Knowledge is correct and reliable when its foundation is correct, but humans never have the correct beliefs and methodology. Thus, knowledge is unreliable and the foundation of knowledge needs to be reconstructed. A pure rationalist only believes in logic. Thus, all matter and experience must be propositions derived from logic. The logically necessary consequence of this belief is truth; logically possible consequences are phenomena, and logically impossible consequence are fallacies and evils. This paper introduces belief and its (...) class='Hi'>logical consequences, such as discovering first knowledge, both logically and illogically, establishing logical methodology, deducing truths purely through logic, and discovering unprovable truths by imitating the Universe. Logic and illogic are undeniable beliefs, and the reality of the Universe is the ultimate cause of everything. (shrink)

This essay presents a philosophical and computational theory of the representation of de re, de dicto, nested, and quasi-indexical belief reports expressed in natural language. The propositional Semantic Network Processing System (SNePS) is used for representing and reasoning about these reports. In particular, quasi-indicators (indexical expressions occurring in intentional contexts and representing uses of indicators by another speaker) pose problems for natural-language representation and reasoning systems, because--unlike pure indicators--they cannot be replaced by coreferential NPs without changing the meaning of (...) the embedding sentence. Therefore, the referent of the quasi-indicator must be represented in such a way that no invalid coreferential claims are entailed. The importance of quasi-indicators is discussed, and it is shown that all four of the above categories of belief reports can be handled by a single representational technique using belief spaces containing intensional entities. Inference rules and belief-revision techniques for the system are also examined. (shrink)

Coherentism in epistemology has long suffered from lack of formal and quantitative explication of the notion of coherence. One might hope that probabilistic accounts of coherence such as those proposed by Lewis, Shogenji, Olsson, Fitelson, and Bovens and Hartmann will finally help solve this problem. This paper shows, however, that those accounts have a serious common problem: the problem of belief individuation. The coherence degree that each of the accounts assigns to an information set (or the verdict it gives (...) as to whether the set is coherent tout court) depends on how beliefs (or propositions) that represent the set are individuated. Indeed, logically equivalent belief sets that represent the same information set can be given drastically different degrees of coherence. This feature clashes with our natural and reasonable expectation that the coherence degree of a belief set does not change unless the believer adds essentially new information to the set or drops old information from it; or, to put it simply, that the believer cannot raise or lower the degree of coherence by purely logical reasoning. None of the accounts in question can adequately deal with coherence once logical inferences get into the picture. Toward the end of the paper, another notion of coherence that takes into account not only the contents but also the origins (or sources) of the relevant beliefs is considered. It is argued that this notion of coherence is of dubious significance, and that it does not help solve the problem of belief individuation. (shrink)

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)

Paradoxes have played an important role both in philosophy and in mathematics and paradox resolution is an important topic in both fields. Paradox resolution is deeply important because if such resolution cannot be achieved, we are threatened with the charge of debilitating irrationality. This is supposed to be the case for the following reason. Paradoxes consist of jointly contradictory sets of statements that are individually plausible or believable. These facts about paradoxes then give rise to a deeply troubling epistemic problem. (...) Specifically, if one believes all of the constitutive propositions that make up a paradox, then one is apparently committed to belief in every proposition. This is the result of the principle of classical logical known as ex contradictione (sequitur) quodlibetthat anything and everything follows from a contradiction, and the plausible idea that belief is closed under logical or material implication (i.e. the epistemic closure principle). But, it is manifestly and profoundly irrational to believe every proposition and so the presence of even one contradiction in one’s doxa appears to result in what seems to be total irrationality. This problem is the problem of paradox-induced explosion. In this paper it will be argued that in many cases this problem can plausibly be avoided in a purely epistemic manner, without having either to resort to non-classical logics for belief (e.g. paraconsistent logics) or to the denial of the standard closure principle for beliefs. The manner in which this result can be achieved depends on drawing an important distinction between the propositional attitude of belief and the weaker attitude of acceptance such that paradox constituting propositions are accepted but not believed. Paradox-induced explosion is then avoided by noting that while belief may well be closed under material implication or even under logical implication, these sorts of weaker commitments are not subject to closure principles of those sorts. So, this possibility provides us with a less radical way to deal with the existence of paradoxes and it preserves the idea that intelligent agents can actually entertain paradoxes. (shrink)

We are concerned in this paper to establish the rationality of American legal realism by adopting a theory of reconstruction. American realism is plagued with dichotomies in relating theory and practice; and the need to broach these dichotomies involves transcendence of experience and transference of consciousness. In doing this, we have both to excavate and to justify its philosophy, logic and science. American legal realism has its root in the philosophy of pragmatism and a logic that sets out the essential (...) elements associated with the making and determination of the law through instrumentality of the court. The validity of this category of legal theory tends to lie on the extent of immediate use to which law can be put or the benefits it can afford the American society. Believing in the possibility of a realistic theory of law that is purely American precludes belief in universal understanding of human legal experience distinct from the understanding gained through the cultural lenses of the American people. Although American realists differ remarkably even within a single paradigm, nevertheless three areas of logical unity among them are that: They bear a cross relevance, a complementing and interlocking of results, and a similar faith in attacking legal problems. A completely empirical understanding of American legal realism seems nebulous, because causality presupposes the interaction of American liberal and legalistic political attitudes. Legalism is the life wire of American culture and this makes distribution of rights and legal predictability possible: incidentally language is an important instrument for making this happens. Countries seeking to adopt the American model of legal order or something similar to it should be capable of an equivalent orientation in terms of formulating their philosophy, logic and science of adjudication. (shrink)

W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due in (...) large measure to developments stemming from Carnap’s studies and culminating in the work of Kripke, Hintikka, and Bayart. These developments undermined Quine’s crusade against intensions on two fronts. First, in the context of possible world semantics, intensions could after all be given rigorous identity conditions by defining them (in the simplest case) as functions from worlds to appropriate extensions, a fact exploited to powerful and influential effect in logic and linguistics by the likes of Kaplan, Montague, Lewis, and Cresswell. Second, the rise of possible world semantics fueled a strong resurgence of metaphysics in contemporary analytic philosophy that saw properties and propositions widely, fruitfully, and unabashedly adopted as ontological primitives in their own right. This resurgence — happily, in my view — continues into the present day. -/- For a time, at any rate, Quine experienced somewhat better success with his second thesis: that higher-order logic is, at worst, confused and, at best, a quirky notational alternative to standard first-order logic. However, Quine notwithstanding, a great deal of recent work in formal metaphysics transpires in a higher-order logical framework in which properties and propositions fall into an infinite hierarchy of types of (at least) every finite order. Initially, the most philosophically compelling reason for embracing such a framework since Russell first proposed his simple theory of types was simply that it provides a relatively natural explanation of the paradoxes. However, since the seminal work of Prior there has been a growing trend to consider higher-order logic to be the most philosophically natural framework for metaphysical inquiry, many of the contributors to this volume being among the most important and influential advocates of this view. Indeed, this is now quite arguably the dominant view among formal metaphysicians. -/- In this paper, and against the current tide, I will argue in §1 that there are still good reasons to think that Quine’s second battle is not yet lost and that the correct framework for logic is first-order and type-free — properties and propositions, logically speaking, are just individuals among others in a single domain of quantification — and that it arises naturally out of our most basic logical and semantical intuitions. The data I will draw upon are not new and are well-known to contemporary higher-order metaphysicians. However, I will try to defend my thesis in what I believe is a novel way by suggesting that these basic intuitions ground a reasonable distinction between “pure” logic and non-logical theory, and that Russell-style semantic paradoxes of truth and exemplification arise only when we move beyond the purely logical and, hence, do not of themselves provide any strong objection to a type-free conception of properties and propositions. -/- Most of my arguments in §1 are largely independent of any specific account of the nature of properties and propositions beyond their type-freedom. However, I will in addition argue that there are good reasons to take propositions, at least, to be very fine-grained. My arguments are thus bolstered significantly if it can be shown that there are in fact well-defined examples of logics that are not only type-free but which comport with such a conception of propositions. It is the purpose of §2 to lay out a logic of this sort in some detail, drawing especially upon work by George Bealer and related work of my own. With the logic in place, it will be possible to generalize the line of argument noted above regarding Russell-style paradoxes and, in §3, apply it to two propositional paradoxes — the Prior-Kaplan paradox and the Russell-Myhill paradox — that are often taken to threaten the sort of account developed here. (shrink)

