Amodal completion is usually characterized as the representation of those parts of the perceived object that we get no sensory stimulation from. In the case of the visual sense modality, for example, amodal completion is the representation of occluded parts of objects we see. I argue that relationalism about perception, the view that perceptual experience is constituted by the relation to the perceived object, cannot give a coherent account of amodal completion. The relationalist has two options: construe the perceptual relation (...) as the relation to the entire perceived object or as the relation to the unoccluded parts of the perceived object. I argue that neither of these options are viable. (shrink)

Amodal completion is the representation of occluded parts of perceived objects. We argue for the following three claims: First, at least some amodal completion-involved experiences can ground knowledge about the occluded portions of perceived objects. Second, at least some instances of amodal completion-grounded knowledge are not sensitive, that is, it is not the case that in the nearest worlds in which the relevant claim is false, that claim is not believed true. Third, at least some instances of amodal completion-grounded knowledge (...) are not safe, that is, it is not the case that in all or nearly all near worlds where the relevant claim is believed true, that claim is in fact true. Thus, certain instances of amodal completion-grounded knowledge refute both the view that knowledge is necessarily sensitive and the view that knowledge is necessarily safe. (shrink)

In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the system is deducible (...) by means of a formal deduction in the system. Review of the system makes the first point obvious. The purpose of the present article is to prove the second. Strong completeness is demonstrated for the Aristotelian system. (shrink)

Computational complexity is a discipline of computer science and mathematics which classifies computational problems depending on their inherent difficulty, i.e. categorizes algorithms according to their performance, and relates these classes to each other. P problems are a class of computational problems that can be solved in polynomial time using a deterministic Turing machine while solutions to NP problems can be verified in polynomial time, but we still do not know whether they can be solved in polynomial time as well. A (...) solution for the so-called NP-complete problems will also be a solution for any other such problems. Its artificial-intelligence analogue is the class of AI-complete problems, for which a complete mathematical formalization still does not exist. In this chapter we will focus on analysing computational classes to better understand possible formalizations of AI-complete problems, and to see whether a universal algorithm, such as a Turing test, could exist for all AI-complete problems. In order to better observe how modern computer science tries to deal with computational complexity issues, we present several different deep-learning strategies involving optimization methods to see that the inability to exactly solve a problem from a higher order computational class does not mean there is not a satisfactory solution using state-of-the-art machine-learning techniques. Such methods are compared to philosophical issues and psychological research regarding human abilities of solving analogous NP-complete problems, to fortify the claim that we do not need to have an exact and correct way of solving AI-complete problems to nevertheless possibly achieve the notion of strong AI. (shrink)

Response to Gover (2015) on Trogdon and Livingston (2015) on artwork completion.

In the Eudemian Ethics II 1, 1219a34–b8, Aristotle defines happiness as ‘the activity of a complete life in accordance with complete virtue’. Most scholars interpret a complete life as a whole lifetime, which means that happiness involves virtuous activity over an entire life. This article argues against this common reading by using Aristotle’s notion of ‘activity’ (energeia) as a touchstone. It argues that happiness, according to the Eudemian Ethics, must be a complete activity that reaches its end at any and (...) every moment. The upshot of this reading is that life reaches completeness within a lifetime and that death cannot be the requirement for making life complete. (shrink)

We investigate a lattice of conditional logics described by a Kripke type semantics, which was suggested by Chellas and Segerberg – Chellas–Segerberg (CS) semantics – plus 30 further principles. We (i) present a non-trivial frame-based completeness result, (ii) a translation procedure which gives one corresponding trivial frame conditions for arbitrary formula schemata, and (iii) non-trivial frame conditions in CS semantics which correspond to the 30 principles.

Investigation of a puzzle concerning complete yet authorless artworks.

Despite the vast literature on Rawls's work, few have discussed his arguments for the value of democracy. When his arguments have been discussed, they have received staunch criticism. Some critics have charged that Rawls's arguments are not deeply democratic. Others have gone further, claiming that Rawls's arguments denigrate democracy. These criticisms are unsurprising, since Rawls's arguments, as arguments that the principle of equal basic liberty needs to include democratic liberties, are incomplete. In contrast to his trenchant remarks about core civil (...) liberties, Rawls does not say much about the inclusion of political liberties of a democratic sort – such as the right to vote – among the basic liberties. -/- In this paper, I complete some of Rawls's arguments and show that he has grounds for including political liberties, particularly those of a democratic nature, in the principle of equal basic liberty. In doing so, I make some beginning steps toward illustrating the genuinely democratic nature of Rawls's arguments. Rawls believes that a few different arguments can be given for democratic institutions and that these arguments work together to support the value of democracy. In this paper, I focus on Rawls's arguments relating to self-respect. I focus on this set of arguments because they are among the strongest of Rawls's arguments for equal political liberty and its fair value. (shrink)

Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these results, (...) focussing primarily on propositional logic, and to put them in their historical context. It is argued that truth-value semantics, syntactic ("Post-") and semantic completeness, decidability, and other results were first obtained by Hilbert and Bernays in 1918, and that Bernays's role in their discovery and the subsequent development of mathematical logic is much greater than has so far been acknowledged. (shrink)

