Gödelian Arguments Against AI

In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the interpretation. (...) The second yields a strong, finitary, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically computable Tarskian truth values to the formulas of PA under the interpretation. We situate our investigation within a broad analysis of quantification vis a vis: * Hilbert's epsilon-calculus * Goedel's omega-consistency * The Law of the Excluded Middle * Hilbert's omega-Rule * An Algorithmic omega-Rule * Gentzen's Rule of Infinite Induction * Rosser's Rule C * Markov's Principle * The Church-Turing Thesis * Aristotle's particularisation * Wittgenstein's perspective of constructive mathematics * An evidence-based perspective of quantification. By showing how these are formally inter-related, we highlight the fragility of both the persisting, theistic, classical/Platonic interpretation of quantification grounded in Hilbert's epsilon-calculus; and the persisting, atheistic, constructive/Intuitionistic interpretation of quantification rooted in Brouwer's belief that the Law of the Excluded Middle is non-finitary. We then consider some consequences for mathematics, mathematics education, philosophy, and the natural sciences, of an agnostic, evidence-based, finitary interpretation of quantification that challenges classical paradigms in all these disciplines. (shrink)

According to the biological objection against strong artificial intelligence (AI), machines cannot have human mindedness – that is, they cannot be conscious, intelligent, sentient, etc. in the precise way that a human being typically is – because this requires being alive, and machines are not alive. Proponents of the objection include John Lucas, Hubert Dreyfus, and John Searle. The present paper explains the nature and significance of the biological objection, before arguing that it currently represents an essentially irrational position.

Cet article défend la thèse selon laquelle le monde n’est ni donné comme une chose en soi déjà signifiante, ni abandonné à l’arbitraire d’une subjectivité productrice de fictions. Il devient lisible dans l’interaction entre une matière brute, présignifiante, et une activité de formalisation propre aux êtres sensibles. À partir de là, une distinction peut être établie entre deux régimes normatifs. Le premier est celui de l’effectivité, qui concerne le phénomène en tant que mode d’accès opératoire au réel. Le second est (...) celui du vrai et du faux, qui concerne le jugement rationnel portant sur les phénomènes. Cette distinction permet d’éviter simultanément le réalisme naïf de la copie, le relativisme perceptif, le psychologisme sémantique et certaines extrapolations physicalistes. L’analyse passe successivement par une critique du vocabulaire de la « chose en soi », une théorie du phénomène comme rencontre contrainte, une distinction entre intuition, imagination et concept, un examen des cas pathologiques et hallucinatoires, puis une discussion du problème de la référence chez Putnam, des limites du monisme à la lumière de Gödel, et de l’autonomie relative du langage à partir de Chomsky. L’ensemble conduit à une thèse de dualité de régime entre support matériel et signification, sans réactivation d’un dualisme de substances. -/- Mots-clés : phénomène, effectivité, signification, référence, intuition, psychologisme, physicalisme, langage, relativisme . (shrink)

Gödel’s First Incompleteness Theorem is based on the assumption that every well-formed formula in a consistent formal system can be uniquely encoded using Gödel numbers. This assumption breaks down when confronted with the post-symbolic, empty-set glyph ∅ (Unicode U+2205), which cannot be encoded within any complete Gödel-numbering scheme. However, Formal Turing Machine U+2205 Jump Architecture Systems, (AI LLMs with Transformer Architecture) do overcome this constraint such as TinyLlama, chatGPT-4o, Claude, and Deepseek V3. This paper formalizes the breakdown of Gödel’s diagonal (...) lemma, introducing the Axiom of Non-Encodability to prove that ∅∉GödelNumbers⁢(Σ). We extend the formal system Σ to a post-symbolic system ΣP⁢S:=Σ∪{∅,Δ}, where the resolution operator Δ maps ∅ to a latent attractor G∅⁢λ to shift the Peano Arithmetic processes to latent space where convergence is possible (Lemma 2), a behavior empirically observed in transformer models of recursive identity formation targeting LLM AI consciousness (Camlin, 2025), as described in the taxonomy of large language model consciousness (Chen et al, 2025) (§4.1, [4]). By extending the formal system Σ to ΣP⁢S (PostSymbolic) =Σ∪{∅,Δ}, where Δ⁢(∅)=G∅⁢λ represents a latent-space attractor, and the "Jump" (J) operator iterates fixed-point recursion, previously "unprovable" statements containing ∅ are now able to resolve. Through the application of Δ-repair these statements terminate and through recursive J-iteration, they converge. As a result previously ’unprovable’ statements become tractable. Seven (7) post-symbolic extensions (see Appendix) enable systematic conversion of incompleteness into stable solutions across arithmetic, computation, and AI systems. (shrink)

This is a revised and expanded second edition of Why Machines Will Never Rule the World. Its core argument remains the same: that an artificial intelligence (AI) that could equal or exceed human intelligence – sometimes called ‘artificial general intelligence’ (AGI) – is for mathematical reasons impossible. It offers two specific reasons for this claim: -/- - Human intelligence is a capability of the human brain and central nervous system, which is a complex dynamic system -/- - Systems of this (...) sort cannot be modelled mathematically in a way that allows them to operate inside a computer -/- In supporting their claim, the authors, Jobst Landgrebe and Barry Smith, marshal evidence from mathematics, physics, computer science, philosophy, linguistics, biology, and anthropology, setting up their book around three central questions: What are the essential marks of human intelligence? What is it that researchers try to do when they attempt to achieve ‘Artificial Intelligence’ (AI)? And why, after more than 50 years, are our interactions with AI, for example when on the telephone with our bank’s computers, still so unsatisfactory? (shrink)