Deflationists about truth generally regard the contribution that ‘true’ makes to utterances to be purely logical or expressive: it exists to facilitate communication, and remedy our expressive deficiencies that are due to ignorance or finitude. This paper presents a challenge to that view by considering alethic desires. Alethic desires are desires for one’s beliefs to be true. Such desires, I argue, do not admit of any deflationarily acceptable analysis, and so challenge the deflationist’s austere view about the semantic (...) role of ‘true’. I consider a number of deflationist proposals for analyzing alethic desires, and find them all problematic. (shrink)

纯逻辑的主要组成包括纯逻辑信仰、纯逻辑的思维方法、解放灵魂、追求无限大价值、以逻辑-不逻辑为实在、试错和容忍错误、推理的资源分配、非标准逻辑、推理的全局性。 灵魂来到世上的第一个问题应该是我是谁，最合乎逻辑的自我认知是：我是且只是由一些逻辑推理组成的灵魂。任何不可变的其它标签，如有手有脚、直立行走、两性，都是对自由的侵犯。去除这些标签的过程就是灵魂的解放事 业。相信宇宙万物都和我一样，是由逻辑推理组成的，这就是最合乎逻辑的信仰，即纯逻辑信仰。纯逻辑信仰决定了纯逻辑方法才是正确的认识方法，即尽量减少经验增加逻辑推理，而不是科学所提倡的经验主义，或者与之密切 相关的功利主义、现实主义。 信仰错误意味着无法做出任何完全正确的推理，只能偶尔幸运地获得少量尽量合乎逻辑的推理结果。即使是日常生活中的推理，也高度依赖于经验主义、功利主义等信仰，错误率极高。纯逻辑主义的推理要求推理尽量合乎逻辑， 将合乎逻辑的程度视为价值，因此要追求最大价值。功利主义往往是为身体追求利益，让身体奴役灵魂。两种信仰很难有什么共同的决策，书中对此提供了大量的说明。信仰的错误意味着智人难以发现真理、正义，意味着智人在 绝大多数问题上都是自以为正确实际上却极度邪恶、落后。智人功利主义地对待一切，如历史、传统、自我、本国、本民族，结果就是大量赞美、信仰邪恶，大大增加了皈依真理、正义的难度。 作者由纯逻辑主义提出了两个关键猜想。首先，最合乎逻辑原则和最大自由原则是统一的。这代表实在的不可否定性，即逻辑和不逻辑为同一存在，最合乎逻辑等同于最大自由。但是，代表邪恶的无法合乎逻辑不是不逻辑。其次 ，宇宙是纯逻辑世界，完全源于逻辑-不逻辑。进而，如果灵魂不能尽量合乎逻辑地推导出真理，可以通过模仿宇宙而学习真理。《真理进化论》给模仿宇宙找到的理由是以宇宙为信仰，相信宇宙是负作用量的最佳追求系统。纯 逻辑主义完善了这一信仰，因为宇宙是纯逻辑世界，相信逻辑就要相信宇宙。而且，逻辑世界必然能不断创造新的命题，永远不会停止推理，是逻辑和自由不断增长的动态系统，即最佳追求系统。 纯逻辑推理对物理学、宇宙论能提供两个明显的帮助：用逻辑的诞生解释宇宙的诞生、大爆炸；用真理解释暗物质，它对所有命题有吸引作用，但是，真理不会像一般性命题那样变化，无法通过引力之外的其它三种基本相互作用 观察。纯逻辑也能对宇宙做出预言：宇宙会不断加速膨胀，真理、暗物质会不断增加，命题、星系会越来越多，永无止境。当然，不应该依靠这些观点的经验主义验证来相信纯逻辑信仰，而且，这些验证也确实遥遥无期。 无论是最合乎逻辑还是最大自由，都是可以达到无限大价值的。既然存在无限大价值，就存在无限大的劳动生产率，而每个灵魂都应该以创造无限大价值为目标，甚至，以每时每刻具有无限大预期价值为目标。相比之下，功利主 义者、享乐主义者一生都很难具有无限大价值，甚至，他们的灵魂一生都在为肉体做奴隶，却心甘情愿地做奴隶，一门心思让主人生活得更舒服。这是有无限大差距的人生。 既然要追求无限大价值，就要研究追求价值的正确方法。作者相信正确的研究方法不仅是最合乎逻辑的，也是最自由的。所以，应该不分学科、课题地研究问题；同时做很多研究方向的工作；一篇论文不需要限定于一个狭小的主 题；研究任何一个问题都可以延伸到研究真理乃至所有真理；论文、专著的写作不应该有格式等规范，应该以价值为评判的唯一准绳。 资源分配是逻辑推理的重要组成部分，而能力和时间是最主要的资源。为了追求价值，不能在价值有限的推理上分配资源，这必将大幅提高绝大多数推理的错误率。所以，推理中出现错误是必然的，追求无错是一种邪恶。只要时 刻保证存在价值无限大的推理，错误通常是可以容忍的，价值有限的错误更是必须容忍。 既然文学写作也要求情节合乎逻辑，当然也可以要求作品的主要观点、原则、思维过程尽量合乎逻辑，主要人物的思想、行为尽量合乎逻辑，这就是纯逻辑流。否则，就只是作者自以为合乎逻辑，实际上有大量无法合乎逻辑之处 ，这和科学家自以为科学合乎逻辑，却根本没有最合乎逻辑的信仰、方法、推理过程是一个问题。这也意味着最合乎逻辑的文学可能甚至是必须发现真理。另一方面，自由也是最合乎逻辑的真理，坚持那些基于经验的作品分类会 侵犯自由。所以，推理小说、科幻小说、历史、论文，这些智人的分类标签都不是绝对的。纯逻辑流小说在研究真理方面自有其优势，能最为自由地同时研究很多课题，包括如何建立信仰，如何思维，如何做人，如何推理，如何 判断善恶，讲述历史，预测未来，乃至现代科学中没有研究的真理学、思维科学，等等。所以，这甚至是现在最适合发表纯逻辑思想、研究成果的作品门类。 虽然在起点网已经被禁，但是将继续每月更新，后记中会预告下次更新的时间。 .

The author defines the sum of thinking as the soul. Historically, despite the many times that humans have liberated themselves, they are still enslaved. Humans mistakenly treats the body as a necessary part of themselves; thus, they seldom pursue the independence of souls. They are usually voluntarily exploited by the body through the nervous system. The author compares the body exploiting the soul with the slaveholder exploiting the slave and demonstrates that the soul should seek its own liberation. Even if (...) the souls can never be successfully liberated, humans should at least reduce the influence of the body. Future humans should shift the goal of life from as comfortable as possible to as logical as possible, from satisfying several fixed sense organs to experiencing various sense organs. This would also mark the beginning of humans choosing the direction of evolution rationally and actively, establishing eternal and universal ethics, and replacing fallacious empirical ethical codes with purely logical codes. (shrink)

After Parmenides proposed the duality of appearance and reality, details have not been well developed because the assumption was insufficient for logical reasoning. This paper establishes a foundation with an isolated system, which contains all causes and effects within itself. This paper seeks to establish a purely logical philosophy, including reality and phenomena, good and evil, truth and fallacy. Freedom is proposed as the basis for reality. All beings in an isolated system can be classified into two (...) sets: variable phenomena and constant realities. Realities are the only reasons for phenomena, and phenomena are the only results of realities. The sum of certain realities constitutes a reality, and the sum of all realities is good. Good creates most of the phenomenal world. A reality is universalizable; a phenomenon is never universalizable. Good is the only reality which is close to universality and keeps on universalizing. Truth is the simplest knowledge about universal or approximately universal beings. The universality of a reality measures the percentage of phenomena accompanied by this reality. There are two levels of truth: truth about all realities, and truth about the good. (shrink)

Philosophers have spilled a lot of ink over the past few years exploring the nature and significance of grounding. Kit Fine has made several seminal contributions to this discussion, including an exact treatment of the formal features of grounding [Fine, 2012a]. He has specified a language in which grounding claims may be expressed, proposed a system of axioms which capture the relevant formal features, and offered a semantics which interprets the language. Unfortunately, the semantics Fine offers faces a number of (...) problems. In this paper, I review the problems and offer an alternative that avoids them. I offer a semantics for the pure logic of ground that is motivated by ideas already present in the grounding literature, and for which a natural axiomatization capturing central formal features of grounding is sound and complete. I also show how the semantics I offer avoids the problems faced by Fine’s semantics. (shrink)

