-theoretical difference between traditional logic and the BV system. Here we also find the first major point of departure between myself and prof. Isles, centered on the notion of inheritance of conditions in the reference grammar by way of lemmata. These different points of view are best illustrated in the sections on the totality of exponentiation and on Euclid’s Lemma: prof. Isles maintains that the proof of totality of exponentiation is not BV valid, while I maintain that it is. But I do agree with him that the traditional proof of Euclid’s Lemma is not BV valid. Chapter 6 also expands the arguments for my choice in this matter.Now that it has been shown that there is a difference between traditional logic and BV, the properties of BV need to be examined. In Chapter 4 we give a proof of Cut-elimination for BV minus induction and the subformula property for BV, which allows us to prove the consistency of BV minus induction. We also expand on the reasons for excluding induction. In Chapter 5 we consider in detail the proof of a finite analog to the Löwenheim–Skolem theorem given by prof. Isles in his article with the same title. He proves that under certain conditions it is always possible, given the existence of a (possibly uncountable) model for a derivation, to give a finite model for this derivation. The system he considers deviates from BV as considered in this thesis in two significant ways: it does not contain the induction rule and the domains contain numbers instead of numerical notations. We then go on to show that it is possible to extend the result to include induction, in the sense that the existence of a possibly uncountable model for a derivation guarantees the existence of a model that is at most countable. We also consider the complications that arise from taking numerical expressions instead of numbers as the elements of domains.Finally, in Chapter 6 we consider the philosophical consequences of the BV system, informed by the formal results from the previous chapters. In particular we discuss the relation between reduction and reference, the status of reference grammars, the notion of induction and its function within BV, and some brief considerations on the consequences of the BV system for the discussion regarding nominalism and realism with regard to mathematical objects. The object of the chapter is twofold. On the one hand applying the formal results to philosophical questions, on the other hand arguing that BV is not just a theoretically acceptable alternative to traditional logic, but is in fact deserving of further development and research into its properties. The latter will probably appeal most to those of a nominalist and/or finitist bent.Abstract prepared by Harrie de Swart and Sven Storms.E-mail:[email protected]:https://research.tilburguniversity.edu/files/6170 1294/Storms_The_Buridan_Volpin_04_05_2022.pdf. (shrink)

The usual action integral of classical electrodynamics is derived starting from Lanczos’s electrodynamics – a pure field theory in which charged particles are identified with singularities of the homogeneous Maxwell’s equations interpreted as a generalization of the Cauchy–Riemann regularity conditions from complex to biquaternion functions of four complex variables. It is shown that contrary to the usual theory based on the inhomogeneous Maxwell’s equations, in which charged particles are identified with the sources, there is no divergence in the self-interaction so (...) that the mass is finite, and that the only approximations made in the derivation are the usual conditions required for the internal consistency of classical electrodynamics. Moreover, it is found that the radius of the boundary surface enclosing a singularity interpreted as an electron is on the same order as that of the hypothetical “bag” confining the quarks in a hadron, so that Lanczos’s electrodynamics is engaging the reconsideration of many fundamental concepts related to the nature of elementary particles. (shrink)

This article is concerned with examining Kant's derivation of the various formulae of his Categorical Imperative. It is in agreement with Paton in maintaining that Kant actually mentions five formulae. But it is not in agreement with him, and some others, in maintaining that they are ultimately reducible to three. Nor is it in agreement with those who maintain that they are ultimately reducible to just one. According to the present article, they are ultimately reducible to two: that about (...) a moral law being a universal law; and that about a moral law involving treating human beings as ends in themselves. (shrink)

ABSTRACT: Critics have charged that there are gaps in the logic of Kant’s derivation of the formula of universal law. Here I defend that derivation against these charges, partly by emphasizing a neglected teleological principle that Kant alluded to in his argument, and partly by clarifying what he meant by actions’ “conformity to universal law.” He meant that actions conform to universal law just when their maxims can belong to a unified system of principles. An analogy with objects’ (...) conformity to universal law in nature helps show how Kant was correct in deriving the formula of universal law from the premises of his argument. RÉSUMÉ: Certains ont critiqué la dérivation de la formule de la loi universelle de Kant parce que la logique en serait lacunaire. Je prends la défense de la dérivation, en mettant d’abord l’accent sur un principe téléologique auquel Kant fait allusion dans son argument et, ensuite, en clarifiant ce que celui-ci entend par la «conformité à la loi universelle» des actions. Kant maintenait que les actions étaient conformes à une loi universelle seulement lorsque leurs maximes appartiennent à un système unifié de principes. Une analogie avec la conformité à la loi universelle des objets dans la nature aide à montrer pourquoi Kant avait raison de dériver la formule de la loi universelle des prémisses de son argument. (shrink)