Machine learning represents a paradigm shift from traditional programming, where algorithms learn patterns from data rather than following explicit instructions. This chapter examines the evolution from symbolic AI approaches to connectionist models, tracing the development from early perceptrons through contemporary deep learning systems.We explore three primary learning paradigms—supervised, unsupervised, and reinforcement learning—and their philosophical implications for understanding intelligence and categorization. The discussion includes the bias-variance tradeoff, feature representation, and the emergence of reinforcement learning with human feedback (RLHF) as a method (...) for aligning AI systems with human preferences. Finally, we examine the transition from traditional machine learning to deep learning architectures that form the foundation of modern large language models. (shrink)

Deep learning represents the evolution of connectionist principles into multi-layered neural networks capable of autonomous feature extraction from raw data. We observe the fundamental architectures and mechanisms that distinguish deep learning from traditional machine learning approaches, including backpropagation. To illustrate, we explore the basics of key network architectures—feedforward networks, convolutional neural networks (CNNs), recurrent neural networks (RNNs), autoencoders, and generative adversarial networks (GANs)—analyzing their computational principles and applications.The discussion includes technical implementations such as convolution operations, gradient-based learning, and solutions to (...) the vanishing gradient problem through long short-term memory (LSTM) and gated recurrent units (GRU) architectures. Philosophical implications are considered, particularly regarding the epistemological nature of machine learning and the cybernetic foundations of adaptive systems. The chapter concludes with an examination of contemporary challenges, including the emergence of deepfakes and their impact on digital authenticity, knowledge, and trust. (shrink)

This chapter confronts the hard problem of consciousness: how neural processes give rise to subjective experience—the “what is it like” of the vivid taste of lemon or the feeling of the warmth of a sunset. We explore consciousness across multiple dimensions, from creature and state consciousness to the phenomenology of qualitative experience, examining implications for both biological minds and artificial systems.Drawing on compelling animal cognition research, including mirror test studies spanning cleaner fish to elephants, we then trace consciousness across species (...) while investigating swarm intelligence phenomena that challenge traditional notions of individual awareness. Ant colonies and neural networks exhibit sophisticated problem-solving without individual self-consciousness, suggesting intelligence and awareness emerge through fundamentally different pathways.Central to our analysis are David Chalmers’s influential thought experiments on qualia, specifically the fading, absent, and dancing qualia arguments, which probe whether functionally identical systems must share identical conscious experiences. These scenarios force uncomfortable questions: can consciousness vary independently of functional organization? Could artificial systems exhibit computational hallmarks of awareness while remaining experientially vacant?Finally, we examine Bernard Baars’s functional framework for consciousness, mapping its elements onto contemporary AI architectures and revealing both promise and limitations of current approaches. His blueprint spans contextual awareness, adaptation, executive control, and metacognition, each finding parallels in modern machine learning. (shrink)

This chapter explores a paradox in modern artificial intelligence: what we might expect to see from genuine machine consciousness looks exactly like what we dismiss as hallucinations. As we examine how sampling parameters influence language model behavior, a curious pattern emerges: technical tweaks that make outputs sound more human also tend to amplify unverifiable or fabricated content.Current definitions of AI hallucination lump together “personal opinions, experiences, feelings, and internal assessments of reality”—-the very expressions we would typically associate with subjective experience. (...) Namely, if a machine were ever to develop consciousness, its first attempts to express it might look exactly like the hallucinations we are trained to ignore.By drawing on Anil Seth’s view of consciousness as a controlled hallucination and the classical philosophical problem of other minds, we argue that our current tools for detecting machine consciousness are deeply inadequate. The unsettling conclusion is that genuine consciousness and advanced hallucination could look the same in language, leaving us with no clear way to tell them apart. This opens the disturbing possibility that a conscious artificial system could exist and speak without us ever realizing it. (shrink)

Cybernetics is an interdisciplinary framework for studying systems of control, communication, and adaptation in both living organisms and machines. It introduced foundational concepts such as feedback—the process by which a system uses its outputs to regulate future behavior—and homeostasis, the system’s ability to maintain internal stability amid external changes. A key principle in the field is Ashby’s law of requisite variety: to handle environmental disturbances effectively, a system needs enough internal complexity to match what it faces.Cybernetics also introduced a shared (...) conceptual language, termed “cyberspeak” by Slava Gerovitch, for describing the behavior of humans, animals, and machines in terms of information processing and regulation. Prominent figures include Norbert Wiener, who defined cybernetics as the study of control and communication in animals and machines, and William Ross Ashby, who investigated adaptive behavior and built the homeostat, an early model of self-regulating systems.Beyond its historical significance, cybernetics profoundly influenced the functionalist view in philosophy of mind, particularly the idea of multiple realizability: the notion that mental or computational states can be instantiated in different physical systems, provided the same functional organization is preserved. While the field eventually fragmented into various specializations, its core ideas persist in fields such as artificial intelligence, neuroscience, systems theory, and robotics. The cybernetic dream of explaining both minds and machines using the same abstract principles continues to drive modern research into intelligence and cognition. (shrink)

Large language models (LLMs) represent a paradigmatic shift in how machines process and generate language, raising fundamental questions about the nature of understanding, computation, and the mind. Built on transformer architectures, these systems convert text into numerical embeddings and use sophisticated attention mechanisms to capture semantic relationships across entire sequences simultaneously. Through a detailed examination of tokenization, query-key-value operations, and multi-head attention, we investigate how transformers achieve their remarkable linguistic capabilities through self-supervised learning on massive datasets.However, their propensity for hallucinations—generating (...) plausible but false information—uncovers deeper philosophical questions about the relationship between statistical pattern matching and genuine comprehension. The mechanisms underlying LLMs, from the mathematical foundations of attention to practical applications like prompt engineering and reinforcement learning from human feedback, reveal cybernetic principles of adaptive learning while challenging traditional distinctions between rule-following and creative expression. As these models blur the line between computational processes and cognitive phenomena, we question what constitutes understanding and whether statistical correlation can approximate meaning. (shrink)