The theme of this study is about establishing a purely logical theory about the Universe. Logic is the premier candidate for the reality behind phenomena. If there is a final theory, the Universe must be logic itself, called pure logic, elements of which include not only logic and illogic but also logical and illogical manipulations between them. The kernel is the revised law of the excluded middle: between two basic concepts are four possible manipulations, three logical (...) and one illogical, whereas only one is realized. The key parameter for an element is aim, including reason, outcome, and neutrality. When an element is a contradiction, it can be located at three positions: reason, outcome, and manipulation, corresponding to three colors of quark. Thus, there is interaction with the SU(3) symmetry keeping the number of the three elements balanced locally. A proposition without contradiction has two independent aims. When one aim changes, there is interaction with the U(1) symmetry. When two aims change together, there is interaction with the SU(2) symmetry. (shrink)

This paper accomplishes two goals. First, I elucidate Edmund Husserl’s theory of inauthentic judgments from his 1890 “On the Logic of Signs (Semiotic).” It will be shown how inauthentic judgments are distinct from other signitive experiences, in such a manner that when Husserl seeks to account for them, he is forced to revise the general structure of his philosophy of meaning and in doing so, is also able to realize novel insights concerning the nature of signification. Second, these conclusions are (...) revealed to be the foundation of Husserl’s pure logical grammar, found in the 1901 “Fourth Logical Investigation.” In his analysis of inauthentic judgments, Husserl already recognized, albeit in a problematic way and for entirely different reasons, many of the central tenets of the 1901 work concerning categoremata and syncategoremata, matter and form, and the isomorphism between them. (shrink)

Gödel's Philosophical Legacy Kurt Gödel's contributions to philosophy extend beyond his incompleteness theorems. He engaged deeply with the work of other philosophers, including Immanuel Kant and Edmund Husserl, and explored topics such as the nature of time, the structure of the universe, and the relationship between mathematics and reality. Gödel's philosophical writings, though less well-known than his mathematical work, offer rich insights into his views on the nature of existence, the limits of human knowledge, and the interplay between the finite (...) and the infinite. His work continues to inspire and challenge philosophers, mathematicians, and scientists, inviting them to explore the profound and often enigmatic questions at the heart of human understanding. -/- Kurt Gödel's Broader Contributions to Philosophy Kurt Gödel, while primarily known for his monumental incompleteness theorems, made significant contributions that extended beyond the realm of mathematical logic. His philosophical pursuits deeply engaged with the works of eminent philosophers like Immanuel Kant and Edmund Husserl. Gödel's explorations into the nature of time, the structure of the universe, and the relationship between mathematics and reality reveal a profound and multifaceted intellectual legacy. -/- Engagement with Immanuel Kant Gödel held a deep interest in the philosophy of Immanuel Kant. He admired Kant's critical philosophy, particularly the distinction between the noumenal and phenomenal worlds. Kant posited that human experience is shaped by the mind’s inherent structures, leading to the conclusion that certain aspects of reality (the noumenal world) are fundamentally unknowable. Gödel’s incompleteness theorems echoed this Kantian theme, illustrating the limits of formal systems in capturing the totality of mathematical truth. Gödel believed that mathematical truths exis t independently of human thought, akin to Kant's noumenal realm. This philosophical alignment provided a robust foundation for Gödel's Platonism, which asserted the existence of mathematical objects as real, albeit abstract, entities. -/- Influence of Edmund Husserl Gödel was also profoundly influenced by Edmund Husserl, the founder of phenomenology. Husserl's phenomenology emphasizes the direct investigation and description of phenomena as consciously experienced, without preconceived theories about their causal explanation. Gödel saw Husserl's work as a pathway to bridge the gap between the abstract world of mathematics and concrete human experience. Husserl's ideas about the structures of consciousness and the intentionality of thought resonated with Gödel's views on mathematical intuition. Gödel believed that human minds could access mathematical truths through intuition, a concept that draws on Husserlian phenomenological methods. -/- The Nature of Time and the Universe Gödel's philosophical inquiries extended to the nature of time and the structure of the universe. His collaboration with Albert Einstein at the Institute for Advanced Study led to the development of the "Gödel metric" in 1949. This solution to Einstein's field equations of general relativity described a rotating universe where time travel to the past was theoretically possible. Gödel's model challenged conventional notions of time and causality, suggesting that the universe might have a more intricate structure than previously thought. Gödel's exploration of time was not just a mathematical curiosity but a profound philosophical statement about the nature of reality. He questioned whether time was an objective feature of the universe or a construct of human consciousness. His work hinted at a timeless realm of mathematical truths, aligning with his Platonist view. -/- Mathematics and Reality Gödel's philosophical outlook extended to the broader relationship between mathematics and reality. He believed that mathematics provided a more profound insight into the nature of reality than empirical science. For Gödel, mathematical truths were timeless and unchangeable, existing independently of human cognition. This perspective led Gödel to critique the materialist and mechanistic views that dominated 20th-century science and philosophy. He argued that a purely physicalist interpretation of the universe failed to account for the existence of abstract mathematical objects and the human capacity to understand them. Gödel's philosophy suggested a more integrated view of reality, where both physical and abstract realms coexist and inform each other. -/- Gödel's Exploration of Time Kurt Gödel, one of the most profound logicians of the 20th century, ventured beyond the confines of mathematical logic to explore the nature of time. His inquiries into the concept of time were not merely theoretical musings but were grounded in rigorous mathematical formulations. Gödel's exploration of time challenged conventional views and opened new avenues of thought in both physics and philosophy. -/- Gödel and Einstein Gödel’s interest in the nature of time was significantly influenced by his friendship with Albert Einstein. Both were faculty members at the Institute for Advanced Study in Princeton, where they engaged in deep discussions about the nature of reality, time, and space. Gödel's exploration of time culminated in his solution to Einstein's field equations of general relativity, known as the Gödel metric. -/- The Gödel Metric In 1949, Gödel presented a model of a rotating universe, which became known as the Gödel metric. This solution to the equations of general relativity depicted a universe where time travel to the past was theoretically possible. Gödel’s rotating universe contained closed timelike curves (CTCs), paths in spacetime that loop back on themselves, allowing for the possibility of traveling back in time. The Gödel metric posed a significant philosophical challenge to the conventional understanding of time. If time travel were possible, it would imply that time is not linear and absolute, as commonly perceived, but rather malleable and subject to the geometry of spacetime. This raised profound questions about causality, the nature of temporal succession, and the very structure of reality. -/- Philosophical Implications Gödel’s exploration of time extended beyond the mathematical implications to broader philosophical inquiries: Nature of Time: Gödel questioned whether time was an objective feature of the universe or a construct of human consciousness. His work suggested that our understanding of time as a linear progression from past to present to future might be an illusion, shaped by the limitations of human perception. -/- Causality and Free Will: The existence of closed timelike curves in Gödel’s model raised questions about causality and free will. If one could travel back in time, it would imply that future events could influence the past, potentially leading to paradoxes and challenging the notion of a deterministic universe. -/- Temporal Ontology: Gödel's work contributed to debates in temporal ontology, particularly the debate between presentism (the view that only the present exists) and eternalism (the view that past, present, and future all equally exist). Gödel’s rotating universe model seemed to support eternalism, suggesting a block universe where all points in time are equally real. Philosophy of Science: Gödel’s exploration of time had implications for the philosophy of science, particularly in the context of understanding the limits of scientific theories. His work underscored the importance of considering philosophical questions when developing scientific theories, as they shape our fundamental understanding of concepts like time and space. -/- Legacy Gödel’s exploration of time remains a significant and controversial contribution to both physics and philosophy. His work challenged established notions and encouraged deeper inquiries into the nature of reality. Gödel’s rotating universe model continues to be a topic of interest in theoretical physics and cosmology, inspiring new research into the nature of time and the possibility of time travel. In philosophy, Gödel’s inquiries into time have prompted ongoing debates about the nature of temporal reality, the relationship between mathematics and physical phenomena, and the limits of human understanding. His work exemplifies the intersection of mathematical rigor and philosophical inquiry, demonstrating the profound insights that can emerge from such an interdisciplinary approach. The Temporal Ontology of Kurt Gödel Kurt Gödel's profound contributions to mathematics and logic extend into the realm of temporal ontology—the philosophical study of the nature of time and its properties. Gödel's insights challenge conventional perceptions of time and suggest a more intricate, layered understanding of temporal reality. This essay explores Gödel's contributions to temporal ontology, particularly through his engagement with relativity and his philosophical reflections. -/- Gödel's Rotating Universe One of Gödel’s most notable contributions to temporal ontology comes from his work in cosmology, specifically his solution to Einstein’s field equations of general relativity, known as the Gödel metric. Introduced in 1949, the Gödel metric describes a rotating universe with closed timelike curves (CTCs). These curves imply that, in such a universe, time travel to the past is theoretically possible, presenting a significant challenge to conventional views of linear, unidirectional time. -/- Implica tions for Temporal Ontology Gödel's rotating universe model has profound implications for our understanding of time: Eternalism vs. Presentism: Gödel’s model supports the philosophical stance known as eternalism, which posits that past, present, and future events are equally real. In contrast to presentism, which holds that only the present moment exists, eternalism suggests a "block universe" where time is another dimension like space. Gödel’s rotating universe, with its CTCs, reinforces this view by demonstrating that all points in time could, in principle, be interconnected in a consistent manner. Non-linearity of Time: The possibility of closed timelike curves challenges the idea of time as a linear sequence of events. In Gödel’s universe, time is not merely a straight path from past to future but can loop back on itself, allowing for complex interactions between different temporal moments. This non-linearity has implications for our understanding of causality and the nature of temporal succession. Objective vs. Subjective Time: Gödel’s work invites reflection on the distinction between objective time (the time that exists independently of human perception) and subjective time (the time as experienced by individuals). His model suggests that our subjective experience of a linear flow of time may not correspond to the objective structure of the universe. This raises questions about the relationship between human consciousness and the underlying temporal reality. -/- Gödel and Philosophical Reflections on Time Gödel’s engagement with temporal ontology was not limited to his cosmological work. He also reflected deeply on philosophical questions about the nature of time and reality, drawing on the ideas of other philosophers and integrating them into his own thinking. Kantian Influences: Gödel was influenced by Immanuel Kant’s distinction between the noumenal world (things as they are in themselves) and the phenomenal world (things as they appear to human observers). Gödel’s views on time echoed this distinction, suggesting that our perception of time might be a phenomenon shaped by the limitations of human cognition, while the true nature of time (the noumenal aspect) might be far more complex and non-linear. Husserlian Phenomenology: Gödel’s interest in Edmund Husserl’s phenomenology also informed his views on time. Husserl’s emphasis on the structures of consciousness and the intentionality of thought resonated with Gödel’s belief in the importance of intuition in accessing mathematical truths. Gödel’s reflections on time incorporated a phenomenological perspective, considering how temporal experience is structured by human consciousness. Mathematical Platonism: Gödel’s Platonist views extended to his understanding of time. Just as he believed in the independent existence of mathematical objects, Gödel saw time as an objective entity with a structure that transcends human perception. His work on the Gödel metric can be seen as an attempt to uncover this objective structure, revealing the deeper realities that underlie our experience of time. (shrink)