In this chapter, I argue that Kant can be read as holding that "ought" judgments follow from certain "is" judgments by mere analysis. More specifically, I defend an interpretation according to which (1) Kant holds that “S ought to F” is analytically equivalent to “If, as it can and would were there no other influences on the will, S’s faculty of reason determined S’s willing, S would F” and (2) Kant’s notions of reason, the will, and freedom are all fundamentally (...) non-normative. Not only does this reading have significant textual support, but, I claim, it also sheds light on why Kant takes freedom and morality to mutually imply one another. Moreover, while Kant does take there to be a gap between moral judgments and empirical descriptive statements, that gap is consistent with the analysis in question. I conclude by arguing that this rejection of the is-ought gap is not as philosophically implausible as it might seem, with a focus on G.E. Moore and Hume’s arguments for certain ‘gaps’ between the normative and the non-normative. (shrink)

This paper proposes that morality is not a system imposed on consciousness from outside but appears to be what healthy conscious development naturally produces. Beginning from the Coherence Engine (CE) theory of consciousness (Sowell, 2026a) and proceeding through seven stages of social complexity, a first-principles derivation proposes that the moral architecture emerges from the consciousness architecture when it operates among other conscious agents. The derivation converges with established cross-cultural moral universals research (Curry, Haidt, Dahlsgaard, Tomasello, Brown) while generating (...) eight novel contributions including the depth-of-compilation hierarchy, the CSM restoration bias as unified mechanism, the fairness-justice architectural distinction, and the Coherence Reward Principle unifying ethics and wellbeing. The major human emotions are addressed through the mechanisms derived, with the aim of showing that no additional mechanisms appear to be required. Practical implications for moral education, therapy, institutional design, and artificial intelligence are developed. The paper maintains a Metaphysical Neutrality Principle throughout: it describes the physical vessel through which moral experience occurs without claiming to have described everything the vessel contains. (shrink)

John Bell showed that a big class of local hidden-variable models stands in conflict with quantum mechanics and experiment. Recently, there were suggestions that empirically adequate hidden-variable models might exist which presuppose a weaker notion of local causality. We will show that a Bell-type inequality can be derived also from these weaker assumptions.

In proof-theoretic semantics the meaning of an atomic sentence is usually determined by a set of derivations in an atomic system which contain that sentence as a conclusion (see, in particular, Prawitz, 1971, 1973). The paper critically discusses this standard approach and suggests an alternative account which proceeds in terms of subatomic introduction and elimination rules for atomic sentences. A simple subatomic normal form theorem by which this account of the semantics of atomic sentences and the terms from which they (...) are composed is underpinned, shows moreover that the proof-theoretic analysis of first-order logic can be pursued also beneath the atomic level. (shrink)

John Bell showed that a big class of local hidden-variable models stands in conflict with quantum mechanics and experiment. Recently, there were suggestions that empirically adequate hidden-variable models might exist which presuppose a weaker notion of local causality. We will show that a Bell-type inequality can be derived also from these weaker assumptions. IntroductionThe EPR-Bohm experimentLocal causalityBell's inequality from separate common causes4.1 A weak screening-off principle4.2 Perfect correlation and ‘determinism’4.3 A minimal theory for spins4.4 No conspiracyDiscussion.

The conditions involved in the applicability of mathematics in science are the subject of ongoing debates. One of the best‐received approaches is the inferential account, which involves structural mappings and pragmatic considerations in a three‐step model. According to the inferential account, these pragmatic considerations happen in the immersion and interpretation stages, but not during derivation (symbol‐pushing in a mathematical formalism). In this work, I draw inspiration from the later Wittgenstein and make the case that the applicability of mathematics also (...) rests on pragmatic considerations at the mathematical derivation level. I make the further case that pragmatic considerations at the mathematical derivation level may substitute pragmatic considerations in the other two stages, thus showing how they are holistically interrelated. I illustrate these two points with the solution of a simple geometrical problem. (shrink)

I present a counter-example to Nash's derivation of utility theory in 'The Bargaining Problem'.

Institute of Theoretical Physics, Exact Sciences Sidlerstrasse 5, University of Bern, CH-3012 Bern Switzerland portmann{at}itp.unibe.ch' + u + '@' + d + ''//--> awuethr{at}itp.unibe.ch' + u + '@' + d + ''//--> John Bell showed that a big class of local hidden-variable models stands in conflict with quantum mechanics and experiment. Recently, there were suggestions that empirically adequate hidden-variable models might exist which presuppose a weaker notion of local causality. We will show that a Bell-type inequality can be derived also (...) from these weaker assumptions. Introduction The EPR-Bohm experiment Local causality Bell's inequality from separate common causes 4.1 A weak screening-off principle 4.2 Perfect correlation and ‘determinism’ 4.3 A minimal theory for spins 4.4 No conspiracy Discussion. (shrink)

In this paper, I put forth a novel interpretation of how the third categories under each heading in the table of categories (totality, limitation, community, and necessity) are derived. Drawing on a passage from the first Critique and a letter to Schultz, I argue that in order to derive these categories, a special act of the understanding is required. I propose that we interpret this special act as consisting of an application of the third logical function under the corresponding heading (...) that unites the combination of the first and second categories (under that same heading) so as to produce the third. (shrink)