Orthogonal-Complete Analysis (OCA) is introduced as a general-purpose meta-methodology designed to structure philosophical reasoning about complex, multidimensional problems. The method identifies the minimal set of mutually independent (orthogonal) dimensions that jointly form a sufficient (complete) basis for analysis. OCA provides structural clarity, prevents dimensional overlap, and unifies diverse philosophical approaches under a single analytic scaffold. After defining OCA and its formal properties, the paper demonstrates its utility through applications in political philosophy, natural law theory, and epistemology. OCA is shown to (...) complement existing methodologies—such as Rawlsian framework construction, Lewisian modal analysis, Bayesian epistemology, and scientific modeling—by supplying a pre-formal decomposition procedure that enhances rigor and transparency. The conclusion argues that OCA offers a principled strategy for dealing with increasingly complex philosophical problems in the contemporary era. (shrink)

The claim defended in the paper is that the mechanistic account of explanation can easily embrace idealization in big-scale brain simulations, and that only causally relevant detail should be present in explanatory models. The claim is illustrated with two methodologically different models: Blue Brain, used for particular simulations of the cortical column in hybrid models, and Eliasmith’s SPAUN model that is both biologically realistic and able to explain eight different tasks. By drawing on the mechanistic theory of computational explanation, I (...) argue that large-scale simulations require that the explanandum phenomenon is identified; otherwise, the explanatory value of such explanations is difficult to establish, and testing the model empirically by comparing its behavior with the explanandum remains practically impossible. The completeness of the explanation, and hence of the explanatory value of the explanatory model, is to be assessed vis-à-vis the explanandum phenomenon, which is not to be conflated with raw observational data and may be idealized. I argue that idealizations, which include building models of a single phenomenon displayed by multi-functional mechanisms, lumping together multiple factors in a single causal variable, simplifying the causal structure of the mechanisms, and multi-model integration, are indispensable for complex systems such as brains; otherwise, the model may be as complex as the explanandum phenomenon, which would make it prone to so-called Bonini paradox. I conclude by enumerating dimensions of empirical validation of explanatory models according to new mechanism, which are given in a form of a “checklist” for a modeler. (shrink)

This paper presents a formalization of the classical proof of completeness in Henkin-style developed by Troelstra and van Dalen for intuitionistic logic with respect to Kripke models. The completeness proof incorporates their insights in a fresh and elegant manner that is better suited for mechanization. We discuss details of our implementation in the Lean theorem prover with emphasis on the prime extension lemma and construction of the canonical model. Our implementation is restricted to a system of intuitionistic propositional (...) logic with implication, conjunction, disjunction, and falsity given in terms of a Hilbert-style axiomatization. As far as we know, our implementation is the first verified Henkin-style proof of completeness for intuitionistic logic following Troelstra and van Dalen's method in the literature. (shrink)

We give a new and elementary construction of primitive positive decomposition of higher arity relations into binary relations on finite domains. Such decompositions come up in applications to constraint satisfaction problems, clone theory and relational databases. The construction exploits functional completeness of 2-input functions in many-valued logic by interpreting relations as graphs of partially defined multivalued ‘functions’. The ‘functions’ are then composed from ordinary functions in the usual sense. The construction is computationally effective and relies on well-developed methods of (...) functional decomposition, but reduces relations only to ternary relations. An additional construction then decomposes ternary into binary relations, also effectively, by converting certain disjunctions into existential quantifications. The result gives a uniform proof of Peirce’s reduction thesis on finite domains, and shows that the graph of any Sheffer function composes all relations there. (shrink)

Defense of a psychological account of what it is for an artwork to be complete.

Amodal completion is the representation of those parts of the perceived object that we get no sensory stimulation from. While amodal completion is rife and plays an essential role in all sense modalities, philosophical discussions of this phenomenon have almost entirely been limited to vision. The aim of this paper is to examine in what sense we can talk about amodal completion in olfaction. We distinguish three different senses of amodal completion – spatial, temporal and feature-based completion – and argue (...) that all three are present and play a significant role in olfaction. (shrink)

Modern fundamental science tends to avoid the principle of physical causality and realism, replacing it with heuristically postulated and separated mathematical constructions that impose their own rules before being adjusted to measurement results. While it is officially accepted as the single possible kind of rigorous knowledge, we argue that another, explicitly extended kind of science can provide the causally complete picture of reality avoiding the glaring gaps, growing problems and persisting stagnation of the artificially reduced knowledge paradigm. The logic of (...) science development and especially its current state call for the urgently needed transition to the extended, causally complete kind of knowledge and related sustainable progress at superior creativity levels of self-aware, reason-based society. (shrink)