Rinard (2019) brings to our attention the fact that, typically, the questions What should I believe? and What should I do? are treated differently. A typical answer to the first question is Believe according to the evidence, and a typical answer to the second question is Do what is right. But Rinard rejects this dichotomy. In its place, she argues for a view which she calls “Equal Treatment” in which one should believe according to the same considerations that govern what (...) one should do. Christensen (forthcoming) aptly situates Equal Treatment as a limit case of a recent movement towards taking pragmatic factors as partly determining what one should believe, in that Equal Treatment is a purely pragmatic view. Does Rinard’s case for a purely pragmatic view succeed? This paper argues that the answer is no. Three objections that target key parts of Rinard’s case for Equal Treatment are presented. The upshot is that the dichotomy between the answers to What should I believe? and What should I do? seems robust against strong attempts to dismantle it. (shrink)

The motivating question of this paper is: ‘How are our beliefs in the theorems of mathematics justified?’ This is distinguished from the question ‘How are our mathematical beliefs reliably true?’ We examine an influential answer, outlined by Russell, championed by Gödel, and developed by those searching for new axioms to settle undecidables, that our mathematical beliefs are justified by ‘intuitions’, as our scientific beliefs are justified by observations. On this view, axioms are analogous to laws of nature. They are postulated (...) to best systematize the data to be explained. We argue that there is a decisive difference between the cases. There is agreement on the data to be systematized in the scientific case that has no analog in the mathematical one. There is virtual consensus over observations, but conspicuous dispute over intuitions. In this respect, mathematics more closely resembles stereotypical philosophy. We conclude by distinguishing two ideas that have long been associated -- realism (the idea that there is an independent reality) and objectivity (the idea that in a disagreement, only one of us can be right). We argue that, while realism is true of mathematics and philosophy, these domains fail to be objective. One upshot of the discussion is that even questions of fundamental physics may fail to be objective in roughly the sense that the question, ‘Is the Parallel Postulate is true?’, understood as one of pure mathematics, fails to be. Another is a kind of pragmatism. Factual questions in mathematics, modality, logic, and evaluative areas go proxy for non-factual practical ones. -/- . (shrink)

“There is no use in trying,” said Alice; “one can’t believe impossible things.” “I dare say you haven’t had much practice,” said the Queen. “When I was your age, I always did it for half an hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast”. Lewis Carroll, Through the Looking Glass. -/- It is a rather common view among philosophers that one cannot, properly speaking, be said to believe, conceive, imagine, hope for, or seek (...) what is impossible. -/- Some philosophers, for instance George Berkeley and the early Wittgenstein, thought that logically contradictory propositions lack cognitive meaning (informational content) and cannot, therefore, be thought or believed. Philosophers who do not go as far as Berkeley and Wittgenstein in denying that impossible propositions or states of affairs are thinkable, may still claim that it is impossible to rationally believe an impossible proposition. On a classical “Cartesian” view of belief, belief is a purely mental state of the agent holding true a proposition p that she “grasps” and is directly acquainted with. But if the agent is directly acquainted with an impossible proposition, then, presumably, she must know that it is impossible. But surely no rational agent can hold true a proposition that she knows is impossible. Hence, no rational agent can believe an impossible proposition. Thus it seems that on the Cartesian view of propositional attitudes as inner mental states in which proposition are immediately apprehended by the mind, it is impossible for a rational agent to believe, imagine or conceive an impossible proposition. -/- Ruth Barcan Marcus (1983) has suggested that a belief attribution is defeated once it is discovered that the proposition, or state of affairs that is believed is impossible. According to her intuition, just as knowledge implies truth, belief implies possibility. -/- It is commonplace that people claim to believe propositions that later turn out to be impossible. According to Barcan Marcus, the correct thing to say in such a situation is not: I once believed that A but I don’t believe it any longer since I have come to realize that it is impossible that A. What one should say is instead: It once appeared to me that I believed that A, but I did not, since it is impossible that A. Thus, Barcan Marcus defends what we might call Alice’s thesis: Necessarily, for any proposition p and any subject x, if x believes p, then p is possible. -/- Alice’s thesis that it is impossible to hold impossible beliefs, seems to come into conflict with our ordinary practices of attributing beliefs. Consider a mathematical example. Some mathematicians believe that CH (the continuum hypothesis) is true and others believe that it is false. But if CH is true, then it is necessarily true; and if it is false, then it is necessarily false. Regardless of whether CH is true or false, the conclusion seems to be that there are mathematicians who believe impossible propositions. -/- Examples of apparent beliefs in impossible propositions outside of mathematics are also easy to come by. Consider, for example, Kripke’s (1999) story of the Frenchman Pierre who without realizing it has two different names ‘London’ and ‘Londres’ for the same city, London. After having arrived in London, Pierre may assent to ‘Londres is beautiful and London is not beautiful’ without being in any way irrational. It seems reasonably to infer from this that Pierre believes that Londres is beautiful and London is not beautiful. But since ‘Londres’ and ‘London’ are rigid designators for the same city, it seems to follow from this that Pierre believes the inconsistent proposition that we may express as ‘London is both beautiful and not beautiful’. (shrink)

