What is the aim of philosophy? There may be too many philosophical branches, traditions, practices, and programs to admit of a single overarching aim. Here I focus on a fairly traditional philosophical project that has recently received increasingly sophisticated articulation, especially by Frank Jackson (1998) and David Chalmers (2012). In §1, I present the project and suggest that it is usefully thought of as ‘total axiomatics’: the project of attempting to axiomatize the total theory of the world. In §2, I (...) raise a problem for the project that I call the ‘problem of multiple axiomatizations.’ I consider some initially alluring but ultimately unpromising approaches to this problem in §3. In §4, I defend a surprising approach to the problem, according to which competing axiomatizations of the total theory of the world are effectively evaluated for their aesthetic virtues. (shrink)

Ernst Mayr argued that the emergence of biology as a special science in the early nineteenth century was possible due to the demise of the mathematical model of science and its insistence on demonstrative knowledge. More recently, John Zammito has claimed that the rise of biology as a special science was due to a distinctive experimental, anti-metaphysical, anti-mathematical, and anti-rationalist strand of thought coming from outside of Germany. In this paper we argue that this narrative neglects the important role played (...) by the mathematical and axiomatic model of science in the emergence of biology as a special science. We show that several major actors involved in the emergence of biology as a science in Germany were working with an axiomatic conception of science that goes back at least to Aristotle and was popular in mid-eighteenth-century German academic circles due to its endorsement by Christian Wolff. More specifically, we show that at least two major contributors to the emergence of biology in Germany—Caspar Friedrich Wolff and Gottfried Reinhold Treviranus—sought to provide a conception of the new science of life that satisfies the criteria of a traditional axiomatic ideal of science. Both C.F. Wolff and Treviranus took over strong commitments to the axiomatic model of science from major philosophers of their time, Christian Wolff and Friedrich Wilhelm Joseph Schelling, respectively. The ideal of biology as an axiomatic science with specific biological fundamental concepts and principles thus played a role in the emergence of biology as a special science. (shrink)

In the TACITUS project for using commonsense knowledge in the understanding of texts about mechanical devices and their failures, we have been developing various commonsense theories that are needed to mediate between the way we talk about the behavior of such devices and causal models of their operation. Of central importance in this effort is the axiomatization of what might be called commonsense metaphysics. This includes a number of areas that figure in virtually every domain of discourse, such as (...) granularity, scales, time, space, material, physical objects, shape, causality, functionality, and force. Our effort has been to construct core theories of each of these areas, and then to define, or at least characterize, a large number of lexical items in terms provided by the core theories. In this paper we discuss our methodological principles and describe the key ideas in the various domains we are investigating. (shrink)

The present text provides a logical theory which originated in the unification of a number of well-known philosophical logics as well as the introduction and study of new operators. Further M-logic contains an object theory. With both the logical part and the object part we achieve a formal calculus that is able to express many metaphysical dogmas.

In this article, I discuss parthood status in mereologi- cally interpreted Daoist metaphysics, based on the Daodejing. I depart from the dao and you interrela- tion, which mereologically overlap by sharing parts. I consider the case of a complete overlap, which (a) challenges proper parthood, according to which a part cannot be identical with the whole that it com- poses, and (b) entails the question of identity that, while complying with classical mereology, cannot be consis- tent with Daoist (...) class='Hi'>metaphysics. The discussion leads to abandoning proper parthood and antisymmetry axiom from classical axiomatics. It also shows a plausible fur- ther direction for mereological reconstruction. (shrink)

Finean essentialists take metaphysical necessity to be metaphysically explained by essence. But whence the explanatory power of essence? A recent wave of criticism against the Finean account has put pressure on essentialists to answer this question. Wallner and Vaidya (2020) have responded by offering an axiomatic account of the explanatory power of essence. This paper discusses their account in light of some recent criticism by Bovey (2022). Building on work by Glazier (2017), Bovey succeeds in showing that Wallner and (...) Vaidya’s account is in need of modification and clarification. In this paper, I take up Bovey’s challenge and argue that Wallner and Vaidya have the resources available to incorporate the necessary modifications. I discuss the details of this modification, specifically, the question of what kind of metaphysical explanation is at work in the explanation of the necessity of essence itself. To get clear on this, I will introduce the distinction between generative and non-generative metaphysical explanation. In this way the paper contributes to both, the debate about whether essences can explain necessity and to the ongoing debate about metaphysical explanation. (shrink)

The Guggenheim’s spring retrospective of the seminal Swedish painter, Hilma Af Klint, has, naturally, evoked a multitude of art critics and visual culture scholars who laud her radical abstraction which, at the beginning of the 20th century, preceded Kandinsky, Malevich, Mondrian. Yet, where much attention has been given to the symbology and motifs riddling Klint’s work – bold, private, untethered and nonrepresentational as they are – there has been a modicum of nuanced thought on how, exactly, esotericism and theology fomented (...) Klint’s pedagogical projects. Jillian Steinhauer, for instance, has underscored Klint’s naturalistic watercolors; featuring flowers and lifelike drawings of women; Summer Landscape (1888) suggests Klint’s technical aptitude for rendering light. Jadranka Ryle, in a clever article titled “Reinventing the Yggdrasil,” invokes Klint’s motif of the Yggdrasil, or the holy tree of Norse mythology, as a political axle for Nordic romanticism. Ryle makes the claim that by redirecting the Yggdrasil towards androgynous abstraction, Klint’s engagement with Norse mythology subverts the nationalist and patriarchal romanticism that previously characterized the nineteenth century’s use of the Yggdrasil. Others have adroitly uncovered biographical fragments from Klint’s life, detailing how she and four friends formed De Fem (“the Five”), an exclusively female coven that met weekly, praying, meditating, and holding seances to commune with spiritual guides. Rather than poise the Swedish maverick within the cannon of abstraction qua a political praxis, feminist subject-being, or historiography – projects that have been exhaustively overwrought, to the point of rendering Klint’s work both mute and reductively technical– I would like to take this time to closely examine simply one of Klint’s paintings and foreground it as an axiomatic modernist injunction between metaphysics and epistemology. (shrink)