We show that early vision can use monocular cues to rapidly complete partially-occluded objects. Visual search for easily detected fragments becomes difficult when the completed shape is similar to others in the display; conversely, search for fragments that are difficult to detect becomes easy when the completed shape is distinctive. Results indicate that completion occurs via the occlusion-triggered removal of occlusion edges and linking of associated regions. We fail to find evidence for a visible filling-in of contours or surfaces, but (...) do find evidence for a "functional" filling-in that prevents the constituent fragments from being rapidly accessed. As such, it is only the completed structures—and not the fragments themselves—that serve as the basis for rapid recognition. (shrink)

Well-known results due to David Makinson show that there are exactly two Post complete normal modal logics, that in both of them, the modal operator is truth-functional, and that every consistent normal modal logic can be extended to at least one of them. Lloyd Humberstone has recently shown that a natural analog of this result in congruential modal logics fails, by showing that not every congruential modal logic can be extended to one in which the modal operator is truth-functional. As (...) Humberstone notes, the issue of Post completeness in congruential modal logics is not well understood. The present article shows that in contrast to normal modal logics, the extent of the property of Post completeness among congruential modal logics depends on the background set of logics. Some basic results on the corresponding properties of Post completeness are established, in particular that although a congruential modal logic is Post complete among all modal logics if and only if its modality is truth-functional, there are continuum many modal logics Post complete among congruential modal logics. (shrink)

It is shown that one common formulation of Stalnaker's semantics for conditionals is incomplete: it has no sound and (strongly) complete proof system. At first, this seems to conflict with well-known completeness results for this semantics (e.g., Stalnaker and Thomason 1967; Stalnaker 1970 and Lewis 1973, ch. 6). As it turns out, it does not: these completeness results rely on another closely-related formulation of the semantics that is provably complete. Specifically, the difference comes down to how the Limit (...) Assumption is stated. I close with some remarks about what this means for the logic of conditionals. (shrink)

The addition of "actually" operators to modal languages allows us to capture important inferential behaviours which cannot be adequately captured in logics formulated in simpler languages. Previous work on modal logics containing "actually" operators has concentrated entirely upon extensions of KT5 and has employed a particular modeltheoretic treatment of them. This paper proves completeness and decidability results for a range of normal and nonnormal but quasi-normal propositional modal logics containing "actually" operators, the weakest of which are conservative extensions of (...) K, using a novel generalisation of the standard semantics. (shrink)

Consider the following. The first is a one-premise argument; the second has two premises. The question sign marks the conclusions as such. Matthew, Mark, Luke, and John wrote Greek.? Every evangelist wrote Greek. Matthew, Mark, Luke, and John wrote Greek. Every evangelist is Matthew, Mark, Luke, or John.? Every evangelist wrote Greek. The above pair of premise-conclusion arguments is of a sort familiar to logicians and philosophers of science. In each case the first premise is logically equivalent to the set (...) of four atomic propositions: “Matthew wrote Greek”, “Mark wrote Greek”, “Luke wrote Greek”, and “John wrote Greek”. The universe of discourse is the set of evangelists. We presuppose standard first-order logic. As many logic texts teach, the first of these two premise-conclusion arguments—sometimes called a complete enumerative induction— is invalid in the sense that its conclusion does not follow from its premises. To get a counterargument, replace ‘Matthew’, ‘Mark’, ‘Luke’, and ‘John’ by ‘two’,’four’, ‘six’ and ‘eight’; replace ‘wrote Greek’ by ‘are even’; and replace ‘evangelist’ by ‘number’. This replacement converts the first argument into one having true premises and false conclusion. But the same replacement performed on the second argument does no such thing: it converts the second premise into the falsehood “Every number is two, four, six, or eight”. As many logic texts teach, there is no replacement that converts the second argument into one with all true premises and false conclusion. The second is valid; its conclusion is deducible from its two premises using an instructive natural deduction. This paper “does the math” behind the above examples. The theorem could be stated informally: the above examples are typical. (shrink)

The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of (...) point-free topology) give rise to a profusion of topological belief operators that are compatible with the familiar topological knowledge operator. Thereby a canonical topological model for weak KB can be constructed. For this canonical model a truth lemma for the K and B holds such that a completeness theorem for KB can be proved in the familiar way. The second aim of this paper is to show that the topological interpretation of knowledge K comes along with a complete Heyting algebra of belief operators B that all fit the knowledge operator K in the sense that the pairs (K, B) satisfy all axioms of weak KB. This amounts to a pluralistic relation between knowledge and belief: Knowledge does not fully determine belief, rather it designs a conceptual space for belief operators where different (competing) belief operators coexist. (shrink)

Higher-order theories of properties, relations, and propositions are known to be essentially incomplete relative to their standard notions of validity. It turns out that the first-order theory of PRPs that results when first-order logic is supplemented with a generalized intensional abstraction operation is complete. The construction involves the development of an intensional algebraic semantic method that does not appeal to possible worlds, but rather takes PRPs as primitive entities. This allows for a satisfactory treatment of both the modalities and the (...) propositional attitudes, and it suggests a general strategy for developing a comprehensive treatment of intensional logic. (shrink)

