Jakub Mácha

This paper defends the thesis that LLM hallucinations are best explained as a truth representation problem: Current models lack an internal representation of propositions as truth-bearers, so truth and falsity cannot constrain generation in the way factual discourse requires. It begins by surveying leading explanations—computational limits on self-verification, deficiencies in training data as truth sources, and architectural factors—and argues that they converge on the same underlying representational deficit. Next, it reconstructs the philosophical background of current LLM design, showing how optimization for fluent continuation aligns with coherence-style evaluation and with broadly structuralist, relational semantics, before turning to David Chalmers’s recent attempt to secure propositional interpretability by drawing on Davidson/Lewis-style radical interpretation and by locating propositional content in “middle-layer” structures; it argues that this approach downplays the ubiquity of hallucination and inherits instability from post-training edits. Finally, the paper offers a positive proposal: Atomic propositions should be represented in the basic vector layer, reviving a logical atomist program as a principled route to reducing hallucination.

This paper defends the thesis that LLM hallucinations are best explained as a truth representation problem: Current models lack an internal representation of propositions as truth-bearers, so truth and falsity cannot constrain generation in the way factual discourse requires. It begins by surveying leading explanations—computational limits on self-verification, deficiencies in training data as truth sources, and architectural factors—and argues that they converge on the same underlying representational deficit. Next, it reconstructs the philosophical background of current LLM design, showing how optimization for fluent continuation aligns with coherence-style evaluation and with a broadly structuralist, relational semantics, before turning to David Chalmers’s recent attempt to secure propositional interpretability by drawing on Davidson/Lewis-style radical interpretation and by locating propositional content in “middle-layer” structures; it argues that this approach downplays the ubiquity of hallucination and inherits instability from post-training edits. Finally, the paper offers a positive proposal: Atomic propositions should be represented in the basic vector layer, reviving a logical-atomist program as a principled route to reducing hallucination.

This book brings together for the first time two philosophers from different traditions and different centuries. While Wittgenstein was a focal point of 20th century analytic philosophy, it was Hegel’s philosophy that brought the essential discourses of the 19th century together and developed into the continental tradition in 20th century. This now-outdated conflict took for granted Hegel’s and Wittgenstein’s opposing positions and is being replaced by a continuous progression and differentiation of several authors, schools, and philosophical traditions. The development is already evident in the tendency to identify a progression from a ‘Kantian’ to a ‘Hegelian phase’ of analytical philosophy as well as in the extension of right and left Hegelian approaches by modern and postmodern concepts. Assessing the difference between Wittgenstein and Hegel can outline intersections of contemporary thinking.

This book offers an original philosophical perspective on exemplarity. Inspired by Wittgenstein's later work and Derrida's theory of deconstruction, it argues that examples are not static entities but rather oscillate between singular and universal moments. There is a broad consensus that exemplary cases mediate between singular instances and universal concepts or norms. In the first part of the book, Mácha contends that there is a kind of différance between singular examples and general exemplars or paradigms. Every example is, in part, also an exemplar, and vice versa. Furthermore, he develops a paracomplete approach to the logic of exemplarity, which allows us to say of an exemplar of X neither that it is an X nor that it is not an X. This paradox is structurally isomorphic to Russell's paradox and can be addressed in similar ways. In the second part of the book, Mácha presents four historical studies that exemplify the ideas developed in the first part. This part begins with Plato's Forms, understood as standards/paradigms, before considering Kant's theory of reflective judgment as a general epistemological account of exemplarity. This is then followed by analyses of Hegel's conceptual moment of particularity and Kuhn's concept of paradigm. The book concludes by discussing the speculative hypothesis that all our knowledge is based on paradigms, which, following the logic of exemplarity, are neither true nor false. The Philosophy of Exemplarity will be of interest to scholars and advanced students working in philosophy of language, logic, history of philosophy, and literary theory.