This three-part chapter explores a higher-order logic we call ‘Classicism’, which extends a minimal classical higher-order logic with further axioms which guarantee that provable coextensiveness is sufficient for identity. The first part presents several different ways of axiomatizing this theory and makes the case for its naturalness. The second part discusses two kinds of extensions of Classicism: some which take the view in the direction of coarseness of grain (whose endpoint is the maximally coarse-grained view that coextensiveness is sufficient for (...) identity), and some which take the view in the direction of fineness of grain (whose endpoint is the maximally fine-grained theory containing all distinctness claims compatible with Classicism). The third part introduces some techniques for constructing models of Classicism, and uses them to prove the consistency of many of the extensions of Classicism introduced in the second part. (shrink)

How does vagueness interact with metaphysical modality and with restrictions of it, such as nomological modality? In particular, how do definiteness, necessity (understood as restricted in some way or not), and actuality interact? This paper proposes a model-theoretic framework for investigating the logic and semantics of that interaction. The framework is put forward in an ecumenical spirit: it is intended to be applicable to all theories of vagueness that express vagueness using a definiteness (or: determinacy) operator. We will show how (...) epistemicists, supervaluationists, and theorists of metaphysical vagueness like Barnes and Williams (2010) can interpret the framework.  We will also present a complete axiomatization of the logic we recommend to both epistemicists and local supervaluationists. . (shrink)

In my dissertation, I address a variety of issues in the metaphysics of space and related areas. I begin by discussing the popular thesis that regions of space are identical to sets of points in space. I present three arguments against this thesis and conclude that we should be skeptical of it. In its place, I propose an axiomatic theory of regions of space that is consistent with both reductive accounts of their nature and with accounts that treat (...) them as sui generis entities. -/- I next explore the consequences of the aforementioned considerations. In particular, I describe five different sorts of structure each of which is such that the claim that space could have that structure is consistent with the axiomatic theory previously proposed. I claim that this fact, together with the skepticism concerning reductive accounts argued for earlier, shows that we should take seriously the claim that space could have any of these structures. -/- Having argued that we should be skeptical of the thesis that regions of space are identical to sets of points in space and suggesting that space could have different sorts of structure, I discuss how best to analyze continuity. I present an analysis of continuity inspired by remarks of Richard Cartwright in his 1975 paper ‘Scattered Objects’. I argue that this Cartwrightian analysis should be rejected because it identifies regions of space with sets of points in space, and I present a modified version of the analysis that does not do so. I note, however, that there is an intuitive notion of continuity that is not captured by this modified Cartwrightian analysis. I present and defend an analysis of continuity that better captures this intuitive notion. -/- I then turn to the issue of how to analyze what it is for a region of space to be open and what it is for a region of space to be closed. Here I argue that Cartwright’s analyses of these notions are incorrect. I then present a series of alternative analyses, revising each in response to objections. This process culminates with my proposed analyses of what it is for a region of space to be open and what it is for a region of space to be closed. -/- Finally, I discuss the Maximally Continuous Account of Simples (MaxCon), originally formulated and defended by Ned Markosian in his 1998 paper ‘Simples’. I argue that Markosian’s version of MaxCon, which identifies regions of space with sets of points in space and relies on the Cartwrightian analysis of continuity, should be rejected. I then formulate a new version of MaxCon that builds on the views defended earlier in my dissertation and defend this new version of MaxCon from objections. (shrink)

This paper develops and explores a new framework for theorizing about the measurement and aggregation of well-being. It is a qualitative variation on the framework of social welfare functionals developed by Amartya Sen. In Sen’s framework, a social or overall betterness ordering is assigned to each profile of real-valued utility functions. In the qualitative framework developed here, numerical utilities are replaced by the properties they are supposed to represent. This makes it possible to characterize the measurability and interpersonal comparability of (...) well-being directly, without the use of invariance conditions, and to distinguish between real changes in well-being and merely representational changes in the unit of measurement. The qualitative framework is shown to have important implications for a range of issues in axiology and social choice theory, including the characterization of welfarism, axiomatic derivations of utilitarianism, the meaningfulness of prioritarianism, the informational requirements of variable-population ethics, the impossibility theorems of Arrow and others, and the metaphysics of value. (shrink)

Hilary Putnam once suggested that “the actual existence of sets as ‘intangible objects’ suffers… from a generalization of a problem first pointed out by Paul Benacerraf… are sets a kind of function or are functions a sort of set?” Sadly, he did not elaborate; my aim, here, is to do so on his behalf. There are well-known methods for treating sets as functions and functions as sets. But these do not raise any obvious philosophical or foundational puzzles. For that, we (...) first need to provide a full-fledged function theory. I supply such a theory: it axiomatizes the iterative notion of function in exactly the same sense that ZF axiomatizes the iterative notion of set. Indeed, this function theory is synonymous with ZF. It might seem that set theory and function theory present us with rival foundations for mathematics, since they postulate different ontologies. But appearances are deceptive. Set theory and function theory provide the very same judicial foundation for mathematics. They do not supply rival metaphysical foundations; indeed, if they supply metaphysical foundations at all, then they supply the very same metaphysical foundations. (shrink)

In this paper the logic of broad necessity is explored. Definitions of what it means for one modality to be broader than another are formulated, and it is proven, in the context of higher-order logic, that there is a broadest necessity, settling one of the central questions of this investigation. It is shown, moreover, that it is possible to give a reductive analysis of this necessity in extensional language. This relates more generally to a conjecture that it is not possible (...) to define intensional connectives from extensional notions. This conjecture is formulated precisely in higher-order logic, and concrete cases in which it fails are examined. The paper ends with a discussion of the logic of broad necessity. It is shown that the logic of broad necessity is a normal modal logic between S4 and Triv, and that it is consistent with a natural axiomatic system of higher-order logic that it is exactly S4. Some philosophical reasons to think that the logic of broad necessity does not include the S5 principle are given. (shrink)