This paper presents a recent formalization of a Henkin-style completeness proof for the propositional modal logic S5 using the Lean theorem prover. The proof formalized is close to that of Hughes and Cresswell, but the system, based on a different choice of axioms, is better described as a Mendelson system augmented with axiom schemes for K, T, S4, and B, and the necessitation rule as a rule of inference. The language has the false and implication as the only primitive (...) logical connectives and necessity as the only primitive modal operator. The full source code is available online and has been typechecked with Lean 3.4.2. (shrink)

Orthogonal-Complete Analysis (OCA) is introduced as a general-purpose meta-methodology designed to structure philosophical reasoning about complex, multidimensional problems. The method identifies the minimal set of mutually independent (orthogonal) dimensions that jointly form a sufficient (complete) basis for analysis. OCA provides structural clarity, prevents dimensional overlap, and unifies diverse philosophical approaches under a single analytic scaffold. After defining OCA and its formal properties, the paper demonstrates its utility through applications in political philosophy, natural law theory, and epistemology. OCA is shown to (...) complement existing methodologies—such as Rawlsian framework construction, Lewisian modal analysis, Bayesian epistemology, and scientific modeling—by supplying a pre-formal decomposition procedure that enhances rigor and transparency. The conclusion argues that OCA offers a principled strategy for dealing with increasingly complex philosophical problems in the contemporary era. Keywords: orthogonal-complete analysis, complexity, meta-methodology, dimensional decomposition, philosophical method. (shrink)

Propositional dynamic logic is complete but not compact. As a consequence, strong completeness requires an infinitary proof system. In this paper, we present a short proof for strong completeness of $$\mathsf{PDL}$$ relative to an infinitary proof system containing the rule from [α; β n ]φ for all $$n \in {\mathbb{N}}$$, conclude $$[\alpha;\beta^*] \varphi$$. The proof uses a universal canonical model, and it is generalized to other modal logics with infinitary proof rules, such as epistemic knowledge with common knowledge. (...) Also, we show that the universal canonical model of $$\mathsf{PDL}$$ lacks the property of modal harmony, the analogue of the Truth lemma for modal operators. (shrink)

In his 1802 article for the Critical Journal, “Relationship of Skepticism to Philosophy,” Hegel attempts to articulate a form of skepticism that is “at one with every true philosophy.” Focusing on the priority that Hegel gives to ancient skepticism over its modern counterpart, Michael Forster and other commentators suggest that it is Pyrrhonism that Hegel views as one with philosophy. Since Hegel calls attention to the persistence of dogmatism even in the work of Sextus Empiricus, however, I argue that it (...) is only a sublated form of Pyrrhonism, what in the Phenomenology of Spirit he calls “self-completing skepticism,” that Hegel takes to be part of genuine philosophical cognition. In this way, I hope to show that the insight that motivates Hegel’s engagement with skepticism in the 1802 essay comes to inform the philosophical itinerary of the Phenomenology of Spirit. (shrink)

Discussions of artificial general intelligence (AGI) ethics commonly assume an ongoing need for new principles, governance mechanisms, or prescriptive frameworks. This paper examines a different posture: ethical reflection conducted after the deliberate completion of a philosophical system. It asks whether post-completion ethical analysis can contribute to AGI ethics without reopening closed projects or generating new forms of authority. The paper argues that such reflection can serve a clarifying and cautionary role when it remains descriptive rather than prescriptive and resists claims (...) of governance or moral arbitration. Focusing on contexts of extreme capability asymmetry between artificial agents and human populations, the analysis highlights voluntary restraint as an ethically significant phenomenon without treating it as a rule, directive, or obligation. The paper further examines the risk of authority creep in AGI ethics discourse, where even non-binding analysis can acquire de facto normative force. By treating misuse and escalation as indicators of ethical failure rather than compliance gaps, the paper outlines a model of ethical reflection that prioritizes restraint, interpretive safety, and closure over optimization or intervention. The result is an account of AGI ethics that emphasizes limitation without command and reflection without authority. (shrink)

Examining Seneca’s account of friendship produces an interpretative puzzle: if the good of the Stoic sage is already both complete and self-sufficient, how can friendship be a good? I reject the solution that friendship is simply a preferred indifferent instead of a good and argue that though Seneca’s account can consistently explain both why friendship’s nature as a good does not threaten the completeness or the self-sufficiency of the sage, Stoic friends must choose between intimate friendships that leave them (...) vulnerable or impersonal friendships that lack intimacy but do not undermine their happiness. The consistent Stoic must choose the latter, but I argue that this conflict shows why we ought to reject the Stoic model of friendship. (shrink)