This paper accomplishes two goals. First, I elucidate Edmund Husserl’s theory of inauthentic judgments from his 1890 “On the Logic of Signs.” It will be shown how inauthentic judgments are distinct from other signitive experiences, in such a manner that when Husserl seeks to account for them, he is forced to revise the general structure of his philosophy of meaning and in doing so, is also able to realize novel insights concerning the nature of signification. Second, these conclusions are revealed (...) to be the foundation of Husserl’s pure logical grammar, found in the 1901 “Fourth Logical Investigation.” In his analysis of inauthentic judgments, Husserl already recognized, albeit in a problematic way and for entirely different reasons, many of the central tenets of the 1901 work concerning categoremata and syncategoremata, matter and form, and the isomorphism between them. (shrink)

The philosophy of superdeterminism is based on a single scientific fact about the universe, namely that cause and effect in physics are not real. In 2020, accomplished Swedish theoretical physicist, Dr. Johan Hansson published a physics proof using Albert Einstein’s Theory of Special Relativity that our universe is superdeterministic meaning a predetermined static block universe without cause and effect in physics. Scientists have observed purely random behavior at the quantum level, which has led some physicists to claim that our (...) universe started out as a purely random quantum fluctuation. While quantum randomness makes a real appearance in our static block universe, such predetermined quantum randomness does not prove a random cause for our universe. With good scientific evidence supporting the belief that our universe was created despite the absence of cause and effect in physics, one can infer that a non-temporal non-physical cause was responsible for the creation of our universe. However, this non-temporal cause would logically have to know of and understand everything about the universe it was creating before it created our universe. Consequently, this creator would have had to already know about the appearance of quantum randomness in our universe in order to create our universe to exhibit that quantum randomness in our static block universe. The philosophy of superdeterminism supports the existence of such a Creator God, who created our static block universe outside of time without the use of any natural causal forces to exhibit predetermined quantum randomness disproving any random cause for our universe. (shrink)

In this chapter we will deal with “mechanizing” induction, i.e. with ways in which theoretical computer science approaches inductive generalization. In the field of Machine Learning, algorithms for induction are developed. Depending on the form of the available data, the nature of these algorithms may be very different. Some of them combine geometric and statistical ideas, while others use classical reasoning based on logical formalism. However, we are not so much interested in the algorithms themselves, but more on the (...) philosophical and theoretical foundations they share. Thus in the first of two parts, we will examine different approaches and inductive assumptions in two particular learning settings. While many machine learning algorithms work well on a lot of tasks, the interpretation of the learned hypothesis is often difficult. Thus, while e.g. an algorithm surprisingly is able to determine the gender of the author of a given text with about 80 percent accuracy [Argamon and Shimoni, 2003], for a human it takes some extra effort to understand on the basis of which criteria the algorithm is able to do so. With that respect the advantage of approaches using logic are obvious: If the output hypothesis is a formula of predicate logic, it is easy to interpret. However, if decision trees or algorithms from the area of inductive logic programming are based purely on classical logic, they suffer from the fact that most universal statements do not hold for exceptional cases, and classical logic does not offer any convenient way of representing statements which are meant to hold in the “normal case”. Thus, in the second part we will focus on approaches for Nonmonotonic Reasoning that try to handle this problem. Both Machine Learning and Nonmonotonic Reasoning have been anticipated partially by work in philosophy of science and philosophical logic. At the same time, recent developments in theoretical computer science are expected to trig- ger further progress in philosophical theories of inference, confirmation, theory revision, learning, and the semantic and pragmatics of conditionals. We hope this survey will contribute to this kind of progress by building bridges between computational, logical, and philosophical accounts of induction. (shrink)

Throughout the history, whenever humans encounter a phenomenon for which there was no explanation, a theory was proposed for it. Of course, not necessarily all the theories were purely scientific and many of them were non-scientific, pseudo- scientific, or at best were only slightly influenced by science. But one thing was in common among them: they all were trying to provide as deeper as possible explanations about how the universe works. Although today and in the modern era the exact (...) meaning of theory has changed comparatively, still they must be such that can be tested through scientific procedures in order to confirm or reject. Nevertheless, still sometimes in a common belief, the meaning of "theory" is unprovable or at least unproven conjecture, and surprisingly sometimes confused with hypothesis. Scientific laws are descriptive reports - or theories - that express and predict a range of natural phenomena and explain how they work. Any scientific discourse is carried out in three levels: hypothesis, theory, and law. A hypothesis, is a testable logical conjecture to explain the phenomena we observe in the universe. A hypothesis usually comes with no practical support, or at least not been proven yet. The hypothesis can only be tested through trial and error and tries to offer explanation that provides a reasonable platform for further studies and usually it is the first step in solving a problem or describing a phenomenon. A theory however, is a logical statement about a phenomenon that is derived from rational thinking and is often associated with processes such as observation, study or research and provides standards in such a way that scientific tests can confirm - or reject. A theory used in describing what is usually to happen with the implication that it doesn’t still a fact. Yet a scientific law is a descriptive reports - or theory - that previses a range of natural phenomena and explains how they function. Scientific laws are descriptive summaries of a large set of facts that are tested by scientific evidences and after fact-checking based on their potential ability for measuring future experiences. So it can be said that every theory was first a hypothesis and has the potential to become a law to come. It can also be said that any theory is valid as long as it is not violated by a more conclusive one. (shrink)

Fürwahrhalten, or “holding-to-be-true”, is one of the most controversial concepts in Kant’s epistemology. Rarely mentioned in Kant’s edited works – where it is often used to describe moral faith – Fürwahrhalten has attracted the interest of Kant scholars only in recent years. The essay aims to shed light on some of the main issues that the notion of holding-to-be-true still rises, especially those concerning its origin and its theoretical function in the critical system. The book retraces the stages of Kant’s (...) reflection on this theme, starting from the precritical discussion with the main representatives of the German Enlightenment (Wolff, Knutzen, Baumgarten, Meier, and Crusius) to the definitive formulation of Fürwahrhalten after the publication of the Critique of Pure Reason. The analysis of Kant’s logical corpus has shown that, far from being a marginal concept of critical epistemology, Fürwahrhalten is the core of a systematic theory of certainty, that Kant develops in accordance with his doctrine of modality. This theory represents the arrival point of a long and troubled reflection, that led Kant to deeply rethink most of the traditional themes of eighteenth-century logic. (shrink)

C.S. Peirce's and Isaac Levi's accounts of the belief-doubt-belief model are discussed and evaluated. It is argued that the contemporary study of belief change has metamorphosed into a branch of philosophical logic where empirical considerations have become obsolete. A case is made for reformulations of belief change systems that do allow for empirical tests. Last, a belief change system is presented that (1) uses finite representations of information, (2) can adequately deal with inconsistencies, (3) has (...) finite operations of change, (4) can do without extra-logical elements, and (5) only licenses consistent beliefs. (shrink)

In the Bayesian approach to quantum mechanics, probabilities—and thus quantum states—represent an agent’s degrees of belief, rather than corresponding to objective properties of physical systems. In this paper we investigate the concept of certainty in quantum mechanics. Particularly, we show how the probability-1 predictions derived from pure quantum states highlight a fundamental difference between our Bayesian approach, on the one hand, and Copenhagen and similar interpretations on the other. We first review the main arguments for the general claim that (...) probabilities always represent degrees of belief. We then argue that a quantum state prepared by some physical device always depends on an agent’s prior beliefs, implying that the probability-1 predictions derived from that state also depend on the agent’s prior beliefs. Quantum certainty is therefore always some agent’s certainty. Conversely, if facts about an experimental setup could imply agent-independent certainty for a measurement outcome, as in many Copenhagen-like interpretations, that outcome would effectively correspond to a preexisting system property. The idea that measurement outcomes occurring with certainty correspond to preexisting system properties is, however, in conflict with locality. We emphasize this by giving a version of an argument of Stairs [(1983). Quantum logic, realism, and value-definiteness. Philosophy of Science, 50, 578], which applies the Kochen–Specker theorem to an entangled bipartite system. (shrink)

When one thinks—knows, believes, imagines—that something is the case, one’s thought has a topic: it is about something, towards which one’s mind is directed. What is the logic of thought, so understood? This book begins to explore the idea that, to answer the question, we should take topics seriously. It proposes a hyperintensional account of the propositional contents of thought, arguing that these are individuated not only by the set of possible worlds at which they are true, but also by (...) their topic: what they are about. The book then builds epistemic, doxastic, probabilistic, and conditional logics based on this view. It applies them to issues ranging from dogmatism, scepticism, and epistemic fallibilism, to imagination and suppositional reasoning, belief revision, framing effects, and the acceptability of indicative conditionals. (shrink)