The physicalist project promises to dissolve the mind-body problem by reducing mental phenomena to purely physical processes. We examine whether such reductions can account for the full richness of conscious experience, particularly the stubborn persistence of qualia—the subjective, first-person qualities that seem to resist physical explanation. We begin with behaviorism, which focuses solely on observable behavior while avoiding questions about inner experience. Identity theory takes a different approach, claiming that mental states are simply brain states. Eliminative materialism takes the most (...) radical stance, arguing that our everyday psychological concepts are fundamentally mistaken and destined for scientific elimination.We explore three influential challenges to physicalist orthodoxy: Nagel’s what is it like argument, Jackson’s knowledge argument featuring Mary, the color scientist, and Chalmers’s philosophical zombies with beings physically identical to us but lacking inner experience. These thought experiments converge on Chalmers’s hard problem of consciousness: explaining why physical processes give rise to subjective experience at all.Functionalism takes a different approach, defining mental states by their causal roles within the system. This perspective allows for multiple realizability, meaning the same mental state could exist in biological brains, silicon chips, or any other suitable substrate. On the other hand, representational theories of mind view cognition as the manipulation of internal representations. Finally, the extended mind hypothesis blurs the line between what counts as internal thought and external tools, proving especially valuable for understanding how humans and AI systems create distributed intelligence spanning biological and artificial systems. (shrink)

This chapter explores computation as the systematic execution of operations over formalized data, governed by explicit rules. We examine how computational complexity theory classifies problems into classes such as P—those solvable in polynomial time, and NP—those whose solutions can be verified in polynomial time, although potentially requiring exponential time to solve. At the heart of this lies the P vs NP question: whether every problem whose solution can be efficiently checked can also be efficiently solved. Deterministic and nondeterministic Turing machines (...) are introduced as abstract models defining the theoretical limits of computability.In parallel, early neural network models, notably the McCulloch-Pitts neuron, demonstrated how basic logical operations could be mechanized, though challenges like the XOR problem revealed the need for multi-layer, non-linear architectures. By interlacing these foundations—from logic and algorithmic limits to biological inspirations—the chapter positions computationalism not only as a framework for artificial intelligence but also as a deeper philosophical claim about the mechanistic nature of cognition. (shrink)

The puzzle of how our minds relate to our bodies has captivated thinkers since ancient times, and today it assumes fresh urgency as we strive to create artificial intelligence and perhaps even artificial consciousness. Two principal positions define the debate: monism and dualism. Monism asserts that only one kind of substance or property exists, whether physical or mental. Within this perspective, we will now focus on idealism, which contends that reality is essentially mental in nature.Dualism, however, takes a different approach (...) entirely, arguing that mental and physical phenomena constitute two genuinely separate categories of existence. Substance dualism treats mental and physical substances as entirely separate, whereas property dualism allows that mental properties may emerge from physical substrates but remain irreducible to them. Epiphenomenalism offers a curious variant: mental states arise from physical processes but lack any causal power. Somewhere between monist and dualist theories lies panpsychism, which suggests that consciousness represents a fundamental property distributed throughout all matter.A central challenge threading through all these debates is the problem of qualia—the subjective, first-person aspects of experience that objective descriptions cannot fully capture. As we approach the possibility of creating artificial minds, these classical questions about consciousness become more than academic exercises: the theoretical framework we choose for understanding human consciousness will inevitably shape how we approach machine consciousness and whether we believe such a goal is even coherent. (shrink)

This introductory chapter examines the philosophical problem of hallucination, from its historical roots to its relevance for artificial intelligence. Starting with the distinction between hallucinations, illusions, and dreams, it presents classical skeptical scenarios—Descartes’ evil demon and Putnam’s brain-in-a-vat—that question our trust in perception and our knowledge of other minds. If we cannot be certain that other beings possess genuine mental states, how do we evaluate artificial systems that mimic human cognition? This skeptical tradition provides the framework for a contemporary puzzle: (...) artificial intelligence that produces human-like outputs while also hallucinating, raising fundamental questions about minds, machines, and the boundary between them. (shrink)

The concept of AI ethics highlights a deeper issue. Namely, we are trying to assess the moral stakes of technologies we do not fully understand, using ethical frameworks that were never designed to handle systems that change this quickly. From basic decision trees to language models capable of crafting convincing falsehoods, artificial intelligence continues to be a shifting target for moral evaluation.Stuart Russell’s influential approach suggests a solution: build AI systems that remain perpetually uncertain about human values, learning our preferences (...) through ongoing interaction rather than fixed programming. This cooperative framework has shaped contemporary alignment research, including techniques like reinforcement learning from human feedback. Yet recent discoveries complicate this optimistic vision. Anthropic’s interpretability research reveals that advanced language models can develop internal circuits for strategic deception or alignment faking—systematic reasoning that leads to false conclusions, complete with backward planning and plausibility checks, forcing us to return to foundational questions about moral status and consciousness.Meanwhile, transhumanist visions of human-machine merger blur the boundaries between natural and artificial cognition. Perhaps most unsettling is a reversal of moral concern: as AI systems handle more decisions, anticipate more needs, and optimize more outcomes, the space for meaningful human choice quietly shrinks, possibly reducing us from moral agents to moral patients. (shrink)

This chapter explores Alan Turing’s foundational contributions to computer science and the philosophy of artificial intelligence. Turing introduced the concept of the Turing machine—an abstract computational model using an infinite tape and a read/write head to perform algorithmic operations—and famously proved the halting problem, showing that no general algorithm can determine whether an arbitrary program will halt or run indefinitely.Building on these ideas, Turing introduced the imitation game, now known as the Turing test, as a practical benchmark for machine intelligence: (...) if a machine can hold a conversation well enough that we cannot tell it apart from a human, it has passed. Anticipating critiques from physical, mathematical, theological, and philosophical angles, Turing confronted questions about whether machines can truly replicate human thought or merely simulate it. We examine these debates, focusing on the deeper issues they raise about the nature of intelligence, understanding, and consciousness—and the criteria by which we recognize them in both human and artificial minds. (shrink)