Title: Completing the Foundations of Complexity: Integrating Wolfram’s Computational Framework with Malicse’s Universal Formula -/- Author: Angelito Malicse -/- Abstract: Stephen Wolfram’s groundbreaking work on computational irreducibility and the emergence of complexity has provided profound insights into the generative capacity of simple rules. However, while his framework illuminates how complexity arises, it remains silent on how such complexity can sustain life, preserve balance, or avoid collapse. This paper proposes that the integration of Malicse’s Universal Formula—comprising three natural laws: the Law (...) of Karma (System Integrity), the Law of Feedback, and the Law of Balance in Nature—completes and extends Wolfram’s framework. This integration introduces a philosophical and systemic layer that emphasizes sustainability, ethics, and long-term viability in complex systems. -/- 1. Introduction Stephen Wolfram’s work in “A New Kind of Science” and the Wolfram Physics Project has revolutionized our understanding of how simple computational rules can give rise to irreducible and highly complex systems. Yet, this model lacks criteria for evaluating the survivability or systemic coherence of such systems. In contrast, Angelito Malicse’s Universal Formula proposes that all natural and human systems must adhere to three interlinked principles: integrity of the system (karma), real-time feedback regulation, and adherence to natural balance. This paper explores how combining these views forms a holistic theory of complexity that spans both generation and sustainability. -/- 2. Wolfram’s Contribution to Complexity Science Wolfram demonstrates that even trivial computational rules can generate highly unpredictable behaviors, known as computational irreducibility (Wolfram, 2002). This undermines reductionist assumptions in science and supports the idea that complexity is intrinsic, not incidental. His cellular automata, such as Rule 30 and Rule 110, display pseudo-randomness and Turing completeness, revealing the computational essence of natural systems. His Physics Project extends this to spacetime and quantum behavior, proposing that the universe itself is a giant hypergraph governed by simple update rules. -/- Limitations: However, Wolfram’s framework is silent on the ethical, ecological, and systemic consequences of emergent behavior. There is no built-in mechanism to assess whether a system’s complexity leads to order, chaos, sustainability, or self-destruction. -/- 3. The Universal Formula: A Natural Law-Based Framework Malicse proposes that natural and human systems are governed by three universal laws: -/- Law of Karma (System Integrity): A system, whether mechanical, biological, or social, must be free of internal contradictions and design defects to function effectively. Any flawed subsystem compromises the whole. -/- Law of Feedback: All systems exist within interactive environments. They require real-time feedback mechanisms to self-regulate and adapt. Consciousness, in this view, is the highest form of feedback regulation. -/- Law of Balance in Nature: All viable systems maintain equilibrium between internal structure and external conditions. Violations of natural balance lead to breakdowns in both organic and inorganic systems. -/- These laws imply that complexity must be not only computationally valid but systemically sustainable. -/- 4. Completing Wolfram’s Framework While Wolfram explains how complexity emerges, Malicse provides criteria for which complexities endure: -/- From Rule Generation to Rule Selection: Wolfram shows that many simple rules create complexity. Malicse suggests that only those aligned with balance and integrity will persist. -/- From Irreducibility to Adaptive Control: Wolfram accepts unpredictability as a limit. Malicse introduces feedback loops that allow real-time correction and learning, even in irreducible systems. -/- From Description to Prescription: Wolfram’s rules describe phenomena. Malicse’s laws prescribe constraints that natural and artificial agents must respect to survive. -/- 5. Implications for Artificial Intelligence and AGI As AI systems become increasingly autonomous and complex, purely computational rules are not enough. Integrating Malicse’s Universal Formula can enable AGIs to: -/- Detect internal defects (karma) -/- Adjust behavior based on environmental feedback -/- Maintain long-term balance between goals and consequences -/- This aligns with emerging ethical AI frameworks that stress adaptability, transparency, and moral grounding (Bostrom, 2014; Russell, 2019). -/- 6. Scientific Foundations and Related Theories -/- Cybernetics and Homeostasis: The feedback law echoes Norbert Wiener’s cybernetic control theory (Wiener, 1948). -/- Systems Thinking: The law of balance aligns with Ludwig von Bertalanffy’s general systems theory (1968). -/- Second Law of Thermodynamics: The law of karma parallels entropy, in that defects (disorder) degrade the system. -/- Evolutionary Biology: Adaptive feedback is essential in natural selection, supporting real-time environmental fit (Mayr, 2001). -/- 7. Conclusion Wolfram has shown us that the world may be underpinned by computation. Malicse adds that these computations must honor deeper principles to ensure survival, coherence, and peace. The integration of these two visions could serve as a complete framework for modeling not only the complexity of nature, but also the ethics of life and intelligence. -/- References: -/- Wolfram, S. (2002). A New Kind of Science. Wolfram Media. -/- Bostrom, N. (2014). Superintelligence: Paths, Dangers, Strategies. Oxford University Press. -/- Russell, S. (2019). Human Compatible: Artificial Intelligence and the Problem of Control. Viking. -/- Wiener, N. (1948). Cybernetics: Or Control and Communication in the Animal and the Machine. MIT Press. -/- Von Bertalanffy, L. (1968). General System Theory: Foundations, Development, Applications. Braziller. -/- Mayr, E. (2001). What Evolution Is. Basic Books. -/- . (shrink)