In this paper, I introduce an intrinsic account of the quantum state. This account contains three desirable features that the standard platonistic account lacks: (1) it does not refer to any abstract mathematical objects such as complex numbers, (2) it is independent of the usual arbitrary conventions in the wave function representation, and (3) it explains why the quantum state has its amplitude and phase degrees of freedom. -/- Consequently, this account extends Hartry Field’s program outlined in Science Without Numbers (...) (1980), responds to David Malament’s long-standing impossibility conjecture (1982), and establishes an important first step towards a genuinely intrinsic and nominalistic account of quantum mechanics. I will also compare the present account to Mark Balaguer’s (1996) nominalization of quantum mechanics and discuss how it might bear on the debate about “wave function realism.” In closing, I will suggest some possible ways to extend this account to accommodate spinorial degrees of freedom and a variable number of particles (e.g. for particle creation and annihilation). -/- Along the way, I axiomatize the quantum phase structure as what I shall call a “periodic difference structure” and prove a representation theorem as well as a uniqueness theorem. These formal results could prove fruitful for further investigation into the metaphysics of phase and theoretical structure. -/- (For a more recent version of this paper, please see "The Intrinsic Structure of Quantum Mechanics" available on PhilPapers.). (shrink)

What are the relationships between an entity and the space at which it is located? And between a region of space and the events that take place there? What is the metaphysical structure of localization? What its modal status? This paper addresses some of these questions in an attempt to work out at least the main coordinates of the logical structure of localization. Our task is mostly taxonomic. But we also highlight some of the underlying structural features and we single (...) out the interactions between the notion of localization and nearby notions, such as the notions of part and whole, or of necessity and possibility. A theory of localization—we argue—is needed in order to account for the basic relations between objects and space, and runs afoul a pure part-whole theory. We also provide an axiomatization of the relation of localization and examine cases of localization involving entities different from material objects. (shrink)

According to Jago (2014a), logical omniscience is really part of a deeper paradox. Jago develops an epistemic logic with principles of indeterminate closure to solve this paradox, but his official semantics is difficult to navigate, it is motivated in part by substantive metaphysics, and the logic is not axiomatized. In this paper, I simplify this epistemic logic by adapting the hyperintensional semantic framework of Sedlár (2021). My first goal is metaphysical neutrality. The solution to the epistemic paradox should not (...) require appeal to a metaphysics of truth-makers, situations, or impossible worlds, by contrast with Jago’s official semantics. My second goal is to elaborate on the proof theory. I show how to axiomatize a family of logics with principles of indeterminate epistemic closure. (shrink)

We develop a theory of necessity operators within a version of higher-order logic that is neutral about how fine-grained reality is. The theory is axiomatized in terms of the primitive of *being a necessity*, and we show how the central notions in the philosophy of modality can be recovered from it. Various questions are formulated and settled within the framework, including questions about the ordering of necessities under strength, the existence of broadest necessities satisfying various logical conditions, and questions about (...) their logical behaviour. We also wield the framework to probe the conditions under which a logicist account of necessities is possible, in which the theory is completely reducible to logic. (shrink)

Aquinas, Ockham, and Burdan all claim that a person can be numerically identical over time, despite changes in size, shape, and color. How can we reconcile this with the Indiscernibility of Identicals, the principle that numerical identity implies indiscernibility across time? Almost all contemporary metaphysicians regard the Indiscernibility of Identicals as axiomatic. But I will argue that Aquinas, Ockham, and Burdan would reject it, perhaps in favor of a principle restricted to indiscernibility at a time.

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be (...) also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators on it. One can interpret special Minkowski space involved by special relativity and the qubit Hilbert space of quantum information as Fourier counterparts immediately noticing that general relativity means gravitation as the Fourier counterpart of non-Hermitian operators implying non-unitarity and the violation of energy conservation and thus destroying Pauli’s particle paradigm. Since the Standard model obeys it, this explains the impossibility of “quantum gravitation” in any framework conservatively generalizing the Standard model so that it would include gravitation along with electromagnetic, weak, and strong interactions. Einstein’s geometrization of gravitation can be continued into a purely mathematical theory of it following Euclid’s realization for geometry to be exhaustively built in a deductive and axiomatic way as well as Riemann’s parametrization of all the class of Euclidean and non-Euclidean geometries by “space curvature”, then being generalized to Minkowski space as the operators on pseudo-Riemannian space as the Einstein field equation means gravitation. The transition from mathematical gravitation to logical one can rely on the historical lesson of the pair of Lobachevski’s and Riemann’s approaches now “reversely”, i.e., from the latter to the former. Logical gravitation is linkable to Hegel’s dialectical logic and ontological dialectics abandoning their interpretations as a new zero logic substituting classical propionyl logic. The approach of ontomathematics generalizing that of ontology, traceable even to Aristotle’s reformation of Plato’s doctrine, needs Hegel’s doctrine to be formalized as a first-order logic naturally containing Boolean algebra, isomorphic to both classical propositional logic and set theory being the class of all first-order logics, as a sub-logic along with Peano arithmetic as another sub-logic. The first-order logic at issue is called Hilbert arithmetic and elaborated in detail in other papers. It allows for both self-foundation of mathematics to be internally proved as complete and furthermore, quantum mechanics reinterpreted as quantum information to be included by the qubit Hilbert space interpretable in turn as a dual and physical counterpart of Hilbert arithmetic in a narrow sense, that is, both counterparts constitute Hilbert arithmetic in a wide sense, being mathematical and physical simultaneously and thus overcoming the Cartesian dualism of “body” gapped from “mind” by an abyss. Then, the proper philosophical interpretation of gravitation to be the fundamental ontomathematical force or interaction overcomes the ridiculous belief of the Big Bang wrongly alleged to be a scientific theory. Ontomathematical gravitation suggests an omnipresent and omnitemporal medium of “God’s” creation “ex nihilo” following only the natural necessity of quantum-information conservation particularly and locally manifested as energy conservation. (shrink)