While defending his speculative materialism, Quentin Meillassoux has accused many thinkers of a « correlationism » in which the cognizing subject is incapable of reaching the reality indifferent to human thought. The prime instances he gives of strong correlationism are Wittgenstein’s Tractatus and Heidegger’s fundamental ontology. In this article, I argue that Meillassoux’s speculative materialism closely resembles Wittgenstein’s Tractatus. They share a fundamental belief in the contingency of all entities. Wittgenstein advances the picture theory of meaning, in which language and reality are correlated. However, on closer inspection, the picture theory operates on two levels: the level of names referring to objects and the level of propositions referring to facts. I argue that the former level is very close to Meillassoux’s theory of the empty sign that is devoid of meaning and capable of identical iteration. This is, he claims, the distinguishing feature of mathematical discourse, which is capable of accessing mind-independent reality. If this is so, then either some correlations are capable of accessing that reality or, more importantly, the notion of correlation must be specified more precisely. At the same time, I wish to argue that Meillassoux’s derivation of the empty sign can be taken as complementing the Tractatus, because Meillassoux argues that a sign is thinkable without any signification. In the final part of the paper, I evaluate Meillassoux’s argument for, the facticity of every correlation, and argue that Wittgenstein’s Tractatus, under certain interpretations, can escape this critique.

I look at the main metaphors used to frame the role of artificial intelligence (AI) in artistic creativity—tool, collaborator, and medium. I argue that these metaphorical framings not only describe but also actively shape our perceptions of AI and its role. By trying to fit AI into traditional categories, they potentially overlook its ability to introduce something radically new. To overcome this limitation, I propose reframing AI itself as a metaphor—a meaning-disrupting force that, much like metaphorical language, generates unforeseen connections, challenges categorical boundaries, and redefines creativity through its inherent unpredictability. This metaphor invites a radical reimagining of art that fuses human and machine ingenuity. I conclude that AI’s most profound disruption lies in its capacity to destabilize the very frameworks through which we conceptualize art.

This study explores the potential of contemporary large language models (LLMs) to achieve Gilles Deleuze’s goal of integrating art into daily life. Deleuze’s philosophy, with its focus on creative repetition, finds a parallel in LLMs, which replicate and innovate artistic styles by transforming text prompts into various artistic expressions. Although LLMs can very effectively blend and mimic these styles, they remain mere tools – as suggested by the metaphor of a stochastic parrot; the true creative force remains the human artist. Currently, these models are experimental, and their artistic outputs, while impressive, are still viewed as pastiches rather than genuine art. Nonetheless, we can expect advances that may soon enable artists to use LLMs to create genuine artworks.

This article gives a Deleuzian analysis of the concept of ornament, focusing primarily on Deleuze’s reversed platonism and his account of conceptual personae. It differentiates between three kinds of platonism – crude, straight and reversed – and argues that the latter two correspond to two general techniques of creating ornament: stamping and incising. The essay then argues that ornamental patterns are essentially signs. Their differences are not cancelled out, as in writing systems, but rather are ‘enveloped’ in intensive series which, in turn, express Ideas that ideally contribute to the depth of the ornamented thing. The text is supplemented by a case study on the Phaistos Disc that provides support for these claims.

This introduction presents the rationale for the special issue and outlines the main motives discussed in the following essays. The special issue redefines the concept of ornamentation based on Gilles Deleuze's philosophy. It presents ornaments as potent instruments for forming social bonds through repetition and a ruminative mental mindset. Essays by various authors explore the connection between ornaments, social bonds and affective integration, drawing on Deleuze's concepts of repetition and folds. This reinterpretation offers new insights into the aesthetic and social attributes of ornamentation, shedding light on their role in shaping individual and communal becomings.

A paradox, according to Wittgenstein, is something surprising that is taken out of its context. Thus, one way of dealing with paradoxical sentences is to imagine the missing context of use. Wittgenstein formulates what I call the paradigm paradox: ‘one sentence can never describe the paradigm in another, unless it ceases to be a paradigm.’ There are several instances of this paradox scattered throughout Wittgenstein’s writings. I argue that this paradox is structurally equivalent to Russell’s paradox. The above quotation is Wittgenstein’s version of the vicious circle principle which counteracts the paradox. The prohibition Wittgenstein describes is, however, limited to a certain language-game. Finally, I argue that there is a structural analogy between a noun being employed as a self-membered set and a paradigmatic sample being included in or excluded from the set it generates. Paradoxical sentences are not prohibited forever; they can indicate a change in our praxis with a given paradigm.