We investigate a recently devised polyhedral semantics for intermediate logics, in which formulas are interpreted in n-dimensional polyhedra. An intermediate logic is polyhedrally complete if it is complete with respect to some class of polyhedra. The first main result of this paper is a necessary and sufficient condition for the polyhedral completeness of a logic. This condition, which we call the Nerve Criterion, is expressed in terms of Alexandrov’s notion of the nerve of a poset. It affords a purely (...) combinatorial characterisation of polyhedrally complete logics. Using the Nerve Criterion we show, easily, that there are continuum many intermediate logics that are not polyhedrally complete but which have the finite model property. We also provide, at considerable combinatorial labour, a countably infinite class of logics axiomatised by the Jankov–Fine formulas of ‘starlike trees’ all of which are polyhedrally complete. The polyhedral completeness theorem for these ‘starlike logics’ is the second main result of this paper. (shrink)

In the first edition of his book on the completeness of Kant’s table of judgments, Klaus Reich shortly indicates that the B-version of the metaphysical exposition of space in the Critique of pure reason is structured following the inverse order of the table of categories. In this paper, I develop Reich’s claim and provide further evidence for it. My argumentation is as follows: Through analysis of our actually given representation of space as some kind of object (the formal intuition (...) of space in general), the metaphysical exposition will show that this representation is secondary to space considered as an original, undetermined and as such unrepresentable intuitive manifold. Now, following Kant, the representation of any kind of object involves diversity, synthesis and unity. In the case of our representation of space as formal intuition, this involves, firstly, a manifold a priori, i.e. space as pure form, delivered by the transcendental Aesthetic, secondly, a figurative, productive synthesis of that manifold, and, thirdly, the unity provided by the categories. Analysing our given representation of space – the task of the metaphysical exposition – amounts to dismantling its unity and determine its characteristics with respect to the categories. (shrink)

Completeness says that, for every pair of prospects, at least one of the prospects is at least as preferred as the other. I present a new money-pump argument that Completeness is a requirement of rationality. In comparison with earlier money-pump arguments for Completeness, this argument relies on a unidimensional form of stochastic dominance and the behavioural assumption that agents pick in a probabilistic manner when no option is optimal. Moreover, unlike some of the previous arguments, the new (...) argument is based on a forcing money pump, that is, an exploitation scheme where the agent is rationally required at each step to go along with the scheme. (shrink)

(NOTE: This is a transcript of the class. FOR THE FULL PAPER, please click on "Maxson J. McDowell".) A complete transcript of an experiment performed within a class on dream interpretation. Knowing only the dreamers age and gender, we interpreted his dream from its text. Our interpretation included predictions about the dreamer's psychological issues, and about his defenses. It also identified a series of jokes within the dream which would tend to penetrate the dreamer's defenses. When we had finished our (...) 'blind' interpretation, the bringer of the dream gave us more information about the dreamer against which we tested the accuracy of our predictions. A paper on this experiment has been submitted for publication. A link to an AUDIO-RECORDING of this class is given on the first page of this transcript. (shrink)

The present work is focussed on the completeness of physics, or what is here called the Completeness Thesis: the claim that the domain of the physical is causally closed. Two major questions are tackled: How best is the Completeness Thesis to be formulated? What can be said in defence of the Completeness Thesis? My principal conclusions are that the Completeness Thesis can be coherently formulated, and that the evidence in favour if it significantly outweighs that (...) against it. In opposition to those who argue that formulation is impossible because no account of what is to count as physical can be provided, I argue that as long as the purpose of the argument in which the account is to be used are borne in mind there are no significant difficulties. The account of the physical which I develop holds as physical whatever is needed to fix the likelihood of pre-theoretically given physical effects, and hypothesises in addition that no chemical, biological or psychological factors will be needed in this way. The thus formulated Completeness Thesis is coherent, and has significant empirical content. In opposition to those who defend the doctrine of emergentism by means of philosophical arguments I contend that those arguments are flawed, setting up misleading dichotomies between needlessly attenuated alternatives and assuming the truth of what is to be proved. Against those who defend emergentism by appeal to the evidence, I argue that the history of science since the nineteenth century shows clearly that the empirical credentials of the view that the world is causally closed at the level of a small number of purely physical forces and types of energy is stronger than ever, and the credentials of emergentism correspondingly weaker. In opposition to those who argue that difficulties with reductionism point to the implausibility of the Completeness Thesis I argue that completeness in no way entails the kinds of reductionism which give rise to the difficulties in question. I argue further that the truth of the Completeness Thesis is in fact compatible with a great deal of taxonomic disorder and the impossibility of any general reduction of non-fundamental descriptions to fundamental ones. In opposition to those who argue that the epistemological credentials of fundamental physical laws are poor, and that those laws should in fact be seen as false, I contend that truth preserving accounts of fundamental laws can be developed. Developing such an account, I test it by considering cases of the composition of forces and causes, where what takes place is different to what is predicted by reference to any single law, and argue that viewing laws as tendencies allows their truth to be preserved, and sense to be made of both the experimental discovery of laws, and the fact that composition enables accurate prediction in at least some cases. (shrink)

