The singularity hypothesis is a radical hypothesis about the future of artificial intelligence on which self-improving artificial agents will quickly become orders of magnitude more intelligent than the average human. Despite the ambitiousness of its claims, the singularity hypothesis has been defended at length by leading philosophers and artificial intelligence researchers. In this paper, I argue that the singularity hypothesis rests on scientifically implausible growth assumptions. I show how leading philosophical defenses of the (...) singularity hypothesis (Chalmers 2010, Bostrom 2014) fail to overcome the case for skepticism. I conclude by drawing out philosophical implications of this discussion for our understanding of consciousness, personal identity, digital minds, existential risk, and ethical longtermism. GPI Working Paper No . 19-2022. (shrink)

Singularity Hypotheses: A Scientific and Philosophical Assessment offers authoritative, jargon-free essays and critical commentaries on accelerating technological progress and the notion of technological singularity. It focuses on conjectures about the intelligence explosion, transhumanism, and whole brain emulation. Recent years have seen a plethora of forecasts about the profound, disruptive impact that is likely to result from further progress in these areas. Many commentators however doubt the scientific rigor of these forecasts, rejecting them as speculative and unfounded. We therefore (...) invited prominent computer scientists, physicists, philosophers, biologists, economists and other thinkers to assess the singularity hypotheses. Their contributions go beyond speculation, providing deep insights into the main issues and a balanced picture of the debate. (shrink)

The tree property at κ+ states that there are no Aronszajn trees on κ+, or, equivalently, that every κ+ tree has a cofinal branch. For singular strong limit cardinals κ, there is tension between the tree property at κ+ and failure of the singular cardinal hypothesis at κ; the former is typically the result of the presence of strongly compact cardinals in the background, and the latter is impossible above strongly compacts. In this paper, we reconcile the two. We (...) prove from large cardinals that the tree property at κ+ is consistent with failure of the singular cardinal hypothesis at κ. (shrink)

Einsteinian gravity, of which Newtonian gravity is a part, is fraught with the problem of singularity that has been established as a theorem by Hawking and Penrose. The _hypothesis_ that founds the basis of both Einsteinian and Newtonian theories of gravity is that bodies with unequal magnitudes of masses fall with the same acceleration under the gravity of a source object. Since, the Einstein’s equations is one of the assumptions that underlies the proof of the singularity theorem, therefore, (...) the above hypothesis is implicitly one of the founding pillars of the same. In this work, I demonstrate how one can possibly write a non-singular theory of gravity which manifests that the above mentioned hypothesis is only valid in an approximate sense in the “large distance” scenario. To mention a specific instance, under the gravity of the earth, a 5 kg and a 500 kg fall with accelerations which differ by approximately \(113.148\times 10^{-32}\) meter/sec \(^2\) and the more massive object falls with less acceleration. Further, I demonstrate why the concept of gravitational field is not definable in the “small distance” regime which automatically justifies why the Einstein’s and Newton’s theories fail to provide any “small distance” analysis. In course of writing down this theory, I demonstrate why the continuum hypothesis as spelled out by Goedel, is undecidable. The theory has several aspects which provide the following realizations: (i) Descartes’ self-skepticism concerning exact representation of numbers by drawing lines (ii) Born’s wish of taking into account “natural uncertainty in all observations” while describing “a physical situation” by means of “real numbers” (iii) Klein’s vision of having “a fusion of arithmetic and geometry” where “a point is replaced by a small spot” (iv) Goedel’s assertion about “non-standard analysis, in some version” being “the analysis of the future”. (shrink)

We prove several results giving lower bounds for the large cardinal strength of a failure of the singular cardinal hypothesis. The main result is the following theorem: Theorem. Suppose κ is a singular strong limit cardinal and 2κ λ where λ is not the successor of a cardinal of cofinality at most κ. If cf > ω then it follows that o λ, and if cf = ωthen either o λ or {α: K o α+n} is confinal in κ (...) for each n ε ω.We also prove several results which extend or are related to this result, notably Theorem. If 2ω ω1 then there is a sharp for a model with a strong cardinal.In order to prove these theorems we give a detailed analysis of the sequences of indiscernibles which come from applying the covering lemma to nonoverlapping sequences of extenders. (shrink)

We show that the Proper Forcing Axiom implies the Singular Cardinal Hypothesis. The proof uses the reflection principle MRP introduced by Moore in [11].