This volume draws connections between Wittgenstein's philosophy and the work of Saul Kripke, especially his Naming and Necessity. Saul Kripke is regarded as one of the foremost representatives of contemporary analytic philosophy. His most important contributions include the strict distinction between metaphysical and epistemological questions, the introduction of the notions of contingent a priori truth and necessary a posteriori truth and original accounts of names, descriptions, identity, necessity and realism. The chapters in this book elucidate the relevant connections between Kripke's work and Wittgenstein, specifically concerning the standard meter, contingent apriori and rule-following. The contributions shed light on how Kripke's philosophical outlook was influenced by Wittgenstein, and how mainstream analytic philosophy and Wittgensteinian philosophy can fruitfully engage with one another. Kripke and Wittgenstein will be of interest to philosophers working on Wittgenstein, Kripke, and the history of analytic philosophy.

The clean separation between manifold phenomena and a systematic order that prevails in them is a basic feature of the rational-scientific orientation system. The first authoritative formulation of this premise is found in Plato. His discussion of constitutive forms of world events has initiated a broad development in the history of philosophy, which is also effective today in the preference for reason-guided analyses of often confusing circumstances. The authors of this volume address the lasting relevance of this idea within two interrelated areas of research, namely Plato scholarship and contemporary Platonism. Of particular interest is the relationship between Plato and Wittgenstein. Following this overall idea, this volume is divided into three sections: Plato scholarship, Platonism, and Plato and Wittgenstein. As the contributions show, Platonism proves to be not only a purely historical-exegetical field of research but rather a fruitful stimulus for contemporary discussions on logical, linguistic, and social topics.

Dieser Aufsatz untersucht den Begriff der moralischen Exemplarität und geht davon aus, dass unsere Moral durch moralische Exemplare − paradigmatische Beispiele tugendhafter Personen oder Handlungen − untermauert wird. Theoretische Grundsätze der moralischen Exemplarität werden in historischen und zeitgenössischen Kontexten untersucht, darunter die Philosophien von Platon, Aristoteles, die stoische und christliche Ethik sowie neuere Arbeiten von Alexandro Ferrara und Linda Zagzebski. Der Aufsatz diskutiert die Notwendigkeit moralischer Exemplare, die intrinsische moralische und epistemische Exemplarität und die Unterscheidung zwischen kategorischer und hypothetischer Exemplarität und verweist auf die paradoxe kantische Ablehnung der moralischen Exemplarität. Er kritisiert die gegenwärtigen Darstellungen der moralischen Exemplarität und schlägt eine transzendentale Erklärung vor, die in einer Untersuchung des „exemplaristischen kategorischen Imperativs“ kulminiert.

Robert Saudek, a Czech graphologist, journalist, diplomat, playwright, and novelist, was heavily influenced in his youth by Fritz Mauthner’s critique of language. Saudek later became a pioneer in the field of psychological graphology. In this article, I examine the impact of Mauthner’s critique on Saudek’s work and evaluate whether Saudek’s approach to graphology aligns with Mauthner’s ideas. I argue that, although Saudek’s graphology is rooted in Mauthner’s critique of experimental psychology, there remains room for further development in the field of psychological graphology, centering on the analysis of language. With this in mind, I compare Saudek’s method and contemporary conceptual metaphor theory. I further suggest that Saudek’s extensive use of the autographs of well-known figures follows a method of working from examples, or specimens, which is not uncommon in the philosophy of science. Based on these findings, I propose a way of understanding Saudek’s graphology that challenges its characterization as a pseudoscience.

I argue that Hegel and Wittgenstein, each in their own specific way, used the idea of God at the beginning of creation as a complex analogy for other kinds of beginning, most notably the beginning of philosophical thought. Hegel’s Logic describes God’s mind before the creation of the world, i.e. God’s pure thinking. For a philosopher, beginning afresh means resolving to consider this kind of abstraction from the existence of the world. Wittgenstein, by contrast, says that the idea of a creator of the world does not explain anything. It marks the terminus ad quem of asking for explanations; we must not ask further who created the creator of the world. Wittgenstein generalizes this for any kind of reasoning: “Explanations come to an end somewhere.” (Philosophical Investigations: §1) Any sort of explanation must eventually arrive at its terminus ad quem, which means only that any kind of reasoning must have its logical beginning.