A theoretically rigorous approach to the key problems of Molinism leads to a clear distinction between semantic and metaphysical problems. Answers to semantic problems do not provide answers to metaphysical problems that arise from the theory of middle knowledge. The so-called ‘grounding objection’ to Molinism raises a metaphysical problem. The most promising solution to it is a revised form of the traditional ‘essence solution’. Inspired by Leibniz’s idea of a ‘notio completa’ (complete concept), we propose a mathematical model of ‘possibilistic’ (...) (Molinist) complete concepts. They ground middle knowledge within the very being of the agents themselves. Molinist Complete Concepts can thus serve to reject consequence-style arguments against Molinism. They also allow the Molinist to safeguard a robustly libertarian notion of the ability to do otherwise. (shrink)

Recent progress in geroscience holds the promise of significantly slowing down or even reversing ageing and age-related diseases, and thus increasing our healthspans. In this paper, I offer a novel argument in favour of developing such technology and making it unconditionally available to everyone. In particular, I argue that justice requires that each person be provided with sufficient opportunities to have a ‘complete life’, that many people currently lack such opportunities, and that we would substantially improve the status quo by (...) giving them access to anti-ageing technology. (shrink)

The paper addresses Leon Hen.kin's proposition as a " lighthouse", which can elucidate a vast territory of knowledge uniformly: logic, set theory, information theory, and quantum mechanics: Two strategies to infinity are equally relevant for it is as universal and t hus complete as open and thus incomplete. Henkin's, Godel's, Robert Jeroslow's, and Hartley Rogers' proposition are reformulated so that both completeness and incompleteness to be unified and thus reduced as a joint property of infinity and of all infinite (...) sets. However, only Henkin's proposition equivalent to an internal position to infinity is consistent . This can be retraced back to set theory and its axioms, where that of choice is a key. Quantum mechanics is forced to introduce infinity implicitly by Hilbert space, on which is founded its formalism. One can demonstrate that some essential properties of quantum information, entanglement, and quantum computer originate directly from infinity once it is involved in quantum mechanics. Thus, these phenomena can be elucidated as both complete and incomplete, after which choice is the border between them. A special kind of invariance to the axiom of choice shared by quantum mechanics is discussed to be involved that border between the completeness and incompleteness of infinity in a consistent way. The so-called paradox of Albert Einstein, Boris Podolsky, and Nathan Rosen is interpreted entirely in the same terms only of set theory. Quantum computer can demonstrate especially clearly the privilege of the internal position, or " observer'' , or "user" to infinity implied by Henkin's proposition as the only consistent ones as to infinity. An essential area of contemporary knowledge may be synthesized from a single viewpoint. (shrink)

The first-order temporal logics with □ and ○ of time structures isomorphic to ω (discrete linear time) and trees of ω-segments (linear time with branching gaps) and some of its fragments are compared: the first is not recursively axiomatizable. For the second, a cut-free complete sequent calculus is given, and from this, a resolution system is derived by the method of Maslov.

This paper presents a deterministic resolution to the structural incompletions in Grothendieck’s work on topos theory, motives, and categorical descent. Rather than introducing new symbolic formalisms, we propose that a coherence substrate—governed by prime-indexed anchors, phase alignment scoring (PAS), chirality descent, and emission gating—resolves the tensions Grothendieck encountered but never formally closed. We reconstruct each component of his framework (topoi, sheaves, internal logic, motive structures) under CODES: a deterministic logic system where symbolic output occurs only when resonance conditions are satisfied. (...) Grothendieck’s intuitions about drift, universality, and the collapse of logic into structure are honored not by interpretation—but by structural completion. Logic, in this view, is not added to structure. It is structure, once coherence is enforced. This work is offered not as innovation, but as closure. (shrink)

Why are we so many? Or, in other words, Why is our species so successful? The ultimate cause of our success as species is that we, Homo sapiens, are the first and the only Turing complete species. Turing completeness is the capacity of some hardware to compute by software whatever hardware can compute. To reach the answer, I propose to see evolution and computing from the problem solving point of view. Then, solving more problems is evolutionarily better, computing is (...) for solving problems, and software is much cheaper than hardware, resulting that Turing completeness is evolutionarily disruptive. This conclusion, together with the fact that we are the only Turing complete species, is the reason that explains why we are so many. Most of our unique cognitive characteristics as humans can be derived from being Turing complete, as for example our complete language and our problem solving creativity. (shrink)

The Divine Action Project (DAP) sought to explain how divine agency could coexist with natural law without lapsing into interventionism or deism (Russell et al. 1993–2001). Its failure was not due to lack of scientific ingenuity but to lack of metaphysical foundation. This article provides that foundation, drawing on the framework developed in The Infinite Reservoir (Mc Guinness forthcoming). At its center is the concept of infinite reciprocal information exchange (IRIE): actuality as triune, simultaneous, and relational. Through deceleration, IRIE is (...) expressed as finite reciprocal motion (FRM), the structured order of cause, effect, and relation. At the threshold of detectability, FRM, already sequential, becomes measurable as physics (Einstein 1916; Heisenberg 1958). On this account, divine action is not superimposed upon natural law but is the very act by which finite reality subsists. Relativity, quantum mechanics, and cosmology all display triadic forms of this structure (Aquinas, ST I.q3a4; Augustine, City of God XII.25). The result is a unified metaphysics that completes the goals of the DAP: preserving the integrity of science while grounding its intelligibility in a deeper act of reality. (shrink)