The purpose of this paper is to present some results which suggest that the Singular Cardinals Hypothesis follows from the Proper Forcing Axiom. What will be proved is that a form of simultaneous reflection follows from the Set Mapping Reflection Principle, a consequence of PFA. While the results fall short of showing that MRP implies SCH, it will be shown that MRP implies that if SCH fails first at κ then every stationary subset of reflects. It will also be (...) demonstrated that MRP always fails in a generic extension by Prikry forcing. (shrink)

We show that o = k++ is necessary for ¬SCH. Together with previous results it provides the exact strenght of ¬SCH.

We show that given ù many supercompact cardinals, there is a generic extension in which the tree property holds at ℵ ω²+1 and the SCH fails at ℵ ω².

This paper attempts to present and organize several problems in the theory of Singular Cardinals. The most famous problems in the area (bounds for the ℶ-function at singular cardinals) are well known to all mathematicians with even a rudimentary interest in set theory. However, it is less well known that the combinatorics of singular cardinals is a thriving area with results and problems that do not depend on a solution of the Singular Cardinals Hypothesis. We present here an annotated (...) collection of representative problems with some references. Where the problems are novel, attribution is attempted and it is noted where money is attached to particular problems. Three closely related themes are represented in these problems: stationary sets and stationary set reflection, variations of square and approachability, and the singular cardinals hypothesis. Underlying many of them are ideas from Shelah's PCF theory. Important subthemes were mutual stationarity, Aronszajn trees, and superatomic Boolean Algebras. The author notes considerable overlap between this paper and the unpublished report submitted to the Banff Center for the Workshop on Singular Cardinals Combinatorics, May 1–5, 2004. (shrink)

According to the singularity hypothesis, rapid and accelerating technological progress will in due course lead to the creation of a human-level artificial intelligence capable of designing a successor artificial intelligence of significantly greater cognitive prowess, and this will inaugurate a series of increasingly super-intelligent machines. But how much sense can we make of the idea of a being whose cognitive architecture is qualitatively superior to our own? This article argues that one fundamental limitation of human cognitive architecture is (...) an inbuilt commitment to a metaphysical division between subject and object, a commitment that could be overcome in an artificial intelligence lacking our biological heritage. (shrink)

[Abstract] Suppose that the Big Bang was the first singularity in the history of the cosmos. Then it would be plausible to presume that the availability of the strong general intelligence should mark the second singularity for the natural human race. The human race needs to be prepared to make it sure that if a singularity robot becomes a person, the robotic person should be a blessing for the humankind rather than a curse. Toward this direction I (...) would scrutinize the implication of the hypothesis that the singularity robot is a member of the human society. I will ask how the robot is equipped to satisfy the ontological criteria such as accountability, consciousness, identity, by demonstrating a possibility that it has the epistemological capacities like conceptual role semantic understanding and non-monotonous inference, and by probing whether it can behave in the way human moral visions expect it to. -/- [Table of contents] 1. Opening: Singularity robots are coming 1) Singularity robots of strong general intelligence 2) A singularity robot is a member of the human community 2. Ontological interpretation of singularity robot 1) Responsibility: thinking, understanding, belief 2) Consciousness: three characteristics – zombie, enjoyment, sympathy 3) Identity: I, body, autonomy, unity 3. Epistmological prospects of singularity robot 1) Semantics of general intelligence: conceptual role semantics 2) Logic for general intelligence: non-monotonous logic 4. Moral horizon of singularity robot 1) When a singularity robot becomes a robot person 2) Humanity independence: singularity robot is a user of human languages 5. Concluding: preemptive humanities. (shrink)

According to some philosophers and social scientists, mainstream economic theories currently play an unprecedented role in shaping human societies. This phenomenon can be linked to the dissemination of methodological individualism, where common goods are interpreted as reducible to aggregates of individuals' well-being. Nonetheless, some emergent difficulties of economics in coping with global institutional issues have encouraged some authors to revise that paradigm. In the last three decades, there has been a parallel growing philosophical interest in investigating social sciences' epistemological and (...) ontological foundations. Unfortunately, these two research trends have often not communicated systematically enough to understand the specific ontology of collective aims. It is still unclear whether some irreducible social goods exist and how the answer to this question can set up a consistent understanding of cooperative actions. This dissertation addresses this issue, drawing on philosophical investigations about collective intentionality. It claims that a coherent ontological taxonomy of irreducible and reducible social goods is theoretically viable and can reframe prevailing approaches to collective action dilemmas influenced by the traditional economic categorisation of goods. The research begins by analysing how the influential theory of public goods has paved the way for some social and moral impasses. Furthermore, some theoretical proposals suggesting the existence of relational goods and common-pool resources are scrutinised. Hence, a refutation of the ontological reduction of all social goods to individual ones is developed, arguing that a specific form of cooperation, grounded in we-intentions and we-reasoning, shows the plausibility of the existence of some kinds of irreducible collective goods. Expanding on that view, a refinement of this categorisation of social goods is put forward by underlying the function of some relational entities, such as trust and shared sensemaking processes, in making cooperation robust in uncertain environments. Finally, by applying the taxonomy to collective action gridlocks regarding climate change, digital information, and public education, the consistency of this hypothesis is tested, showing that a pluralistic ontological account of social goods might improve the moral understanding of current social dilemmas. (shrink)