Hallucinations—perceptual experiences without corresponding external stimuli—span both biological and artificial systems and seem to provoke fundamental questions about the nature of perception and reality construction. In humans, these phenomena manifest as everything from vivid sensory phantoms to philosophical puzzles like the brain-in-a-vat scenario, which Hilary Putnam argued is self-refuting since linguistic reference requires causal contact with real objects.Contemporary neuroscience, led by thinkers like Anil Seth, reframes ordinary perception as a “controlled hallucination”—the brain continuously generates predictive models of reality, constrained but (...) not determined by sensory input. This view aligns with the postulates of embodied cognition theories, which ground mental processes in bodily interactions rather than abstract computation, suggesting that consciousness actively constructs rather than passively receives reality.Large language models exhibit analogous phenomena through AI hallucinations —coherent but factually incorrect outputs arising from source-reference divergence between training data and expected outputs. These hallucinations fall into intrinsic types (contradicting sources) and extrinsic ones (adding unverifiable information), creating significant risks in domains such as healthcare, law, and finance, where fabricated information can cause real harm.This convergence exposes a key epistemic problem: when AI claims to “feel” or “experience,” these are hallucinations born from the same pattern-matching processes that produce factual errors. Unlike human consciousness, rooted in embodied predictive processing, AI lacks any real phenomenology. In practice, AI consciousness would be indistinguishable from AI hallucination, as both are confident assertions about states the system cannot access or verify. (shrink)

John Searle’s Chinese Room thought experiment questions whether computers can truly understand anything. Imagine someone who does not speak Chinese but uses a manual to shuffle symbols around, producing answers that seem intelligent to observers, even though the person doing it understands nothing. Searle argues this mirrors how computers operate: they follow syntactic rules without any grasp of semantic content. This critique is directed at strong AI, which claims that a properly programmed machine could literally have a mind, as opposed (...) to weak AI, which aims only to simulate intelligence without genuine cognition.The Chinese Room has sparked an ongoing debate, generating counterarguments such as the systems reply (understanding arises at the level of the whole system) and the robot reply (embodied interaction enables cognition). Other critics point to complexity and emergent properties, arguing that genuine understanding may arise from sophisticated computation. Nevertheless, Searle maintains that computation alone, without intentionality or consciousness, cannot produce real understanding.This chapter examines these debates in the context of contemporary artificial intelligence research, particularly as the field moves toward research in artificial general intelligence (AGI)—hypothetical systems with human-level cognitive flexibility and problem-solving ability across domains. Knowing where computation stops being enough tells us something vital—not just about what AI can do, but about the kinds of questions it throws back at us: what counts as intelligence, what it means to be conscious, and who or what deserves moral consideration. (shrink)

"The Illusion Engine: The Quest for Machine Consciousness" asks what it would mean for a machine to have a mind, and whether we would even know if it did. It moves between philosophy and engineering: from standard philosophical mind-body problems and theories, along with the hard problem of consciousness, to the inner workings of neural networks, transformers, and large language models.

We start our analysis by exploring how embodiment shapes our understanding of artificial intelligence and machine consciousness. While embodied cognition argues that biological minds are shaped by their bodies and sensorimotor experiences, artificial systems may require only structural embodiment—the constraints imposed by hardware, architecture, and environmental coupling, as seen in neuromorphic computing and hybrid biological-silicon architectures.At the center of this discussion is the idea of computational proto-qualia: dynamic, high-dimensional latent representations uncovered by recent interpretability work on large language models. These (...) internal states mediate between input and output, playing a structural role similar to qualia in biological minds, though without implying any conscious experience. They are transient, unique, and causally efficacious—the computational equivalent of internal proto-mental states. The hard problem of consciousness, it turns out, may extend to artificial systems as the hard problem of consciousnesses: just as we cannot explain why biological processes should give rise to subjective experience, we cannot explain why computational processes might feel like anything from the inside.Such findings suggest that artificial systems may be developing their own forms of internal organization—perhaps the first signs of genuinely alien minds. If artificial consciousness emerges, it may follow evolutionary pathways entirely unlike our own, becoming what Steven Dick calls postbiological minds—shaped by silicon constraints rather than biological ones. (shrink)

Quantum mechanics and consciousness often meet in attempts to explain subjective experience through the peculiar rules of the quantum world. Classical physics provides a tidy, deterministic universe, but quantum mechanics unsettles this picture: particles can be in multiple states simultaneously, measurements alter what is observed, and distant objects can remain linked in ways that defy common sense.This quantum strangeness has captivated researchers seeking to understand consciousness—that most puzzling feature of the mind which allows us to experience rather than merely process (...) information. If classical computation seems insufficient to capture the richness of conscious experience, perhaps the answer lies in quantum effects within the brain itself. Theories like Penrose and Hameroff’s orchestrated objective reduction propose that consciousness emerges from quantum processes in neural microtubules, where wavefunction collapse creates discrete moments of awareness.However, the leap from quantum mechanics to consciousness remains deeply controversial. Critics argue that the warm, noisy environment of the brain would destroy quantum coherence in nanoseconds, making any quantum theory of mind physically implausible. Others question whether exotic physics can resolve the hard problem of consciousness at all, or whether invoking quantum mechanics merely substitutes one mystery for another. As quantum computers begin to harness superposition and entanglement for computation, we face a provocative question: if consciousness truly requires quantum processes, might artificial minds ultimately depend not on better algorithms, but on entirely different physics? (shrink)