This book offers an original philosophical perspective on exemplarity. Inspired by Wittgenstein’s later work and Derrida’s theory of deconstruction, it argues that examples are not static entities but rather oscillate between singular and universal moments. There is a broad consensus that exemplary cases mediate between singular instances and universal concepts or norms. In the first part of the book, Mácha contends that there is a kind of différance between singular examples and general exemplars or paradigms. Every example is, in part, also an exemplar, and vice versa. Furthermore, he develops a paracomplete approach to the logic of exemplarity, which allows us to say of an exemplar of X neither that it is an X nor that it is not an X. This paradox is structurally isomorphic to Russell’s paradox and can be addressed in similar ways. In the second part of the book, Mácha presents four historical studies that exemplify the ideas developed in the first part. This part begins with Plato’s Forms, understood as standards/paradigms, before considering Kant’s theory of reflective judgment as a general epistemological account of exemplarity. This is then followed by analyses of Hegel’s conceptual moment of particularity and Kuhn’s concept of paradigm. The book concludes by discussing the speculative hypothesis that all our knowledge is based on paradigms, which, following the logic of exemplarity, are neither true nor false.

Both Hegel and the later Wittgenstein were concerned with the problem of how to begin speculation, or the problem of beginning. I argue that despite many differences, there are surprising similarities between their thinking about the beginning. They both consider different kinds of beginnings and combine them into complex analogies. The beginning has a subjective and an objective moment. The philosophizing subject has to begin with something, with an object. For Hegel, the objective moment is pure being. For Wittgenstein, the objective moment is something that cannot be doubted. As regards the subjective moment, the philosophizing subject has to decide, without any reason, to conclude her quest for the presuppositionless beginning and finally begin at the beginning. The arational moment of this decision is echoed throughout any rational thought. Any application of a (rational) rule is, ultimately, a blind decision to apply this rule.

In the sense-certainty chapter of the Phenomenology of Spirit, we find one of Hegel’s famous puns, which utilizes homophonic affinities and differences between the verb beiherspielen and the noun Beispiel. I argue that the effect of this pun is that the word Beispiel acquires, beyond its usual meaning of ‘example’ or ‘instance’, the meaning of a play of something inessential, a play in passing. After reviewing all available translations into English, I suggest that, in order to preserve this wordplay, one can translate Beispiel as ‘by-play’. Furthermore, I analyse other occurrences of the word beiherspielen in the Phenomenology and elsewhere in Hegel’s texts. Next, I focus on the crucial importance of this pun for Derrida’s interpretation and critique of Hegel’s dialectic. Only for a certain loose translation of beiherspielen does Derrida’s reasoning appear plausible. I conclude with a discussion of the ideal of terminological uniformity in translating Hegel’s texts. In preserving the wordplay by translating Beispiel as ‘by-play’, one is forced to sacrifice the uniformity of translation.

Understanding Hegel's account of particularity has proven to be anything but straightforward. Two main accounts of particularity have been advanced: the particular as an example or instance and the particular as a subjective perspective on a universal concept. The problem with these accounts is that they reduce particularity either to singularity or to universality. As Derrida's analyses make apparent, the ‘structure of exemplarity’ in Hegel is quite intricate. Hegel uses ‘example’ in three senses: it means (1) ‘instance’, ‘illustration’, or (2) ‘model’, ‘exemplary individual’, ‘paradigm’, or (3) a by-play (a meaning derived from Hegel's neologismbeiherspielen, in whichBeispielis understood quasi-etymologically as a ‘by-play’ of accidental moments). ABeispielin the first sense can be replaced by another instance in a free play (by-play). This play of accidental moments, however, is not entirely free; it generates a series (of replacements) that ultimately leads to an example in the second sense, to an exemplary individual. I argue that particularity can be taken as exemplarity of this kind, oscillating between a singular example and a universal paradigm. Within this by-play, the universal concept, its law, is supposed to be mediated and determined. However, out of the differences between the examples the by-play induces another law, the law of non-mediation, which may, in Derrida's view, actually negate the dialectical movement towards universality. I argue, utilizing Malabou's concept of plasticity, that this disruption may be recovered. This implies that each individual example within a series is a particular determination of the universal. Hence, we can take literally Hegel's claim that the movement of the concept is play.