Katerina Kolozova is a Macedonian philosopher whose publications from last two decades aim to analyze various topics using François Laruelle’s “non-philosophy” or “non-standard philosophy.” Non-philosophy could be roughly described as radicalized deconstruction: Laruelle claims that not everything can be grasped by a philosophy: for Laruelle, “philosophy is too serious an affair to be left to the philosophers alone.”1 Non-philosophy opposes the “principle of sufficient philosophy” through which philosophy determines and decides what is real. According to Laruelle, the ultimate limit of (...) philosophical thought and its self-proclaimed sufficiency lies in its inherent tendency to close itself in a transcendental system of autofetishist conceptions, which presume that one can grasp the Real (“The Real is neither capable of being known or even ‘thought,’ but can be described in axioms. [...] Even ‘immanence’ only serves to name the Real which tolerates nothing but axiomatic descriptions or formulations.”) by a philosophical thought, or that the Real could be mediated only through human thought. Laruelle criticizes this tendency of philosophy, which is usually expressing itself through the structure of “philosophical Decision.” (“To philosophize is to decide Reality and the thoughts that result from this, i.e. to believe to be able to order them in the universal order of the Principle of Reason [Logos].”) Katerina Kolozova use Laruelle’s non-philosophy to explore more explicitly political topics. In the Cut Of Th e Real (2014), she criticized certain dogmatism of poststructuralist philosophy and feminist theory, namely their symptomatic rejection of the Real and the One. In Toward a Radical Metaphysics of Socialism (2015) and The Lived Revolution (2016) Kolozova presented a rereading of Marx, whose work she found relevant for the critique of speculative philosophical dimension of the capitalist economy, embodied in the 2008 global finance crisis, and in the latter book, she explored the possibility of a new political solidarity, based on “bodies in pain.” Kolozova doesn’t call to philosophically reconstruct Marx’s thought for the current situation, but she goes back to Marx with the help of Laruelle’s non-Marxism, contrary to the usual approach of Marxist philosophers, who often try to create certain philosophical system of Marx’s work. Together with Eileen A. Joy, Kolozova edited the anthology After the “Speculative Turn” (2016), which addressed recent realist and materialist tendencies in feminist philosophy. In her most recent book, Capitalism’s Holocaust of Animals (2019), Kolozova aimed to explore broader philosophical foundations of neoliberal capitalism, and its dealing with nonhuman animals and their suffering. According to Kolozova, “We have to start by coming to terms with what we did to the animals in the constitutive act of philosophy and via proxy to all those dehumanised that belong to the species of man ‘by courtesy’ only.” . (shrink)

Diagrams by Connor Camburn -/- The relationship between axiomatization, mechanization, creative individuation, and virtual/physical individuation presents a fascinating interplay of concepts that have significantly influenced various fields, including mathematics, physics, philosophy, and art. This essay explores these relationships by drawing insights from André Weil's "From Metaphysics to Mathematics," Gilles Châtelet's works, and Schmid's discussion on Gnostic Futurism. -/- Axiomatization: Weil and Grothendieck -/- Axiomatization, as discussed in André Weil's "From Metaphysics to Mathematics," represents the transformation of metaphysical concepts (...) into formal mathematical structures. Weil's document highlights the progression from vague metaphysical ideas to concrete mathematical theories. This process is evident in the works of mathematicians like Lagrange and Galois, where initial metaphysical notions eventually crystallized into the formal structures of modern algebra. Similarly, Alexander Grothendieck's work in algebraic geometry involved the creation of an abstract framework that could unify various mathematical concepts, demonstrating the power of axiomatization in providing a foundational structure for complex ideas. -/- Mechanization: Oppenheimer, Watson-Crick, and Von Neumann -/- Mechanization, in the context of scientific development, refers to the application of mechanical principles to solve problems and the automation of processes. Figures like Oppenheimer in physics, Watson and Crick in biology, and Von Neumann in computing and mathematics, represent the pinnacle of mechanization in their respective fields. Their work exemplifies how mechanization has enabled the simplification and automation of complex processes, leading to alienating discoveries such as the atomic bomb, the structure of DNA, and the development of modern computers. -/- Creative Individuation: Gnostic Futurism -/- Eric Schmid's discussion on Gnostic Futurism, as found in his document, offers a perspective on creative individuation. Gnostic Futurism, rooted in Kantian-Hegelian transcendental universalism, represents a departure from conventional realism, emphasizing a transcendental nature and integration of mythopoeia. This movement in art and philosophy underscores the role of creativity and individual expression in transcending traditional forms and norms. It embodies the idea of creative individuation, where individual creativity leads to the formation of new, often revolutionary, artistic and philosophical expressions. -/- Virtual/Physical Individuation: Châtelet's Perspective -/- Gilles Châtelet's works, particularly "Figuring Space: Philosophy, Mathematics, and Physics," delve into the concept of virtual/physical individuation. Châtelet discusses the configuration of space in mathematics and physics, emphasizing the role of diagrams in scientific discovery. This exploration of space, both virtual (as in mathematical abstractions) and physical (as in tangible representations), reflects the process of individuation in both realms. Châtelet's perspective highlights how mathematical and physical representations are not just tools for understanding the world but are also expressions of individual and collective intellectual endeavors. -/- Interconnections and Synthesis -/- The synthesis of these concepts reveals a complex tapestry of intellectual development across disciplines. Axiomatization provides a foundational structure that enables the mechanization of processes, as seen in the works of Oppenheimer, Watson-Crick, and Von Neumann. This mechanization, in turn, paves the way for creative individuation, where individuals can transcend established norms and frameworks, as exemplified in Gnostic Futurism. Finally, the concept of virtual/physical individuation, as explored by Châtelet, represents the culmination of these ideas, where the abstract and the tangible intersect, leading to new forms of understanding and expression. -/- In conclusion, the relationship between axiomatization, mechanization, creative individuation, and virtual/physical individuation is a testament to the dynamic and interconnected nature of intellectual progress. From the formal structures of mathematics to the revolutionary changes in art and philosophy, these concepts demonstrate how human thought and creativity continue to evolve, challenging existing paradigms and forging new paths of understanding and expression. (shrink)