In this paper we discuss the two-system framework, examine its strengths, point out a fundamental weakness concerning the unity of conscious experience, and then propose a new hypothesis that avoids that weakness and other related concerns. According to our strong emergence hypothesis, what emerges are not merely mental properties in specialized, distributed neural areas, but also a new, irreducibly singular entity that functions in a recurrent manner to integrate its mental properties and to rewire its brain. We argue (...) that the former function is suggested, in part, by the effects of anesthetics on sensory integration, and that the latter function is suggested by evidence garnered from the neuroscience of mindfulness, constraint-induced movement therapy for stroke, and neuroimaging data surrounding mental illness. We then discuss how our strong emergence hypothesis relates to the description and treatment of neuropsychiatric disorders. Finally, potential objections are addressed. (shrink)

The purpose of this communication is to present some recent advances on the consequences that forcing axioms and large cardinals have on the combinatorics of singular cardinals. I will introduce a few examples of problems in singular cardinal combinatorics which can be fruitfully attacked using ideas and techniques coming from the theory of forcing axioms and then translate the results so obtained in suitable large cardinals properties.The first example I will treat is the proof that the proper forcing axiom PFA (...) implies the singular cardinal hypothesis SCH, this will easily lead to a new proof of Solovay's theorem that SCH holds above a strongly compact cardinal. I will also outline how some of the ideas involved in these proofs can be used as means to evaluate the “saturation” properties of models of strong forcing axioms like MM or PFA.The second example aims to show that the transfer principle ↠ fails assuming Martin's Maximum MM. Also in this case the result can be translated in a large cardinal property, however this requires a familiarity with a rather large fragment of Shelah's pcf-theory.Only sketchy arguments will be given, the reader is referred to the forthcoming [25] and [38] for a thorough analysis of these problems and for detailed proofs. (shrink)

From large cardinals we obtain the consistency of the existence of a singular cardinal κ of cofinality ω at which the Singular Cardinals Hypothesis fails, there is a bad scale at κ and κ ++ has the tree property. In particular this model has no special κ +-trees.

The present study focuses on the situation in which mind-reading machines will be connected, initially through the incorporation of weak AI, and then in conjunction to strong AI, an aspect that, ongoing, will no longer have a simple medical role, as is the case at present, but one of surveillance and monitoring of individuals—an aspect that is heading us towards a future techno-panoptic singularity. Thus, the general objective of this paper raises the problem of the ontological stability of human (...) nature which, within the limits of the technological singularity of mind-reading machines, leads to the loss of autonomy and a reduction in freedom when it comes to human thoughts. In this paradigm, the hypothesis of a future era of technological singularity is prefigured to be a cumulation of factors in which artificial intelligence holds a dominant position in relation to the human agent, in a techno-panoptic system of human supervision, in the form of a new world order of manifestation/imposition of power—that of a “singleton.” The theoretical objective analyzes the phenomenon of “deterritorrialization” of the Foucauldian panoptic mechanism —which is based on the “biopolitical” system of “biopower”—and its “reterritorialization” in the “territory” of the techno-panoptic singularity, where the scenario of a strong AI “singleton”, represents the alienation of the Being into a hard technological determinism. (shrink)

In their paper from 1981, Milner and Sauer conjectured that for any poset $\langle P,\le\rangle$ , if $cf(P,\le)=\lambda>cf(\lambda)=\kappa$ , then P must contain an antichain of size κ. We prove that for λ > cf(λ) = κ, if there exists a cardinal μ < λ such that cov(λ, μ, κ, 2) = λ, then any poset of cofinality λ contains λ κ antichains of size κ. The hypothesis of our theorem is very weak and is a consequence of many (...) well-known axioms such as GCH, SSH and PFA. The consistency of the negation of this hypothesis is unknown. (shrink)