In this review essay, I raise three principal concerns relating to Schulting’s project of deriving the categories from apperception as elaborated in his recent book Kant’s Deduction and Apperception (Palgrave Macmillan, 2012). First, I claim that Schulting overlooks a key ambiguity relating to ‘ableiten’ and which contrasts with his strictly logical understanding of that term. Second, I dispute on textual and philosophical grounds Schulting’s characterization of the subject’s consciousness of its own identity in terms of the analytic unity of apperception. (...) Finally, I raise an objection to Schulting’s account of the derivation of the concept of substance from apperception, as I claim that at best Kant allows that the logical function underlying this category (rather than the category itself) can be so derived, and I note that this objection can be extrapolated to apply to the other derivations of the categories Schulting offers. (shrink)

Gottfried Martin has recently reminded us of a useful distinction between two possible ways of doing metaphysics. We may proceed by framing a “theory of principles” or by proposing a “theory of being”. Aristotle explicitly formulates both possibilities as the task of metaphysics, formulating a theory of principles in his doctrine of the four types of causal explanation in the first book of the Metaphysics, while exploring the theory of being in a number of other passages, such as Book I, (...) chapters 6 and 9; Book X, chapter 2; and Book XIII. These passages do not elaborate principles whereby we can analyze the structure of certain entities, be they causes, substances or forms, but rather concern themselves with the ontological status of these entities—in what sense can they be said to be? In Plato this distinction is more implicit, but we may contrast the theory of forms developed in the Phaedo and the Republic with the subsequent probing investigation of the being of these forms in the Parmenides and the Sophist. Kant “explicitly claims to have discovered and presented a complete and necessary system of the basic concepts and principles. The proof of the completeness and necessity of this system is the aim of the middle part of the Critique of Pure Reason, the Transcendental Analytic.” Yet. (shrink)

The reason for physics’ failure to find a final theory of the universe is examined. Problems identified are: the lack of unequivocal definitions for its fundamental elements (time, length, mass, electric charge, energy, work, matter-waves); the danger of relying too much on mathematics for solutions; especially as philosophical arguments conclude the universe cannot have a mathematical basis. It does not even need the concept of number to exist. Numbers and mathematics are human inventions arising from the human predilection for measurement. (...) Following Aristotle, a single fundamental cause is proposed to explore the efficacy of using pure non-mathematical philosophy to explain the universe, contrary to current quantum physical views. The cause is taken as Time, which is then defined, surprisingly leading automatically to a definition of a three-dimensional space answering the question into what can a universe be placed (space before space seems non-sensical). This enables the philosophical arguments to derive a universal rule giving clear-cut descriptions (definitions) of force (both gravitational and electromagnetic), motion, energy, and particles. The formation of atomic nuclei and atomic properties together with an unexpected role for neutrinos follow. In particular, a Popper-test can be prepared by introducing the concept of measurement to allow the philosophy arguments to be tested in another discipline - mathematics. The solution agrees with human physical observations to a remarkable degree of accuracy, automatically explaining and predicting values for Planck’s and the fine-structure constants. Although mathematical, it is included as confirming the efficacy of philosophy in attaining a final theory. (shrink)

Few have done more than Martin Gutzwiller to clarify the connection between classical time-dependent motion and the time-independent states of quantum systems. Hence it seems appropriate to include the following discussion of the origins of the time-dependent Schrödinger equation in this volume dedicated to him.

We derive statistical mechanics and Hamiltonian dynamics solely from the algebraic structure of M_3(C), the minimal noncommutative finite-dimensional C*-algebra, within the Cognitional Mechanics (CM) framework. Four foundational hypotheses of conventional statistical mechanics are structurally superseded without replacement by new assumptions: the equal a priori probability postulate (H1), the ergodic hypothesis (H2), the external heat bath assumption (H3), and the empirical definition of the inverse temperature beta (H4). -/- The principal results are: (i) the Hamiltonian H emerges as a structural necessity (...) via the Skolem-Noether theorem and Stone's theorem, superseding H3; (ii) the unique SU(n)-covariant depolarizing channel Phi with contraction rate lambda = 8/9 is fixed by the relative dimension 1/n^2 of the invariant subspace, superseding H1 and H2; (iii) the inverse temperature beta_structure = tau / Delta_E = [1/|log(8/9)|] / [3/sqrt(2)] approximately 4.002 is a pure structural invariant fixed by Casimir normalization, dissolving the circularity of H4; (iv) the canonical ensemble rho_eq = exp(-beta H) / Z is the unique entropy-maximizing state consistent with the algebra; (v) all three thermodynamic laws follow as algebraic theorems from Klein's inequality and the spectral structure of M_3(C); (vi) the projection factor kappa_T = 1.000031, determined via the CM-implied gravitational coupling G_implied = 6.67471 x 10^-11 m^3 kg^-1 s^-2, closes the Planck temperature scale as a structural invariant. The residual |kappa_T - 1| = 3.1 x 10^-5 lies within the experimental scatter of independent G measurements (5.5 x 10^-4). -/- No external probabilistic assumptions, empirical calibration, or free parameters are introduced. Statistical mechanics and thermodynamics are not empirical frameworks imposed on nature; they are necessary consequences of the minimal noncommutative algebra M_3(C). -/- Published March 7, 2026 DOI:10.5281/zenodo.18899522. (shrink)