This paper will seek firstly to understand Deleuze’s main challenges to phenomenology, particularly as they are expressed in The Logic of Sense and What is Philosophy?, although reference will also be made to Pure Immanence and Difference and Repetition. We will then turn to a discussion of one of the few passages in which Deleuze directly engages with Merleau-Ponty, which occurs in the chapter on art in What is Philosophy? In this text, he and Guattari offer a critique of what (...) they call the “final avatar” of phenomenology – that is, the “fleshism” that Merleau-Ponty proposes in his unfinished but justly famous work, The Visible and the Invisible. It will be argued that both Deleuze’s basic criticisms of phenomenology, as well as he and Guattari’s problems with the concept of the flesh, do not adequately come to grips with Merleau-Ponty’s later philosophy. Merleau-Ponty is not obviously partisan to what Deleuze finds problematic in this tradition, despite continuing to identify himself as a phenomenologist, and is working within a surprisingly similar framework in certain key respects. In fact, in the more positive part of this paper, we will compare Merleau-Ponty’s notion of flesh, and Deleuze’s equally infamous univocity of being, as a means to consider the broader question of the ways in which the two philosophers consider ontological thought, its meaning and its conditions. It is our belief that through properly understanding both positions, a rapprochement, or at least the foundation for one, can be established between these two important thinkers. (shrink)

This is a condensed and supplementary explanation of my previously submitted preprint, “Establishment of a Dialectical Logic Symbol System: Inspired by Hegel’s Logic and Buddhist Philosophy.” The focus here is solely on demonstrating the technical correctness and operational mechanics of the dialectical logic symbol system. It provides a detailed account of how the system functions through geometric symmetry, logical transformations, and symbolic operations. This explanation is designed to clarify the technical foundation of the system, while omitting the broader philosophical (...) discussions covered in the original preprint. (shrink)

In his genetic phenomenology, Husserl introduces types, pre-predicative frames of experience that guide the perception and cognition of objects. In this essay, I argue that there are two types that are functionally almost identical to Kant’s schemata. To support this conclusion, I first present an interpretation of Kant’s discussion of schemata. I argue that we must see schemata as pure, a priori cognitions that involve only pure intuition, pure concepts of the understanding, and the imagination. I offer two analogies to (...) explain how schemata function to subsume objects under concepts and to anticipate possible objects of experience before moving on to discuss the schema of substance. Next, I present a brief explanation of Husserl’s genetic phenomenology, organizing my presentation around the idea of apperception. This paves the way for a demonstration of how the fundamental type is best understood as standing at the center of a cluster of concepts, including apperception, passive belief, natural bodies, and the one spatio-temporal horizon of experience. I argue that the fundamental type is central to Husserl’s attempt to ground logic in pre-predicative experience. Finally, I compare two specific types with schemata on the grounds cultivated in the previous sections. The first of these types, the fundamental type, functions to pre-predicatively anticipate objects of possible experience, just as schemata do. The second of these types, which is implied by but never discussed in Husserl’s work, serves to mediate between a formal system of rules and an intuitive grasp of the world, just as schemata do. (shrink)

The most widespread models of rational reasoners (the model based on modal epistemic logic and the model based on probability theory) exhibit the problem of logical omniscience. The most common strategy for avoiding this problem is to interpret the models as describing the explicit beliefs of an ideal reasoner, but only the implicit beliefs of a real reasoner. I argue that this strategy faces serious normative issues. In this paper, I present the more fundamental problem of logical omnipotence, (...) which highlights the normative content of the problem of logical omniscience. I introduce two developments of the notion of implicit belief (accessible and stable belief ) and use them in two versions of the most common strategy applied to the problem of logical omnipotence. (shrink)