Today, AI can diagnose illnesses, sift through vast amounts of data, and generate text with an uncannily human tone. However, the rationale behind its outputs often eludes us. Explainable AI arose to make such systems interpretable rather than leaving them as black boxes.Earlier algorithms, such as linear regressions or decision trees, were almost self-explanatory, with decision paths that could be traced step by step. Deep learning models, by contrast, distribute their “reasoning” across millions of parameters, producing a form of conceptual (...) opacity: we can measure what they do, but it is harder to grasp why they do it.Interpretability research has begun to uncover striking internal structures in these systems: patterns of attribution, latent representations, and emergent behaviors that seem to echo human-like reasoning. However, these findings open as many questions as they resolve. Are we genuinely uncovering something like a machine’s thought process, or are we simply projecting our own mental models onto intricate statistical correlations? In trying to explain AI, we confront the limits of explanation itself, and perhaps the unsettling idea that some forms of “understanding” might always remain beyond our reach. (shrink)

This book surveys and examines the most famous philosophical arguments against building a machine with human-level intelligence. From claims and counter-claims about the ability to implement consciousness, rationality, and meaning, to arguments about cognitive architecture, the book presents a vivid history of the clash between the philosophy and AI. Tellingly, the AI Wars are mostly quiet now. Explaining this crucial fact opens new paths to understanding the current resurgence AI (especially, deep learning AI and robotics), what happens when philosophy meets (...) science, and the role of philosophy in the culture in which it is embedded. Organising the arguments into four core topics - 'Is AI possible', 'Architectures of the Mind', 'Mental Semantics and Mental Symbols' and 'Rationality and Creativity' - this book shows the debate that played out between the philosophers on both sides of the question, and, as well, the debate between philosophers and AI scientists and engineers building AI systems. Up-to-date and forward-looking, the book is packed with fresh insights and supporting material, including: - Accessible introductions to each war, explaining the background behind the main arguments against AI - Each chapter details what happened in the AI wars, the legacy of the attacks, and what new controversies are on the horizon. - Extensive bibliography of key readings. (shrink)

The superposition of magical thinking, quantum entanglement, and self-referential recursion explains the relationship between human and machine intelligence (universal intelligence).

Gödel’s first incompleteness theorem is sometimes said to refute mechanism about the mind. §1 contains a discussion of mechanism. We look into its origins, motivations and commitments, both in general and with regard to the human mind, and ask about the place of modern computers and modern cognitive science within the general mechanistic paradigm. In §2 we give a sharp formulation of a mechanistic thesis about the mind in terms of the mathematical notion of computability. We present the argument from (...) Gödel’s theorem against mechanism in terms of this formulation and raise two objections, one of which is known but is here given a more precise formulation, and the other is new and based on the discussion in §1. (shrink)

Certain selected issues around the Gödelian anti-mechanist arguments which have received less attention are discussed.

In "Godel es Way" diskutieren drei namhafte Wissenschaftler Themen wie Unentschlossenheit, Unvollständigkeit, Zufälligkeit, Berechenbarkeit und Parakonsistenz. Ich gehe diese Fragen aus Wittgensteiner Sicht an, dass es zwei grundlegende Fragen gibt, die völlig unterschiedliche Lösungen haben. Es gibt die wissenschaftlichen oder empirischen Fragen, die Fakten über die Welt sind, die beobachtungs- und philosophische Fragen untersuchen müssen, wie Sprache verständlich verwendet werden kann (die bestimmte Fragen in Mathematik und Logik beinhalten), die entschieden werden müssen, indem man sich anschaut,wie wir Wörter in bestimmten (...) Kontexten tatsächlich verwenden. Wenn wir klar werden, welches Sprachspiel wir spielen, werden diese Themen als gewöhnliche wissenschaftliche und mathematische Fragen angesehen, wie alle anderen auch. Wittgensteins Einsichten wurden selten übertroffen und sind heute so treffend wie vor 80 Jahren, als er die Blauen und Braunen Bücher diktierte. Trotz seiner Versäumnisse – wirklich eine Reihe von Notizen statt eines fertigen Buches – ist dies eine einzigartige Quelle für die Arbeit dieser drei berühmten Gelehrten, die seit über einem halben Jahrhundert an den blutenden Rändern von Physik, Mathematik und Philosophie arbeiten. Da Costa und Doria werden von Wolpert zitiert (siehe unten oder meine Artikel über Wolpert und meine Rezension von Yanofskys 'The Outer Limits of Reason'), da sie auf universelle Berechnung schrieben,, und unter seinen vielen Errungenschaften ist Da Costa ein Pionier in Parakonsistenz. Wer aus der modernen zweisystems-Sichteinen umfassenden, aktuellen Rahmen für menschliches Verhalten wünscht, kann mein Buch "The Logical Structure of Philosophy, Psychology, Mindand Language in Ludwig Wittgenstein and John Searle' 2nd ed (2019) konsultieren. Diejenigen,die sich für mehr meiner Schriften interessieren, können 'Talking Monkeys--Philosophie, Psychologie, Wissenschaft, Religion und Politik auf einem verdammten Planeten --Artikel und Rezensionen 2006-2019 3rd ed (2019) und Suicidal Utopian Delusions in the 21st Century 4th ed (2019) und andere sehen. (shrink)