It is an assumed view in Chinese philosophy that the grammatical differences between English or Indo-European languages and classical Chinese explain some of the differences between the Western and Chinese philosophical discourses. Although some philosophers have expressed doubts about the general link between classical Chinese philosophy and syntactic form of classical Chinese, I discuss a specific hypothesis, i.e., the mass-noun hypothesis, in this essay. The mass-noun hypothesis assumes that a linguistic distinction such as between the singular terms (...) and the predicates is sufficient to justify or necessarily leads to a specific ontological distinction such as the distinction between the particular and the universal. I argue that one cannot read off semantic properties simply from syntactic ones and hence the syntactic differences do not automatically translate into the semantic differences between languages, that the syntactic features of Chinese nouns do not have explanatory significance in explaining why the particular-universal problem does not arise in the classical period of Chinese philosophy, and that the part-whole ontology allegedly informed by the mass-noun-like semantics does not provide a natural or intuitive picture of the language-world relation. (shrink)

We attempt to defend the species-as-individuals hypothesis by examining the logical role played by the binomials (e.g., "Homo sapiens," "Pinus ponderosa") in biological discourse about species. Those who contend that the binomials can be properly understood as functioning in biological theory as singular terms opt for an objectual account of species and view species as individuals. Those who contend that the binomials can in principle be eliminated from biological theory in favor of predicate expressions opt for a predicative account (...) of species and view species as kinds. We contend that biologists' talk about species is talk about species as individuals, and we conclude that the most plausible account of species is an objectual account. (shrink)

Recent progress in artificial intelligence (AI) has drawn attention to the technology’s transformative potential, including what some see as its prospects for causing large-scale harm. We review two influential arguments purporting to show how AI could pose catastrophic risks. The first argument — the Problem of Power-Seeking — claims that, under certain assumptions, advanced AI systems are likely to engage in dangerous power-seeking behavior in pursuit of their goals. We review reasons for thinking that AI systems might seek power, that (...) they might obtain it, that this could lead to catastrophe, and that we might build and deploy such systems anyway. The second argument claims that the development of human-level AI will unlock rapid further progress, culminating in AI systems far more capable than any human — this is the Singularity Hypothesis. Power-seeking behavior on the part of such systems might be particularly dangerous. We discuss a variety of objections to both arguments and conclude by assessing the state of the debate. (shrink)

Given a regular cardinal λ and λ many supercompact cardinals, we describe a type of forcing such that in the generic extension there is a cardinal κ with cofinality λ, the Singular Cardinal Hypothesis at κ fails, and the tree property holds at κ+.

We determine exact consistency strengths for various failures of the Singular Cardinals Hypothesis (SCH) in the setting of the Zermelo-Fraenkel axiom system ZF without the Axiom of Choice (AC). By the new notion of parallel Prikry forcing that we introduce, we obtain surjective failures of SCH using only one measurable cardinal, including a surjective failure of Shelah's pcf theorem about the size of the power set of $\aleph _{\omega}$ . Using symmetric collapses to $\aleph _{\omega}$ , $\aleph _{\omega _{1}}$ (...) , or $\aleph _{\omega _{2}}$ , we show that injective failures at $\aleph _{\omega}$ , $\aleph _{\omega _{1}}$ , or $\aleph _{\omega _{2}}$ can have relatively mild consistency strengths in terms of Mitchell orders of measurable cardinals. Injective failures of both the aforementioned theorem of Shelah and Silver's theorem that GCH cannot first fail at a singular strong limit cardinal of uncountable cofinality are also obtained. Lower bounds are shown by core model techniques and methods due to Gitik and Mitchell. (shrink)

In Part I of this series [A. Poveda, A. Rinot and D. Sinapova, Sigma-Prikry forcing I: The axioms, Canad. J. Math. 73(5) (2021) 1205–1238], we introduced a class of notions of forcing which we call [Formula: see text]-Prikry, and showed that many of the known Prikry-type notions of forcing that center around singular cardinals of countable cofinality are [Formula: see text]-Prikry. We showed that given a [Formula: see text]-Prikry poset [Formula: see text] and a [Formula: see text]-name for a non-reflecting (...) stationary set [Formula: see text], there exists a corresponding [Formula: see text]-Prikry poset that projects to [Formula: see text] and kills the stationarity of [Formula: see text]. In this paper, we develop a general scheme for iterating [Formula: see text]-Prikry posets and, as an application, we blow up the power of a countable limit of Laver-indestructible supercompact cardinals, and then iteratively kill all non-reflecting stationary subsets of its successor. This yields a model in which the singular cardinal hypothesis fails and simultaneous reflection of finite families of stationary sets holds. (shrink)