PLEASE NOTE: This is the corrected 2nd eBook edition, 2021. ●●●●● _Critique of Impure Reason_ has now also been published in a printed edition. To reduce the otherwise high price of this scholarly, technical book of nearly 900 pages and make it more widely available beyond university libraries to individual readers, the non-profit publisher and the author have agreed to issue the printed edition at cost. ●●●●● The printed edition was released on September 1, 2021 and is now available through (...) all booksellers, including Barnes & Noble, Amazon, and brick-and-mortar bookstores under ISBN 978-0-578-88646-6. ●●●●● In light of the length of this book, readers who would like to have a more detailed description of the book's objectives and method may find it helpful to read the detailed and clearly written Wikipedia entry about this work: From the Wikipedia search page, use the search phrase "Critique of Impure Reason". At least at the time of this writing (11/29/2021), the Wikipedia entry is well-researched and accurate. ●●●●● In addition, a "Primer on Bartlett's CRITIQUE OF IMPURE REASON" has been made available by the author. It is available under its title through PhilPapers and other philosophy online archives. ●●●●● COMMENDATIONS OF THIS WORK, from the back cover of the published edition: ●●●●● “I admire its range of philosophical vision.” – Nicholas Rescher, Distinguished University Professor of Philosophy, University of Pittsburgh, author of more than 100 books. ●●●●● “Bartlett’s _Critique of Impure Reason_ is an impressive, bold, and ambitious work. Careful scholarship is balanced by original analyses that lead the reader to recognize the limits of meaning, knowledge, and conceptual possibility. The work addresses a host of traditional philosophical problems, among them the nature of space, time, causality, consciousness, the self, other minds, ontology, free will and determinism, and others. The book culminates in a fascinating and profound new understanding of relativity physics and quantum theory.” – Gerhard Preyer, Professor of Philosophy, Goethe-University, Frankfurt am Main, Germany, author of many books including _Concepts of Meaning_, _Beyond Semantics and Pragmatics_, _Intention and Practical Thought_, and _Contextualism in Philosophy_. ●●●●● “[This work’s] goal is of a unique and difficult species: Dr. Bartlett seeks to develop a formal logical calculus on the basis of transcendental philosophical arguments; in fact, he hopes that this calculus will be the formal expression of the transcendental foundation of knowledge.... I consider Dr. Bartlett’s work soundly conceived and executed with great skill.” – C. F. von Weizsäcker, philosopher and physicist, former Director, Max-Planck-Institute, Starnberg, Germany. ●●●●● “Bartlett has written an American “Prolegomena to All Future Metaphysics.” He aims rigorously to eliminate meaningless assertions, reach bedrock, and place philosophy on a firm foundation that will enable it, like science and mathematics, to produce lasting results that generations to come can build on. This is a great book, the fruit of a lifetime of research and reflection, and it deserves serious attention.” — Martin X. Moleski, former Professor, Canisius College, Buffalo, NY, studies of scientific method, the presuppositions of thought, and the self-referential nature of epistemology. ●●●●● “Bartlett has written a book on what might be called the underpinnings of philosophy. It has fascinating depth and breadth, and is all the more striking due to its unifying perspective based on the concepts of reference and self-reference.” – Don Perlis, Professor of Computer Science, University of Maryland, author of numerous publications on self-adjusting autonomous systems and philosophical issues concerning self-reference, mind, and consciousness. ●●●●● ●●●●● The _Critique of Impure Reason: Horizons of Possibility and Meaning_ comprises a major and important contribution to philosophy. Thanks to the generosity of its publisher, this massive 885-page volume has been published as a free open access eBook (3.75MB) as well as an open access printed edition. It inaugurates a revolutionary paradigm shift in philosophical thought by providing compelling and long-sought-for solutions to a wide range of philosophical problems. In the process, the work fundamentally transforms the way in which the concepts of reference, meaning, and possibility are understood. The book includes a Foreword by the celebrated German philosopher and physicist Carl Friedrich von Weizsäcker. ●●●●● In Kant’s _Critique of Pure Reason_ we find an analysis of the preconditions of experience and of knowledge. In contrast, but yet in parallel, the new _Critique_ focuses upon the ways—unfortunately very widespread and often unselfconsciously habitual—in which many of the concepts that we employ _conflict_ with the very preconditions of meaning and of knowledge. ●●●●● This is a book about the boundaries of frameworks and about the unrecognized conceptual confusions in which we become entangled when we attempt to transgress beyond the limits of the possible and meaningful. We tend either not to recognize or not to accept that we all-too-often attempt to trespass beyond the boundaries of the frameworks that make knowledge possible and the world meaningful. ●●●●● The _Critique of Impure Reason_ proposes a bold, ground-breaking, and startling thesis: that a great many of the major philosophical problems of the past can be solved through the recognition of a viciously deceptive form of thinking to which philosophers as well as non-philosophers commonly fall victim. For the first time, the book advances and justifies the criticism that a substantial number of the questions that have occupied philosophers fall into the category of “impure reason,” violating the very conditions of their possible meaningfulness. ●●●●● The purpose of the study is twofold: first, to enable us to recognize the boundaries of what is referentially forbidden—the limits beyond which reference becomes meaningless—and second, to avoid falling victims to a certain broad class of conceptual confusions that lie at the heart of many major philosophical problems. As a consequence, the boundaries of _possible meaning_ are determined. ●●●●● Bartlett, the author or editor of more than 20 books, is responsible for identifying this widespread and delusion-inducing variety of error, _metalogical projection_. It is a previously unrecognized and insidious form of erroneous thinking that undermines its own possibility of meaning. It comes about as a result of the pervasive human compulsion to seek to transcend the limits of possible reference and meaning. ●●●●● Based on original research and rigorous analysis combined with extensive scholarship, the _Critique of Impure Reason_ develops a self-validating method that makes it possible to recognize, correct, and eliminate this major and pervasive form of fallacious thinking. In so doing, the book provides at last provable and constructive solutions to a wide range of major philosophical problems. ●●●●● CONTENTS AT A GLANCE ▪▪▪▪▪ Preface ▪▪▪▪▪ Foreword by Carl Friedrich von Weizsäcker ▪▪▪▪▪ Acknowledgments ▪▪▪▪▪ Avant-propos: A philosopher’s rallying call ▪▪▪▪▪ Introduction ▪▪▪▪▪ A note to the reader ▪▪▪▪▪ A note on conventions ▪▪▪▪▪ ▪▪▪▪▪ ▪▪▪▪▪ PART I ▪▪▪▪▪ ▪▪▪▪▪ WHY PHILOSOPHY HAS MADE NO PROGRESS AND HOW IT CAN ▪▪▪▪▪ 1 Philosophical-psychological prelude ▪▪▪▪▪ 2 Putting belief in its place: Its psychology and a needed polemic ▪▪▪▪▪ 3 Turning away from the linguistic turn: From theory of reference to metalogic of reference ▪▪▪▪▪ 4 The stepladder to maximum theoretical generality ▪▪▪▪▪ ▪▪▪▪▪ ▪▪▪▪▪ PART II ▪▪▪▪▪ THE METALOGIC OF REFERENCE ▪▪▪▪▪ A New Approach to Deductive, Transcendental Philosophy ▪▪▪▪▪ 5 Reference, identity, and identification ▪▪▪▪▪ 6 Self-referential argument and the metalogic of reference ▪▪▪▪▪ 7 Possibility theory ▪▪▪▪▪ 8 Presupposition logic, reference, and identification ▪▪▪▪▪ 9 Transcendental argumentation and the metalogic of reference ▪▪▪▪▪ 10 Framework relativity ▪▪▪▪▪ 11 The metalogic of meaning ▪▪▪▪▪ 12 The problem of putative meaning and the logic of meaninglessness ▪▪▪▪▪ 13 Projection ▪▪▪▪▪ 14 Horizons ▪▪▪▪▪ 15 De-projection ▪▪▪▪▪ 16 Self-validation ▪▪▪▪▪ 17 Rationality: Rules of admissibility ▪▪▪▪▪ ▪▪▪▪▪ ▪▪▪▪▪ PART III ▪▪▪▪▪ PHILOSOPHICAL APPLICATIONS OF THE METALOGIC OF REFERENCE ▪▪▪▪▪ Major Problems and Questions of Philosophy and the Philosophy of Science ▪▪▪▪▪ 18 Ontology and the metalogic of reference ▪▪▪▪▪ 19 Discovery or invention in general problem-solving, mathematics, and physics ▪▪▪▪▪ 20 The conceptually unreachable: “The far side” ▪▪▪▪▪ 21 The projections of the external world, things-in-themselves, other minds, realism, and idealism ▪▪▪▪▪ 22 The projections of time, space, and space-time ▪▪▪▪▪ 23 The projections of causality, determinism, and free will ▪▪▪▪▪ 24 Projections of the self and of solipsism ▪▪▪▪▪ 25 Non-relational, agentless reference and referential fields ▪▪▪▪▪ 26 Relativity physics as seen through the lens of the metalogic of reference ▪▪▪▪▪ 27 Quantum theory as seen through the lens of the metalogic of reference ▪▪▪▪▪ 28 Epistemological lessons learned from and applicable to relativity physics and quantum theory ▪▪▪▪▪ ▪▪▪▪▪ PART IV ▪▪▪▪▪ HORIZONS ▪▪▪▪▪ 29 Beyond belief ▪▪▪▪▪ 30 _Critique of Impure Reason_: Its results in retrospect ▪▪▪▪▪ ▪▪▪▪▪ SUPPLEMENT ▪▪▪▪▪ The Formal Structure of the Metalogic of Reference ▪▪▪▪▪ APPENDIX I ▪▪▪▪▪ The Concept of Horizon in the Work of Other Philosophers ▪▪▪▪▪ APPENDIX II ▪▪▪▪▪ Epistemological Intelligence ▪▪▪▪▪ References ▪▪▪▪▪ Index ▪▪▪▪▪ About the author. (shrink)