The purpose of this essay is exegesis. I explicate Nicolas Malebranche's (1674, 1678, 1688, 1714) concept of intelligible extension. I begin by detailing how the concept matured throughout Malebranche's work, and the new functions it took on within his metaphysical system. I then examine Gustav Bergmann's “axiomatic” interpretation, as well as the criticism of it offered by Daise Radner. I argue that Radner's criticism of the interpretation is only partly successful; some of her objections can be met; others cannot. (...) I then develop a novel interpretation of the concept, given insights from this dispute. I call it the “programmatic interpretation.” I argue that this interpretation coheres well with Malebranche's famous Vision in God thesis, as well as many of his other commitments. I conclude by considering a certain pertinent objection to my proposal, summarizing the dialectic, and forcefully restating my case. (shrink)

A critical review of Wittgenstein's 'On Certainty' which he wrote in 1950-51 and was first published in 1969. Most of the review is spent presenting a modern framework for philosophy(the descriptive psychology of higher order thought) and positioning the work of Wittgenstein and John Searle in this framework and relative to the work of others. It is suggested that this book can be regarded as the foundation stone of psychology and philosophy as it was the first to describe the two (...) systems of thought and shows how our unshakable grasp of the world derives from our innate axiomatic System 1 and how this interacts with System 2. -/- 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)

Major Research Paper Abstract -/- A Part of This World: Deleuze & The Logic Of Creation. -/- Is there a particular danger in following Deleuze’s philosophy to its end result? According to Peter Hallward and Alain Badiou, Deleuze’s philosophy has some rather severe conclusions. Deleuze has been known as a vitalist thinker of life and affirmation. Hallward & Badiou seek to challenge the accepted view of Deleuze; showing that these accepted norms in Deleuzian scholarship should be challenged; and that initially (...) Deleuze calls for the evacuation of political action in order to remain firm in the realm of pure contemplation. I intend to investigate and defend Deleuze’s philosophy and against critics like Badiou and Hallward; and that not only is Deleuze’s philosophy creative and vital but also highly revolutionary and ‘a part of this world.’ I will look at several works in Deleuze’s corpus, as well as look at Deleuzian scholars whom defend Deleuze’s position -/- Hallward sees Deleuze as a theophantic thinker of the one and like Spinoza an individual mode must align oneself with the intellectual love of god, so that creativity and expressivity may mediate through them. Thus, according to Hallward the major theme of Deleuze’s philosophy is creativity; and a subject or a creature must tap into this vital spark of creation, which, is also a form of creatural confinement. Hallward states this creative act can only occur in the realm of the virtual, by lines of flight leading 'out of this world'. The subject is then re-introduced to an extra-worldly existence of contemplation and remains further away from decisions and lived experience. Deleuze, according to Hallward, falls prey to a cosmological pantheism. -/- Badiou has similar concerns. Deleuze’s philosophy is too systematic and abstract. The entirety of Deleuzes’ work is surrounded by metaphysics of the one; and essentially its repercussions lead to an overt asceticism. Badiou notes that Deleuze wants us all to surrender thought to a renewed concept of the one. Through the surrender of the one, the multiple is lost and incorporated into the realm of simulacra. Everything in this Deleuzian world is ‘always-already’ in the infinite and inhuman totality of the one. According to Badiou, this entire process is articulated in the power of inorganic life that operates through all of us. Like Hallward, Badiou sees Deleuze demolishing the subject, who is stuck between machinery and exteriority. Subjects are forced to transcend and go beyond their limits, slowly collapsing into an infinite virtuality. Badiou believes this is a powerful metaphor for a philosophy of death. Thus the conditions of Deleuzian thought are contingent upon asceticism, making a Deleuzian world a sort of ‘crowned anarchy’. Badiou sees Deleuze’s ascetic mission intimately linked with a philosophy of death, and like Hallward we should pay careful attention to the outcome of such an aristocratic philosophy. Death according to Badiou, symbolizes Deleuzian thought, not only making it dangerous, but also actualizing it as an ineffective position. Badiou also points out that Deleuze’s conceptual sources are not only limited but also repeated time and time again through a monotonous selection of concepts. Is this a fair critique and representation of Deleuzian thought? -/- Eugene Holland states, that both Hallward and Badiou have misrepresented Deleuze. Deleuze does invoke the creation of a new earth but one which we all fully believe in. The only world Deleuze wants to get out of is the world of habits, conformity, power; and forces that block creative being. According to Holland, Hallward presents us a Deleuze that inhibits an engagement with the world. However Deleuze’s creative enterprise is insistent on forming concepts that can change and transform our world. -/- So the question arises where does the problem of misrepresentation begin? It begins with both Badiou and Hallward having an erroneous account of the actual/virtual distinction in Deleuze’s Philosophy. According to Protevi, Hallward posits a dualism between the actual and the virtual, denying the role of the intensive. Hallward initially sees the relationship between the intensive and the virtual, ignoring the fact that the intensive has its own ontological register that mediates both the virtual and the actual. However, Protevi notes if one could not accept the intensive for an ontological register and had to place it with one or the other; you would have to accept an interrelationship between the actual and the intensive. Hallward places it in the realm of the virtual, thus, leading us to his major claim that Deleuze’s philosophy leads us out of the world. Protevi states, intensive processes happen in our world they are a part of this world. Hallward completely empties all creativity from the actual, thus depending on the virtual and its slippery slope. Both Hallward and Badiou have missed the point altogether. We live in an intensive/actual world and the main point about Deleuze’s politics has to do with experimentation and social interaction and the transformation and intervention of the concept. As Daniel W. Smith states, unlike Badiou, Deleuze is not searching for an axiomatic approach to the world, one that is prone to reductionism but rather with problematic, inventive and creative methods to transform a society. (shrink)