Journal of Mathematical Logic, Volume 22, Issue 03, December 2022. In Part I of this series [A. Poveda, A. Rinot and D. Sinapova, Sigma-Prikry forcing I: The axioms, Canad. J. Math. 73(5) (2021) 1205–1238], we introduced a class of notions of forcing which we call [math]-Prikry, and showed that many of the known Prikry-type notions of forcing that center around singular cardinals of countable cofinality are [math]-Prikry. We showed that given a [math]-Prikry poset [math] and a [math]-name for a non-reflecting (...) stationary set [math], there exists a corresponding [math]-Prikry poset that projects to [math] and kills the stationarity of [math]. In this paper, we develop a general scheme for iterating [math]-Prikry posets and, as an application, we blow up the power of a countable limit of Laver-indestructible supercompact cardinals, and then iteratively kill all non-reflecting stationary subsets of its successor. This yields a model in which the singular cardinal hypothesis fails and simultaneous reflection of finite families of stationary sets holds. (shrink)

In the age of ubiquitous technology, humans are reshaped through each transaction they are involved in. AI-driven networks, online games, and multisensory interactive environments make up alternate realities. Within such alternate worlds, users are reshaped as deterministic agents. Technology’s focus on reducing complexity leads to a human being dependent on prediction-driven machines and behaving like them. Meaning and information are disconnected. Existence is reduced to energy processes. The immense gain in efficiency translates as prosperity. Citizens of advanced economies, hurrying in (...) the rhythm of machine-driven interactions, feel entitled to it. Successful at the price of self-awareness, they no longer know what this means. Happiness and prosperity are not consubstantial. Lack of happiness leads to aggression. This is the image of the world as we see it, no longer looking at each other, eye to eye, but screen to screen. The questions eliminated in the process of transferring responsibility from the individual to machines will inevitably become society’s new focus. When the goal is to get everyone to behave like a machine, the Singularity hypothesis becomes self-fulfilling prophecy. If, in addition to having exhausted natural resources, society does not want to end up making the human mind superfluous, it has to seek a better understanding of what makes anticipation possible. As a definitory characteristic of the living, corresponding to its complexity, anticipation can no longer be taken for granted, while every effort is made to reduce complexity for efficiency’s sake. Awareness of the processes conducive to its expression in successful human action will position human beings as masters of their destiny, not slaves of their own making. Antecapere ergo sum might be the counterclaim to Descartes’ Dubito ergo sum . To resist being perfected into oblivion, that is, unsustainable prosperity, means to reclaim the knowledge corresponding to higher levels of complexity. (shrink)

In my book Posthuman Life: Philosophy at the Edge of the Human (Routledge 2014) I set out a recursive account of the conditions for posthumanity: the Disconnection Thesis (DT). The DT states that a being is posthuman iff: -/- 1) It has ceased to belong to WH (the "Wide Human" socio-technical network) as a result of technical alteration; 2) Or it is a wide descendent of such a being (outside WH) (PHL 112) -/- Jon Cogburn's "Galapagos objection" attempts to show (...) that there could be life forms whose evolution satisfies the disconnection criteria but which lack the degree of autonomy that elicits our moral concern with the prospect posthumans. In this post I respond to Jon's objection and briefly discuss other philosophical objections to my account of posthumanity. -/- Roden, David. 2012. “The Disconnection Thesis”. In The Singularity Hypothesis: A Scientific and Philosophical Assessment, A. Eden, J. Søraker, J. Moor & E. Steinhart (eds), 281–98. London: Springer. -/- Roden, David. 2014. Posthuman Life: Philosophy at the Edge of the Human. London: Routledge. -/- . (shrink)

The article's intent is to demonstrate the following two points: first, essential aspects of Reckwitz' singularization hypothesis are to find in the work of Georg Simmel. Second, the article highlights the timeliness of Simmel as an important impulse for the science of collectivities. Finally, the three parts - Reckwitz' theory of singularization, the science of collectivities, and Georg Simmel's thinking - find common ground in relating collectivity and individuality.