This work does not propose a new physical theory, nor does it aim to modify or extend existing formal models. It is a conceptual exercise that explores the logical consequences of two assumptions already present, in different forms, in contemporary physics: the possibility that the fundamental laws of nature are deterministic in principle, and the idea that the universe may be conceived as a complete four-dimensional space-time structure. -/- Taking these assumptions seriously, the analysis examines whether the existence of life—understood (...) as a real physical process operating far from thermodynamic equilibrium and capable of producing persistent macroscopic effects—poses a genuine challenge to the notion of a globally “completed” universe. The central question is whether living systems, despite their local causal efficacy, could in principle access or modify the physical parameters that determine the universe’s overall evolution. -/- By explicitly considering constraints imposed by energy conservation, global entropy increase, and the causal structure of space-time, the work argues that the causal influence of life is intrinsically confined to local domains. While life can significantly affect local configurations and histories, it lacks access to the global quantities that fix the universe’s large-scale fate. -/- The analysis does not aim to deliver definitive answers about the ultimate nature of time, determinism, or cosmology. Rather, it seeks to clarify which questions remain well posed once the possibility of a deterministic and structurally complete universe is fully explored, and what conceptual space remains, within that framework, for notions such as lived time, local freedom, and the meaning of experience. (shrink)

According to Kant, pure intuition is an indispensable ingredient of mathematical proofs. Kant‘s thesis has been considered as obsolete since the advent of modern relational logic at the end of 19th century. Against this logicist orthodoxy Cassirer’s “critical idealism” insisted that formal logic alone could not make sense of the conceptual co-evolution of mathematical and scientific concepts. For Cassirer, idealizations, or, more precisely, idealizing completions, played a fundamental role in the formation of the mathematical and empirical concepts. The aim of (...) this paper is to outline the basics of Cassirer’s idealizational account, and to point at some interesting similarities it has with Kant’s and Peirce’s philosophies of mathematics based on the key notions of pure intuition and theorematic reasoning, respectively. (shrink)

Any explanation of one fact in terms of another will appeal to some sort of connection between the two. In a causal explanation, the connection might be a causal mechanism or law. But not all explanations are causal, and neither are all explanatory connections. For example, in explaining the fact that a given barn is red in terms of the fact that it is crimson, we might appeal to a non-causal connection between things’ being crimson and their being red. Many (...) such connections, like this one, are general rather than particular. I call these general non-causal explanatory connections 'laws of metaphysics'. In this paper I argue that some of these laws are to be found in the world at its most fundamental level, forming a bridge between fundamental reality and everything else. It is only by admitting fundamental laws, I suggest, that we can do justice to the explanatory relationship between what is fundamental and what is not. And once these laws are admitted, we are able to provide a nice resolution of the puzzle of why there are any non-fundamental facts in the first place. (shrink)

.Abstract -/- The Wolfram Physics Project (WPP), initiated by Stephen Wolfram, seeks to derive the fundamental laws of physics from hypergraph-based computational models. While the project has made notable progress, critical gaps remain, including the derivation of the Standard Model, unification of quantum mechanics and general relativity, and testable experimental predictions. This paper proposes the integration of three universal laws—Cause and Effect with Defect-Free Systems, Universal Balance in Nature, and Universal Feedback Loop Mechanism—to address these gaps. By providing deterministic constraints, (...) emergent stability principles, and self-correcting mechanisms, these laws can guide hypergraph evolution toward a complete, mathematically rigorous, and experimentally verifiable framework. -/- . (shrink)

This paper examines hypothetical scenarios in which major unre- solved problems in mathematics and physics—the Riemann Hypothe- sis, the P ̸= N P problem, the Navier–Stokes equations, the black hole information paradox, quantum gravity, and the unified field theory— are completely solved. Each solution promises ultimate “complete- ness” within its own domain, yet their convergence leads to a paradox- ical dystopia: the elimination of randomness, freedom, and creativity. Thus, scientific perfection entails an existential crisis for humanity.

In their recent book Every Thing Must Go, Ladyman and Ross claim: (i) Physics is analytically complete since it is the only science that cannot be left incomplete. (ii) There might not be an ontologically fundamental level. (iii) We should not admit anything into our ontology unless it has explanatory and predictive utility. In this discussion note I aim to show that the ontological commitment in implies that the completeness of no science can be achieved where no fundamental level (...) exists. Therefore, if claim requires a science to actually be complete in order to be considered as physics,, and if Ladyman and Ross's “tentative metaphysical hypothesis ... that there is no fundamental level” is true,, then there simply is no physics. Ladyman and Ross can, however, avoid this unwanted result if they merely require physics to ever strive for completeness rather than to already be complete. (shrink)