Wittgenstein (W) is for me easily the most brilliant thinker on human behavior and this is his last work and crowning achievement. It belongs to his third and final period, yet it is not only his most basic work (since it shows that all behavior is an extension of innate true-only axioms and that our conscious ratiocination is but icing on unconscious machinations), but as Daniele Moyal-Sharrock has recently noted, is a radical new epistemology and the foundation for all description (...) of animal behavior, revealing how the mind works and indeed must work. The "must" is entailed by the fact that all brains share a common ancestry and common genes, and so there is only one basic way they work, that this necessarily has an axiomatic structure, that all higher animals share the same evolved psychology based on inclusive fitness, and in humans this is extended into a personality based on throat muscle contractions (language) that evolved to manipulate others (with variations that can be regarded as trivial). This book, and arguably all of W's work and all useful discussion of behavior is a development of or variation on these ideas. -/- 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)

Dialectica: Mathematica and Physica, Truth and Justice, Trick and Life. Mathematica as the Constructive Metaphysica and Ontology. Mathematica as the constructive existential method. Сonsciousness and Mathematica: Dialectica of "eidos" and "logos". Mathematica is the Total Dialectica. The basic maternal Structure - "La Structure mère". Mathematica and Physica: loss of existential certainty. Is effectiveness of Mathematica "unreasonable"? The ontological structure of space. Axiomatization of the ontological basis of knowledge: one axiom, one principle and one mathematical object. The main ideas and concepts (...) of the ontological construction/ "Point with a vector germ" and "heavenly triangle". "Ordo geometricus" and "Ordo onto-topological". Architecture of the onto-topological basis of knowledge: general framework structure, carcass and foundation. The absolute space and the absolute field. The absolute (natural) system of coordinates of Universum. Eidos of "idea of ideas", the symbol and the "formula of Justice". (shrink)

Wittgenstein (W) is for me easily the most brilliant thinker on human behavior and this is his last work and crowning achievement. It belongs to his third and final period, yet it is not only his most basic work (since it shows that all behavior is an extension of innate true-only axioms and that our conscious ratiocination is but icing on unconscious machinations), but as Daniele Moyal-Sharrock has recently noted, is a radical new epistemology and the foundation for all description (...) of animal behavior, revealing how the mind works and indeed must work. The "must" is entailed by the fact that all brains share a common ancestry and common genes, and so there is only one basic way they work, that this necessarily has an axiomatic structure, that all higher animals share the same evolved psychology based on inclusive fitness, and in humans this is extended into a personality based on throat muscle contractions (language) that evolved to manipulate others (with variations that can be regarded as trivial). This book, and arguably all of W's work and all useful discussion of behavior is a development of or variation on these ideas. -/- 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)

François Laruelle has rightfully earned the title of contemporary French philosophy’s archetypical heretic, having fostered the “non-standard” method of univocal genericity and spurred an altogether radical praxis, inciting a new generation of loyal followers that include Jason Barker and Ray Brassier. Laruelle’s method, often referred to as “non-philosophy” (though “non-philosophy” is an abbreviation of “non-standard philosophy”), withdraws from the metaphysical precept of separating the world into binarisms, perhaps epitomized by the formative division between “universals” and “particulars” in Kant’s Transcendental Deduction. (...) Laruelle’s method also rejects the “evental” nature of Being described by Heiddegger as the foundation for philosophy's “standard model,” which Heidegger termed Ereignis (often translated as “the event of Appropriation”). In its immanence, Laruelle’s “One” is understood as generic identity - an identity/commonality that reverses the classical metaphysics found in philosophy’s bastion thinkers (a lineage that runs from Plato to Badiou), where the transcendental is upheld as a necessary precondition for grounding reality. Instead, Laruelle asserts the “One” as the immanent real: generic, non-philosophical and axiomatic. (shrink)

Treating groups as agents is not at all difficult; teenagers and social scientists do it all the time with great success. Reading Group Agency, though, makes it look like rocket science. According to List and Pettit, groups can be real, and such real groups can cause, as well as bear ethical responsibility for, events. Apparently, not just any collective qualifies as an agent, so a lot turns on how the attitudes and actions of individual members are aggregated. Although I am (...) unsure who will read this book, I can envisage four relatively distinct population segments: philosophers, decision theorists, activists, and social scientists. Philosophers who take questions of ontology seriously will likely find this book evasive. Decision theorists who enjoy axiomatic model building for its own sake will find much to keep them occupied. Activists who have taken it upon themselves to “raise group consciousness” (193) will probably skip ahead to the third part and feel emboldened by the thought that the model builders are busy with the first two. However, since the normative questions (about responsibility and so on) are answerable to prior metaphysical questions for which Group Agency supplies vacillating answers at best, a transition to advocacy would seem hasty. As for social scientists, either they will glance at the book’s dust jacket and (wrongly) assume that philosophers have now “proven” the existence of the groups they study, or they will engage with List and Pettit’s model only to discover that, unless they happen to specialize in commercial corporations, the model’s many stipulations impede rather than facilitate/elucidate their usual group intentional ascriptions. (shrink)

The two manuscripts of the Korte Verhanedling that were discovered in the mid-nineteenth century contain two appendices. These appendices are even more enigmatic than the KV itself, and it is the first appendix that is the subject of this study. Unfortunately, there are very few studies of this text, and its precise nature seems to be still in question after more than a century and a half of scholarship. It is commonly assumed that the appendices were written after the body (...) of the KV and I am not going to challenge this assumption. The first appendix is written in a geometric manner, and it contains seven axioms and four propositions. Strikingly, it does not include any definitions. This is in sharp contrast with Spinoza's Ethics and his 1663 book on Descartes' Principles of Philosophy, which are similarly written in a geometric manner but include both definitions and axioms. One could perhaps suspect that the text we currently have is merely a fragment from a more extensive work which included definitions. In my paper, I will show that this is not the case, and that the first appendix belongs to a genuine work of Spinoza that never contained definitions. I would further argue that the first appendix is most probably the earliest draft we currently have of Spinoza's magnum opus, the Ethics, but we have a long way to go before we reach that conclusion. (shrink)

We present an axiomatization of non-relativistic Quantum Mechanics for a system with an arbitrary number of components. The interpretation of our system of axioms is realistic and objective. The EPR paradox and its relation with realism is discussed in this framework. It is shown that there is no contradiction between realism and recent experimental results.