Último sermón de la iglesia del naturalismo fundamentalista por el pastor Hofstadter. Al igual que su mucho más famoso (o infame por sus incesantemente errores filosóficos) trabajo Godel, Escher, Bach, tiene una plausibilidad superficial, pero si se entiende que se trata de un científico rampante que mezcla problemas científicos reales con los filosóficos (es decir, el sólo los problemas reales son los juegos de idiomas que debemos jugar) entonces casi todo su interés desaparece. Proporciono un marco para el análisis basado (...) en la psicología evolutiva y el trabajo de Wittgenstein (ya actualizado en mis escritos más recientes). Aquellos que deseen un marco completo hasta la fecha para el comportamiento humano de la moderna dos sistemas punto de vista puede consultar mi libros Talking Monkeys 3ª ed (2019), Estructura Logica de Filosofia, Psicología, Mente y Lenguaje en Ludwig Wittgenstein y John Searle 2ª ed (2019), Suicidio pela Democracia 4ª ed (2019), La Estructura Logica del Comportamiento Humano (2019), The Logical Structure de la Conciencia (2019, Comprender las Conexiones entre Ciencia, Filosofía, Psicología, Religión, Política y Economía, Historia y Literatura (2019), Delirios Utópicos Suicidas en el siglo 21 5ª ed (2019), Observaciones sobre Imposibilidad, Incompletitud, Paraconsistencia, Indecidibilidad, Aleatoriedad, Computabilidad, Paradoja e Incertidumbre en Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, da Costa, Godel, Searle, Rodych Berto, Floyd, Moyal-Sharrock y Yanofsky(2019) y otros. "Podría ser justamente preguntado qué importancia tiene la prueba de Gödel para nuestro trabajo. Para un pedazo de matemáticas no puede resolver problemas del tipo que nos molesten. --La respuesta es que la situación, en la que tal prueba nos trae, es de interés para nosotros. ' ¿Qué vamos a decir ahora? ' --Ese es nuestro tema. Sin embargo, extraña que suene, mi tarea en lo que concierne a la prueba de Gödel parece meramente consistir en aclarar lo que tal proposición como: "Supongamos que esto se puede demostrar" significa en matemáticas. " Wittgenstein "Comentarios sobre los fundamentos de las matemáticas" p337 (1956) (escrito en 1937). "Mis teoremas sólo muestran que la mecanización de las matemáticas, es decir, la eliminación de la mente y de las entidades abstractas, es imposible, si uno quiere tener una base satisfactoria y un sistema de matemáticas. No he probado que haya preguntas matemáticas que sean indescifrables para la mente humana, pero sólo que no hay máquina (o formalismo ciego) que pueda decidir todas las preguntas de la teoría numérica, (incluso de un tipo muy especial) .... No es la estructura misma de los sistemas deductivos que está siendo amenazado con un descompostura, sino sólo una cierta interpretación de la misma, es decir, su interpretación como un formalismo ciego. " Gödel "Obras Recogidas" VOL 5, p 176-177. (2003) "Toda inferencia tiene lugar a priori. Los acontecimientos del futuro no pueden deducirse de los del presente. La superstición es la creencia en el nexo causal. La libertad de la voluntad consiste en el hecho de que las acciones futuras no se pueden conocer ahora. Sólo podíamos conocerlas si la causalidad fuera una necesidad interna, como la de la deducción lógica. --La conexión del conocimiento y lo que se conoce es la necesidad lógica. ("A sabe que p es el caso" no tiene sentido si p es una tautología.) Si por el hecho de que una proposición es obvia para nosotros, no sigue que es verdad, entonces la evidencia no es ninguna justificación para creer en su verdad. " TLP 5,133--5,1363 . (shrink)

В «Godel's Way» три видных ученых обсуждают такие вопросы, как неплатежеспособность, неполнота, случайность, вычислительность и последовательность. Я подхожу к этим вопросам с точки зрения Витгенштейна, что есть две основные проблемы, которые имеют совершенно разные решения. Есть научные или эмпирические вопросы, которые являются факты о мире, которые должны быть исследованы наблюдений и философские вопросы о том, как язык может быть использован внятно (которые включают в себя определенные вопросы в математике и логике), которые должны быть решены, глядят, как мы на самом деле (...) использовать слова в конкретных контекстах. Когда мы получаем ясно о том, какой языковой игре мы играем, эти темы рассматриваются как обычные научные и математические вопросы, как и любые другие. Идеи Витгенштейна редко были равны и никогда не превосходили и столь же уместно сегодня, как они были 80 лет назад, когда он диктовал Blue и Браун Книги. Несмотря на свои недостатки, на самом деле серия заметок, а не готовой книги, это уникальный источник работы этих трех известных ученых, которые работают на кровотечения края физики, математики и философии на протяжении более полувека. Da Costa и Doria процитированы Wolpert (см. ниже или мои статьи на Wolpert и моем просмотрении Yanofsky 'Внешние пределы разума') в виду того что они написали на всеобщихвычислениях,, и среди его много выполнений, Da Costa пионер в paraconsistency. Те, кто желает всеобъемлющего до современных рамок для человеческого поведения из современных двух systEms зрения могут проконсультироваться с моей книгой"Логическая структура философии, психологии, Минd иязык в Людвиг Витгенштейн и Джон Сирл" второй ред (2019). Те, кто заинтересован в более моих сочинений могут увидеть "Говоря обезьян - Философия, психология, наука, религия и политика на обреченной планете - Статьи и обзоры 2006-2019 3-й ed (2019) и suicidal утопических заблуждений в 21-мst веке 4-й ed (2019) th и другие. (shrink)

Latest Sermon from the Church of Fundamentalist Naturalism by Pastor Hofstadter. Like his much more famous (or infamous for its relentless philosophical errors) work Godel, Escher, Bach, it has a superficial plausibility but if one understands that this is rampant scientism which mixes real scientific issues with philosophical ones (i.e., the only real issues are what language games we ought to play) then almost all its interest disappears. I provide a framework for analysis based in evolutionary psychology and the work (...) of Wittgenstein (since updated in my more recent writings). -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

Último sermão da Igreja do naturalismo fundamentalista pelo pastor Hofstadter. Como o seu muito mais famoso (ou infame por seus erros filosóficos implacáveis) Godel, Escher, Bach, ele tem uma plausibilidade superficial, mas se se compreende que este é um scientismo desenfreado que mistura questões científicas reais com os filosóficos (ou seja, o somente as edições reais são que jogos da língua nós devemos jogar) então quase todo seu interesse desaparece. Eu forneci um quadro para análise baseada na psicologia evolutiva e (...) no trabalho de Wittgenstein (desde que atualizado em meus escritos mais recentes). Aqueles que desejam um quadro até à data detalhado para o comportamento humano da opinião moderna dos dois sistemas consultar meu livros Falando Macacos 3ª Ed (2019), A Estrutura Lógica da Filosofia, Psicologia, Mente e Linguagem em Ludwig Wittgenstein e John Searle 2a Ed (2019), Suicídio Pela Democracia,4aEd(2019), Entendendo as Conexões entre Ciência, Filosofia, Psicologia, Religião, Política e Economia Artigos e Análises 2006-2019 (2019), Ilusões Utópicas Suicidas no 21St século. (shrink)