Based on the presentation of a research framework (the shared work of teachers), this text uses an empirical approach to examine the hypothesis of a co-elaboration of the professional situation. To do so, the empirical investigation, based on the Goffman framework, analyzes the process of reconstructing a teaching session (reference situation) over the course of a pedagogical counselling session (support situation) characterized by interaction between a beginning teacher and a trainer. The invalidation of the hypothesis leads to a (...) suggested conceptualization of the professional situation combining definitional approaches (emphasizing the duality between its singularity and its genericity) and methodological approaches. -/- A partir de la présentation d’un cadre de recherche (le travail partagé des enseignants), ce texte soumet à l’empirie l’hypothèse de la co-élaboration de la situation professionnelle. Pour ce faire, en s’appuyant sur le cadre de Goffman, l’enquête empirique analyse le processus de reconstruction d’une séance d’enseignement (situation de référence) au cours d’une séance de conseil pédagogique (situation support) caractérisée par l’interaction entre une enseignante débutante et un formateur. L’invalidation de l’hypothèse débouche sur une proposition de conceptualisation de la situation professionnelle qui combine des approches définitoires (insistant sur la dualité entre sa singularité et sa généricité) et méthodologiques. (shrink)

The ‘Mind-Upload’ hypothesis, a radical version of the Brain-in-a-Vat thought experiment, asserts that a whole mind can safely be transferred from a brain to a digital device, after being exactly encoded into substrate independent informational patterns. Prima facie, MU seems the philosophical archenemy of the Embodied Mind theory, which understands embodiment as a necessary and constitutive condition for the existence of a mind and its functions. In truth, whether and why MU and EM are ultimately incompatible is unobvious. This (...) paper, which aims to answer both questions, will not simply confirm that MU and EM actually are incompatible. It will also show the true reason of their incompatibility: while EM implies that a mind’s individual identity is contingent upon the details of its physical constituents, MU presupposes that minds can be relocated from one material vessel to another. A systematic comparison between these conflicting assumptions reveals that the real shortcoming of MU is not the one usually discussed by the philosophical literature: it has nothing to do with MU’s functionalist or computationalist prerequisites, and is only secondarily related to the artificial implementability of consciousness; the real problem is that MU presupposes that minds could still be individuated and numerically identified while being reduced to immaterial formal patterns. EM seems committed to refute this assumption, but does it have sufficient resources to succeed? (shrink)

Based on the presentation of a research framework (the shared work of teachers), this text uses an empirical approach to examine the hypothesis of a co-elaboration of the professional situation. To do so, the empirical investigation, based on the Goffman framework, analyzes the process of reconstructing a teaching session (reference situation) over the course of a pedagogical counselling session (support situation) characterized by interaction between a beginning teacher and a trainer. The invalidation of the hypothesis leads to a (...) suggested conceptualization of the professional situation combining definitional approaches (emphasizing the duality between its singularity and its genericity) and methodological approaches. A partir de la présentation d’un cadre de recherche (le travail partagé des enseignants), ce texte soumet à l’empirie l’hypothèse de la co-élaboration de la situation professionnelle. Pour ce faire, en s’appuyant sur le cadre de Goffman, l’enquête empirique analyse le processus de reconstruction d’une séance d’enseignement (situation de référence) au cours d’une séance de conseil pédagogique (situation support) caractérisée par l’interaction entre une enseignante débutante et un formateur. L’invalidation de l’hypothèse débouche sur une proposition de conceptualisation de la situation professionnelle qui combine des approches définitoires (insistant sur la dualité entre sa singularité et sa généricité) et méthodologiques. (shrink)

Gilles Deleuze’s research during the 1980s focused on the 17th century German thinker G. W. Leibniz. In 1988, Deleuze published Le Pli, which forms part of a series of works on modern philosophy. This book displays Deleuze’s attention to the interpretations of contemporary commentators on modern philosophy, in this case, on Leibniz. In this context, there occurred a brief and important dialogue between Deleuze and Christiane Frémont, the French commentator and translator of Leibniz, with regard to their respective interpretations of (...) the great German philosopher. This article intends to give an account of the main topics present in that conversation. Firstly, we can say they involve 1) the problem of body and the Leibnizian vinculum substantiale, 2) the question of singularities, 3) the principle of economy and incompossibility, and 4) the Deleuzian concept of vice-diction. Our hypothesis in this study is that the readings made by both authors of the German thinker are mutually involved. It is essential, in order to support this hypothesis, to make precise the demarcations of relations between such readings. For this reason, our research will focus on Frémont’s study Singularités, individus et relations dans le système de Leibniz (2003) and on Deleuze’s work Le Pli (1988). We hope to determine the topics that emerge in the relationship, and to specify convergences and divergences of interpretation. (shrink)