This is part one of a two-part paper, in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. This allows us to connect theories of partial ground with axiomatic theories of truth. In this part of the paper, we develop an axiomatization of the relation of partial ground over the truths of arithmetic and (...) show that the theory is a proof-theoretically conservative extension of the theory PT of positive truth. We construct models for the theory and draw some conclusions for the semantics of conceptualist ground. (shrink)

According to the analysis of concessive conditionals suggested by Crupi and Iacona, a concessive conditional \(p{{\,\mathrm{\hookrightarrow }\,}}q\) is adequately formalized as a conjunction of conditionals. This paper presents a sound and complete axiomatic system for concessive conditionals so understood. The soundness and completeness proofs that will be provided rely on a method that has been employed by Raidl, Iacona, and Crupi to prove the soundness and completeness of an analogous system for evidential conditionals.

In this chapter, I investigate a problem for Kant’s claim that metaphysics can reach the status of science. The problem arises when one considers Kant’s account of the “architectonic unity” of metaphysics in the Architectonic of Pure Reason. Attaining architectonic unity is a condition for becoming a science for any body of cognitions that purports to be such. This is achieved when the cognitions belonging to a science are systematically organized according to the “idea of reason” which lies (...) at the basis of that science. However, Kant suggests that nobody can ever legitimately claim to have matched the idea of the philosopher, where this appears to imply that nobody can justifiably claim that she has fully grasped the idea of metaphysics. This generates a problem. I suggest that when Kant claims that the idea of the philosopher must remain an ideal or an archetype, he has a particular conception of philosophy in mind, that is, philosophy as a doctrine of wisdom. According to this understanding, philosophy must provide an example of how one can become virtuous. However, this is only a partial solution to our problem, for reasons that will be illustrated. (shrink)

This is part two of a two-part paper in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. In this part of the paper, we extend the base theory of the first part of the paper with hierarchically typed truth-predicates and principles about the interaction of partial ground and truth. We show that our theory (...) is a proof-theoretically conservative extension of the ramified theory of positive truth up to. (shrink)

A certain type of inference rules in modal logics, generalizing Gabbay's Irreflexivity rule, is introduced and some general completeness results about modal logics axiomatized with such rules are proved.

This is a critical, but sympathetic, examination of the manifesto for naturalized metaphysics that forms the first chapter of James Ladyman and Don Ross's 2006 book, Every Thing Must Go, but it has wider implications than this description suggests.

There has been an explosion of interest in the metaphysics of fundamentality in recent decades. The consensus view, called metaphysical foundationalism, maintains that there is something absolutely fundamental in reality upon which everything else depends. However, a number of thinkers have chal- lenged the arguments in favor of foundationalism and have proposed competing non-foundationalist ontologies. This paper provides a systematic and critical introduction to metaphysical foundationalism in the current literature and argues that its relation to ontological dependence and substance (...) should be qualified in important ways. (shrink)

The paper argues against a commitment to metaphysical necessity, semantic modalities are enough. The best approaches to elucidate the semantic modalities are (still) versions of lingustic ersatzism and fictionalism, even if only developed in parts. Within these necessary properties and the difference between natural and semantic laws can be accounted for. The proper background theory for this is an updated version of Logical Empiricism, which is congenial to recent trends in Structural Realism. The anti-metaphysical attitude of Logical Empiricism deserves revitalization. (...) Another target besides metaphysical necessity are substantial forms of iterated modalities, as used, for instance, in the philosophy of religion. (shrink)

Prompted by the thesis that an organism’s umwelt possesses not just a descriptive dimension, but a normative one as well, some have sought to annex semiotics with ethics. Yet the pronouncements made in this vein have consisted mainly in rehearsing accepted moral intuitions, and have failed to concretely further our knowledge of why or how a creature comes to order objects in its environment in accordance with axiological charges of value or disvalue. For want of a more explicit account, theorists (...) writing on the topic have relied almost exclusively on semiotic insights about perception originally designed as part of a sophisticated refutation of idealism. The end result, which has been a form of direct givenness, has thus been far from convincing. In an effort to bring substance to the right-headed suggestion that values are rooted in the biological and conform to species-specific requirements, we present a novel conception that strives to make explicit the elemental structure underlying umwelt normativity. Building and expanding on the seminal work of Ayn Rand in metaethics, we describe values as an intertwined lattice which takes a creature’s own embodied life as its ultimate standard; and endeavour to show how, from this, all subsequent valuations can in principle be determined. (shrink)

Distributive justice deals with allocations of goods and bads within a group. Different principles and results of distributions are seen as possible ideals. Often those normative approaches are solely framed verbally, which complicates the application to different concrete distribution situations that are supposed to be evaluated in regard to justice. One possibility in order to frame this precisely and to allow for a fine-grained evaluation of justice lies in formal modelling of these ideals by metrics. Choosing a metric that is (...) supposed to map a certain ideal has to be justified. Such justification might be given by demanding specific substantiated axioms, which have to be met by a metric. This paper introduces such axioms for metrics of distributive justice shown by the example of needs-based justice. Furthermore, some exemplary metrics of needs-based justice and a three dimensional method for visualisation of non-comparative justice axioms or evaluations are presented. Therewith, a base worth discussing for the evaluation and modelling of metrics of distributive justice is given. (shrink)