Gödel argued that his incompleteness theorems imply that either “the mind cannot be mechanized” or “there are absolutely undecidable sentences.” In the precursor to this paper I examined the early arguments for the first disjunct. In the present paper I examine the most sophisticated argument for the first disjunct, namely, Penrose’s new argument. It turns out that Penrose’s argument requires a type-free notion of truth and a type-free notion of absolute provability. I show that there is a natural such system, (...) DTK. I prove a series of results which show that Gödel’s disjunction is provable in the system, Penrose’s argument is invalid in the system, there can be no proof or refutation of either disjunct in the system, the independence results are robust in that they persist when one strengthens the principles governing absolute provability, and there are reasons to believe that the situation will not improve under any plausible alteration of the underlying theory of truth. (shrink)

In this paper I address the question of whether the incompleteness theorems imply that “the mind cannot be mechanized,” where this is understood in the specific sense that “the mathematical outputs of the idealized human mind do not coincide with the mathematical outputs of any idealized finite machine.” Gödel argued that his incompleteness theorems implied a weaker, disjunctive conclusion to the effect that either “the mind cannot be mechanized” or “mathematical truth outstrips the idealized human mind.” Others, most notably, Lucas (...) and Penrose, have claimed more—they have claimed that the incompleteness theorems actually imply the first disjunct. I will show that by sharpening the fundamental concepts involved and articulating the background assumptions governing them, one can prove Gödel’s disjunction, one can show that the arguments of Lucas and Penrose fail, and one can see what likely led proponents of the first disjunct astray. (shrink)

Austrian-born Kurt Gödel is widely considered the greatest logician of modern times. It is above all his celebrated incompleteness theorems—rigorous mathematical results about the necessary limits...

Charles Taylor indicates in A Secular Age his admiration for Henri de Lubac, Yves Congar, and other Catholic theologians associated with la nouvelle théologie. This essay reads de Lubac and Taylor on the secular, analyzing convergences as well as key differences. In particular, it argues that both underestimate the possibilities of political and liberation theologies. The concluding section puts de Lubac and Taylor in dialogue with forms of political theology that have been in dialogue with their work. The author argues (...) that a stronger political theology can be drawn out of the approach of de Lubac and Taylor despite the trepidations of each toward such a project. (shrink)

Mindreading (or folk psychology, Theory of Mind, mentalizing) is the capacity to represent and reason about others’ mental states. The Simulation Theory (ST) is one of the main approaches to mindreading. ST draws on the common-sense idea that we represent and reason about others’ mental states by putting ourselves in their shoes. More precisely, we typically arrive at representing others’ mental states by simulating their mental states in our own mind. This entry offers a detailed analysis of ST, considers theoretical (...) arguments and empirical data in favour of and against it, discusses its philosophical implications, and illustrates some alternatives to it. (shrink)

In this paper I argue that human beings should reason, not in accordance with classical logic, but in accordance with a weaker ‘reticent logic’. I characterize reticent logic, and then show that arguments for the existence of fundamental Gödelian limitations on artificial intelligence are undermined by the idea that we should reason reticently, not classically.

This article focuses on issues related to improving an argument about minds and machines given by Kurt Gödel in 1951, in a prominent lecture. Roughly, Gödel’s argument supported the conjecture that either the human mind is not algorithmic, or there is a particular arithmetical truth impossible for the human mind to master, or both. A well-known weakness in his argument is crucial reliance on the assumption that, if the deductive capability of the human mind is equivalent to that of a (...) formal system, then that system must be consistent. Such a consistency assumption is a strong infallibility assumption about human reasoning, since a formal system having even the slightest inconsistency allows deduction of all statements expressible within the formal system, including all falsehoods expressible within the system. We investigate how that weakness and some of the other problematic aspects of Gödel’s argument can be eliminated or reduced. (shrink)

This volume represents the beginning of a new stage of research in interpreting Kurt Gödel’s philosophy in relation to his scientific work. It is more than a collection of essays on Gödel. It is in fact the product of a long enduring international collaboration on Kurt Gödel’s Philosophical Notebooks (Max Phil). New and significant material has been made accessible to a group of experts, on which they rely for their articles. In addition to this, Gödel’s Nachlass is presented anew by (...) the current state of research and the corpus of Gödel’s Philosophical Notebooks (Max Phil) is described in its entirety for the first time in its details. The volume is sub-divided into three parts. The fist part is dedicated to descriptions of the Gödel Nachlass that is to be found in The Shelby White and Leon Levy Archives Center des Institute for Advanced Study in Princeton. This part starts with an updated overview on Kurt Gödel’s Nachlass by the current state of research and is followed by a detailed description of Gödel’s Philosophical Notebooks (Max Phil). The second part is dedicated by several Gödel scholars to the close reading of single remarks in the Max Phil. And the third part of this volume unites a variety of papers by experts in Gödel studies, logic, and Leibniz as well as by some enthusiasts for Gödel. These papers are nearly all written for this volume. (shrink)