This chapter provides an introduction to higher-order metaphysics as well as to the contributions to this volume. We discuss five topics, corresponding to the five parts of this volume, and summarize the contributions to each part. First, we motivate the usefulness of higher-order quantification in metaphysics using a number of examples, and discuss the question of how such quantifiers should be interpreted. We provide a brief introduction to the most common forms of higher-order logics used in metaphysics, (...) and indicate a number of questions which can be raised in such systems using logical vocabulary alone. Using a further example, we return to applications of higher-order logics in metaphysics. We also mention key developments in the history of higher-order logic as it pertains to metaphysics. Finally, we mention certain arguments which have been raised against the use of higher-order logic, and some ways of responding to them. (shrink)

The present text is the revised and corrected English translation of the book published in German by the Lang Verlag, Bern 2008. Unfortunately the text still has some minor flaws (especially in the Index Locorum) but they do not concern the main thesis or the arguments. It will still be the final version, especially considering my age. It is among the most widespread and the least questioned convictions that in Metaphysics Lambda Aristotle presents a theology which has its basis (...) in a metaphysics of substance. Doubts about theological interpretation are beginning to stir in a growing number of publications, but nevertheless the majority of research literature, compendiums and histories of philosophy argues within this frame. A closer look at the facts reveals that this conviction has no basis in the text. Quite the contrary it is based on a reception with theological interests. It arised over centuries, starting from Patristic times and the Middle Ages; it was influenced by Neoplatonic texts as the Liber de Causis or the Theologia Aristotelis, texts for a long time considered as original Aristotelian books. And, if you read not translations but the Greek text, you see that the word 'god' occurs much less than in a theological book should be. In some translations we find more occurences of that word, and especially in French, Italian, English translations some words as le Bien, l'Intelligence etc. are written with capitals to inticate that it is about god. To make it even more clear, we read often the term 'First Mover' or 'Unmoved Mover' as an other name for god, but this expression is never used by Aristotle. So the reader has the impression that Aristotle speaks continuously about god. In addition, in the present book you will find arguments which clean up with the outdated concept of substance in the Aristotelian text, a concept which was developed for quite other problems than Aristotle had, namely theolgical ones. And, if there is no substance, there is no corresponding metaphysics of substance and no theology or onto-theology. If substance, metyphysics, theology play no role in Metaphysics Lambda, what else is its content and aim? That is not so difficult to say because Aristotle says it sufficiently clear in his first sentence, περὶ οὐσίας ἡ θεωρία: our inquiry is about being; its aim is to develop the Frage nach dem Sein and to state a speculative answer: being is noesis, Sein ist Gewahren. (shrink)

A variation of Fitch’s paradox is given, where no special rules of inference are assumed, only axioms. These axioms follow from the familiar assumptions which involve rules of inference. We show (by constructing a model) that by allowing that possibly the knower doesn’t know his own soundness (while still requiring he be sound), Fitch’s paradox is avoided. Provided one is willing to admit that sound knowers may be ignorant of their own soundness, this might offer a way out of the (...) paradox. (shrink)

This paper investigates Ockhamism from a metaphysical point of view. Its main point is that the claim that future contingents are true or false is less demanding than usually expected, as it does not require particularly contentious assumptions about the future. First it will be argued that Ockhamism is consistent with a wide range of metaphysical views. Then it will be shown that each of these views leaves room for the claim that the future is open, at least on some (...) plausible interpretations of that claim. (shrink)

INTRODUCTION I. CETERIS PARIBUS LAWS An alleged law of nature—like Newton's law of gravitation—is said to be a ceteris paribus law if it does not hold under ...

Abstract Theories are metaphysically equivalent just if there is no fact of the matter that could render one theory true and the other false. In this paper I argue that if we are judiciously to resolve disputes about whether theories are equivalent or not, we need to develop testable criteria that will give us epistemic access to the obtaining of the relation of metaphysical equivalence holding between those theories. I develop such ?diagnostic? criteria. I argue that correctly inter-translatable theories are (...) metaphysically equivalent, and what we need are ways of determining whether a putative translation is correct or not. To that end I develop a number of tools we can employ to discern whether a translation is a correct one. (shrink)

Aristotle talks about 'the first philosophy' throughout the Metaphysics – and it is metaphysics that Aristotle considers to be the first philosophy – but he never makes it entirely clear what first philosophy consists of. What he does make clear is that the first philosophy is not to be understood as a collection of topics that should be studied in advance of any other topics. In fact, Aristotle seems to have thought that the topics of Metaphysics are (...) to be studied after those in Physics. In what sense could metaphysics be the first philosophy in the context of contemporary metaphysics? This is the question examined in this essay. Contemporary topics such as fundamentality, grounding, and ontological dependence are considered as possible ways to understand the idea of first philosophy, but I will argue that the best way to understand it is in terms of essence. (shrink)

How ought you to evaluate your options if you're uncertain about what's fundamentally valuable? A prominent response is Expected Value Maximisation (EVM)—the view that under axiological uncertainty, an option is better than another if and only if it has the greater expected value across axiologies. But the expected value of an option depends on quantitative probability and value facts, and in particular on value comparisons across axiologies. We need to explain what it is for such facts to hold. Also, EVM (...) is by no means self-evident. We need an argument to defend that it’s true. This book introduces an axiomatic approach to answer these worries. It provides an explication of what EVM means by use of representation theorems: intertheoretic comparisons can be understood in terms of facts about which options are better than which, and mutatis mutandis for intratheoretic comparisons and axiological probabilities. And it provides a systematic argument to the effect that EVM is true: the theory can be vindicated through simple axioms. The result is a formally cogent and philosophically compelling extension of standard decision theory, and original take on the problem of axiological or normative uncertainty. (shrink)