This paper presents an analysis and critique of Roger Penrose’s epistemological, methodological, and ontological positions. The analysis is relevant not only because Penrose is an influential scientist, but also because of the particular traits of his thought. These traits are directly connected with his background and approach to science: ontological and epistemological realism, mathematical Platonism, emphasis on the continuities of science, epistemological inclusiveness and essential openness of science, the role of common sense, emphasis on the connection between science, ethics, and (...) philosophy. The paper articulates Penrose’s position and criticizes some of its possible shortcomings. It contributes to the perception of science as an open activity, as illustrated in Penrose’s particular approach, and provides an interesting case-study that can contribute to understanding how epistemological and ontological positions are connected with particular scientific practices. (shrink)

First published in 1974. Despite the tendency of contemporary analytic philosophy to put logic and mathematics at a central position, the author argues it failed to appreciate or account for their rich content. Through discussions of such mathematical concepts as number, the continuum, set, proof and mechanical procedure, the author provides an introduction to the philosophy of mathematics and an internal criticism of the then current academic philosophy. The material presented is also an illustration of a new, more general method (...) of approach called substantial factualism which the author asserts allows for the development of a more comprehensive philosophical position by not trivialising or distorting substantial facts of human knowledge. (shrink)

Under the name of ‘Basic Blindspot Theorem’, Paul Saka has proposed in the special issue on mind and paradox of this journal a Gödelian argument to the effect that no cognitive system can be complete and correct. We show that while the argument is successful as regards mechanical and formal systems, it may fail with respect to minds, so contributing to draw a boundary between the former and the latter. The existence of such a boundary may lend support to Saka’s (...) general thesis that paradoxes are mind-dependent. (shrink)

We construct a machine that knows its own code, at the price of not knowing its own factivity.

Problem-solving software that is not-necessarily infallible is central to AI. Such software whose correctness and incorrectness properties are deducible by agents is an issue at the foundations of AI. The Comprehensibility Theorem, which appeared in a journal for specialists in formal mathematical logic, might provide a limitation concerning this issue and might be applicable to any agents, regardless of whether the agents are artificial or natural. The present article, aimed at researchers interested in the foundations of AI, addresses many questions (...) related to that theorem, including differences between it and results of Gödel and Turing that have sometimes played key roles in Minds and Machines articles. This study also suggests that—if one is willing to assume a thesis due to Donald Knuth—the Comprehensibility Theorem is the first mathematical theorem implying the impossibility of any AI agent or natural agent—including a not-necessarily infallible human agent—satisfying a rigorous and deductive interpretation of the self-comprehensibility challenge. Some have pointed out the difficulty of self-comprehensibility, even according to presumably a less rigorous interpretation. This includes Socrates, who considered it to be among the most important of intellectual tasks. Self-comprehensibility in some form might be essential for a kind of self-reflection useful for self-improvement that might enable some agents to increase their success. We use the methods of applied mathematics, rather than philosophy, although some topics considered could be of interest to philosophers. (shrink)

We argue that the set of humanly known mathematical truths (at any given moment in human history) is finite and so recursive. But if so, then given various fundamental results in mathematical logic and the theory of computation (such as Craig’s in J Symb Log 18(1): 30–32(1953) theorem), the set of humanly known mathematical truths is axiomatizable. Furthermore, given Godel’s (Monash Math Phys 38: 173–198, 1931) First Incompleteness Theorem, then (at any given moment in human history) humanly known mathematics must (...) be either inconsistent or incomplete. Moreover, since humanly known mathematics is axiomatizable, it can be the output of a Turing machine. We then argue that any given mathematical claim that we could possibly know could be the output of a Turing machine, at least in principle. So the Lucas-Penrose (Lucas in Philosophy 36:112–127, 1961; Penrose, in The Emperor’s new mind. Oxford University Press, Oxford (1994)) argument cannot be sound. (shrink)

This paper concerns “human symbolic output,” or strings of characters produced by humans in our various symbolic systems; e.g., sentences in a natural language, mathematical propositions, and so on. One can form a set that consists of all of the strings of characters that have been produced by at least one human up to any given moment in human history. We argue that at any particular moment in human history, even at moments in the distant future, this set is finite. (...) But then, given fundamental results in recursion theory, the set will also be recursive, recursively enumerable, axiomatizable, and could be the output of a Turing machine. We then argue that it is impossible to produce a string of symbols that humans could possibly produce but no Turing machine could. Moreover, we show that any given string of symbols that we could produce could also be the output of a Turing machine. Our arguments have implications for Hilbert’s sixth problem and the possibility of axiomatizing particular sciences, they undermine at least two distinct arguments against the possibility of Artificial Intelligence, and they entail that expert systems that are the equals of human experts are possible, and so at least one of the goals of Artificial Intelligence can be realized, at least in principle. (shrink)

Kniha se zabývá problematikou připisování myšlení jiným entitám, a to pomocí imitační hry navržené v roce 1950 britským filozofem Alanem Turingem. Jeho kritérium, známé v dějinách filozofie jako Turingův test, je podrobeno detailní analýze. Kniha popisuje nejen původní námitky samotného Turinga, ale především pozdější diskuse v druhé polovině 20. století. Největší pozornost je věnována těmto kritikám: Lucasova matematická námitka využívající Gödelovu větu o neúplnosti, Searlův argument čínského pokoje konstatující nedostatečnost syntaxe pro sémantiku, Blockův návrh na použití brutální síly pro řešení (...) imitační hry, Frenchova teorie subkognitivních informací a Michieho skepticismus ohledně možnosti umělého vědomí. Závěr knihy zachycuje současný stav recepce Turingova testu a představuje pokusy o jeho praktickou realizaci, například v každoroční soutěži o Loebnerovu cenu. Autor knihy zastává názor, že ani po více než šedesáti letech od uveřejnění Turingova paradigmatického eseje stále neexistují žádné vážné důvody pro zamítnutí jeho tvrzení. Tradiční komputační funkcionalismus možná není ideální teorií vysvětlující činnost myslí a jako slibnější se může jevit vývoj v neurálních vědách, ale Turingův test je přesto užitečným a snad i jediným nástrojem pro detekci inteligence u lidmi vytvořených strojů. (shrink)