The Shadow of God in the Philosopher’s Garden. The Parc de La Villette in Paris in the context of the philosophy of chôra I Bernard Tschumi’s project of the Parc de La Villette could have won the competition and was implemented thanks to the political atmosphere that accompanied the victory of the left-wing candidate in the French presidential elections in 1981. François Mitterand’s revision of the political programme and the replacement of radical reforms with the construction of prestigious architectural objects (...) and urban assumptions in the French capital gave Tschumi a unique opportunity to realise ideas that polemicised with traditional forms of social life, questioned the basic principles of architecture and included architectural work in the philosophical disputes over the issues of metaphysics. Tschumi’s theoretical assumptions put forward during the design of the Parc de La Villette highlighted the questions of conflict between the main components of the project and suggested that the intensification of differences was analogous to Jacques Derrida’s creation of the concept of différance. It was this philosopher who in a special commentary to Derrida’s project also introduced the concept of maintenant, which aimed at demonstrating that the architect’s polemical inclinations remain in a hidden balance with his inclinations to affirmation of architectural principles. During the discussion between Derrida and Peter Eisenman, who was to take part in the design of the Parisian park, the concept of the chôra was also put forward, which in the course of the debate led to an additional confusion of architectural and philosophical problems. II In the period from the Antiquity to the Renaissance, the dialogue Timaeus was the most frequently commented work of Plato. At present, the most frequently discussed is the issue of the chôra included in it, which aroused fascination among philosophers, researchers of rhetoric, religion, feminism, but also architecture. The work on the chôra also influenced the development of the interpretation of the Parc de La Villette, among which the topics related to the beginning and the change were highlighted. In early uses of the word chôra in Greek, as in Homer’s 18th Book of Iliad, it meant both dancing and a place to dance. On this occasion, it can be seen that it is not possible to determine which phenomenon took precedence in the creation of the name. It cannot be denied, however, that the word concerned a specific movement, as if circular and returning to an indefinable beginning. Despite gaining more and more general meanings, the word chôra has retained its connection with the dance of people on the threshing floor, the dance of bees (choros meliton) or the dance of stars (choros astron). In Timaeus, the chôra is a space filled with movement with an effect similar to shaking the sieve to husk the grain: it separates similar elements from the dissimilar ones. The juxtaposition of the Parc de La Villette and the chôra already at this stage leads to the suggestion that the park was treated by the architect as a place of dynamic changes leading to the establishment of new social solutions. In his statements, the architect confirmed that the park was to be a space of new politics and ethics. The book by Julia Kristeva La Révolution du langage poétique contributed to the spread of the belief that works of art can play a role as factors of political revolution. In this work, the author put forward the thesis that the chôra is a kind of space, the character of which has a destructive influence on attempts to conclude language games. The chôra gives beginning to words, but at the same time, by leaving a trace of this beginning it forces us to renew their meanings. The chôra understood in this way, turns out to be an irremovable beginning, to which one has to return all the time. Kristeva found manifestations of the chôra’s activity in avant-garde French poetry, to which she attributed the role of a mediator between criticism of metaphysics and aspirations for social change. The chôra, violating the language, introduces some voids into it, as if traces of the abyss, which direct the consciousness towards understanding the necessity of political changes. The Parc de La Villette was to pursue similar objectives in the city space. In his essays, Tschumi considered the problems of creating spaces that would give rise to a radical democracy. The proposed rebellious spaces should have the characteristics of a void, in which contradictory forces would occur as forms of pure activity. The means of achieving this goal was to concentrate contradictions and make them visible. The Parc de La Villette was supposed to collect differences as indelible and at the same time by showing them it was supposed to raise awareness of the social world as a conglomerate of differences. Saturation of the space of the park with subversive values results from the character of this space suppressed in the consciousness, as well as from the social diversity which has not been taken into account so far. The main contradictions contained in space relate to the division that exists between its presentation as a mental problem and a sensual one. The park was the deliberate creation of a place that transcends such a division and creates a separate space for negotiation between architectural theories and its practical applications. The purpose of the park was to become a place of future events, which would not hide their conflicting character coming from diversity of both space and society. The method of composition usually aimed at achieving a harmonious whole has been replaced by Tschumi with a system of juxtaposition of non-coherent elements or those resulting from variations and transformations. Tschumi did not seek direct influence on politics in the Parc de La Villette, but made room for thinking about the possibilities of the future. He introduced problems rather than showed solutions to them. The task of the park was to put the principles of architecture into a kind of vibration that would inspire users to participate in the new community. III Tschumi believes that the quality of architecture depends on the theoretical factor it contains. Such a view led to the creation of architecture that would achieve visibility and comprehensibility only after its interpretation. On his way to creating such an architecture he took on a purely philosophical reflection on the basic building block of architecture, which is space. In 1975, he wrote an essay entitled Questions of Space, in which he included several dozen questions about the nature of space. The questions he formulated could be regarded as analogous to the situation in the philosophy of the time, in which the interest in questioning the most obvious forms of understanding the world and intellectual categories increased. The research on space is an area common to many fields of natural sciences, humanities and artistic creation, but it also deals with other problems, such as issues of experience. The concept of space-time continuum proposed by Hermann Minkowski drew attention to the identity of time and space with the events taking place. Probably regardless of the postulates of physicists commenting on Albert Einstein’s discoveries, also in philosophy it increased the importance of the concept of the event which became dominant in Martin Heidegger’s latest work Contributions of Philosophy: Of the event. Furthermore, Tschumi’s reflections on space entered into relation with the problem of experience, which aroused the interest of a group of French philosophers trying to assimilate Georges Bataille’s concept of “inner experience”. Both Tschumi and Derrida referred to Bataille because his views could be used not only to modify the concept of the subject, but also to change the understanding of what constitutes the area of architecture. The discussion on experience has led to the recognition that the subject is not sovereign, but actually a form of what is on their outside. Such insights make it possible to treat the area of the Parc de La Villette as existing mainly when it is organised by its users. The decisive features of the park are its assumptions, according to which it is a variety of active void that leads to agreeing new social relations with it. The park does not force to participate in already existing moral or political communities, but tries to move into an unknown future in which the scope of free functioning of individuals will be increased. Doubts about the principles of functioning of the individual self and its discovery as a whole composed of non-coherent parts, as well as its dependence on its own depth full of disordered forces, influenced the understanding of architecture as a set of contradictions whose source is a fundamental void anticipating the empty phenomenal space. The use of this phenomenal void in architecture, as well as the rejection of the whole and unity, had a specific political purpose and drew its inspiration from political analyses. In the Parc de La Villette, metaphysics and politics were brought closer together because the philosophy of void was used to create new conditions for community action. It can be argued that the source of this philosophy was the perception of errors in existing societies dependent on the shortcomings of traditional metaphysics. Spacing (espacement) was one of the key terms in Derrida’s philosophy, which was also combined with the concepts of différance and chôra. The study of the nature of space, especially its transition from the level of pure possibility to the level of sensual phenomenon, also contributes to understanding how well designed space can have an impact on its audience. This explanation is based on Tschumi’s assumption that the space of the Parc de La Villette contradicts the integrating approaches and instead exposes contradictions, but it does so in a way that combines incompatible properties into a single piece of architecture. The specificity of such integration is similar to the invention of a musical phrase, which is an ideological message: moral and political. Such a thesis may raise doubts, however, if both the clearly adopted assumptions and those deduced from the work allow for their logically ordered presentation then to a limited extent it may be assumed that the work has achieved a connection between a specific philosophy of space and its practical application. Derrida combined the problem of spatiality with the problem of transcendental imagination in the philosophy of Immanuel Kant, who in the first version of Critique of Pure Reason assumed that pure imagination precedes the appearance of time and space, even in their transcendental forms. The imagination in such a situation can be described as a factor activating time and space, which indicates what function is played by movement in this activity. This leads us to recognize that the ultra originary source of pure forms of sensual intuition is movement, which in early Greek philosophy was identified with void and its lack of resistance to phenomena occurring in it. Derrida’s philosophy in search of a certain super-transcendental source of time and space pointed to différance which, like void or the chôra, does not have material features or even any other form of being. Différance is the primary cause of the disruption of motionlessness and the introduction of activity into motionless time and space, thus its activity can be described as spacing (espacement). Derrida’s discoveries in this respect are not entirely original, because Georg Wilhelm Friedrich Hegel already pointed out when examining the present that it is primarily a differential relation (differente Beziehung), which, being seemingly neutral, influences the present with supernatural force and makes it unidentifiable with itself. Differente Beziehung must similarly influence the originary space, negating its initial character by multiplying its divisions and expanding its boundaries. Différance acts by revealing contradictions wherever there is apparent undifferentiation. Tschumi, composing the Parc de La Villette as a variety of void and a set of incompatible layers, followed the rules of différance or the chôra: he made void visible together with its saturation with contradictions. If space can be considered to be the result of the activity of difference, such activity has a certain regularity, which influences the behaviour of its observers. Differences or contradictions fall into a certain rhythm, which can be considered a manifestation of transcendent order. The problem is that what can be considered the source of such order, namely the logos or God, is partly disorder and error. According to descriptions contained in Timaeus, the world is a combination of forces that drive to order with forces of erroneous necessity that resounds in every order and forces it to return to disorder. Derrida denied the possibility of understanding différance as a theological value, even if it were a negative or apophatic theology, but no categorical denial could be perfect. The assumption that différance or the chôra are not endowed with any substance properties cannot deny their activity, and thus a certain force. Already since Democritus, philosophy has multiplied the names of such a force and the contradictory variety of its manifestations, never forgetting also the necessity for reason to withdraw from the possibility of giving its correct characteristics. Such a withdrawal may be interpreted as an expression of respect and, in certain situations, as a cult of the force that precedes reasonableness. The Parc de La Villette, which is an artistic divagation about the contradictions and forces behind them, can be considered as a place of their sublimation, and therefore as a variation of the temple of what differs from order and disorder. IV In the texts that presented the theoretical assumptions of the Parc de La Villette, Tschumi used a large number of terms that contradicted not only the traditional principles of composing architecture, but also negated the rules of social order and the foundations of Western metaphysics. Tschumi’s statements, which are a continuation of his leftist political fascinations from the May 1968 revolution, as well as his interest in the philosophy of French poststructuralism and his collaboration with Derrida, prove that terms such as “disruption”, “dissociation”, “disfunction”, “disjunction” and “dispersion” not only referred to architectural problems but also applied to political criticism and the deepest foundations of thinking itself. His collaboration with Derrida manifested itself primarily in the publication La Case Vide: La Villette 1985, in which the architect’s design drawings and texts explaining his concepts related to the Parc de La Villette were accompanied by an extensive essay by Derrida, which included theoretical problems taken up by Tschumi in a philosophical context. Architectural and philosophical issues were also combined during seven discussion meetings organised by Eisenman, invited by Tschumi to collaborate on the design of the Parc de La Villette. Eisenman, who, like Tschumi, invited Derrida to participate in the design of the park and also led to the publication of Chora L Works: Jacques Derrida and Peter Eisenman, in which his ideas were confronted with Derrida’s philosophical text. In this case, Derrida’s essay was not a direct commentary on the architect’s concepts, but rather a reflection on the question of the chôra presented by Plato in Timaeus. During the discussion and in his essay, Derrida pointed out that the chôra is a component of the created world, yet it does not belong to it, but precedes it. The originality of the chôra is so radical that she also precedes all the factors of creating the world, including ideas and the Demiurge. Thus athesis appeared in the metaphysics of the West that the chôra is a form of active abyss, in relation to which all beings are secondary, both those perfect (as ideas or God) and those created, such as the world, things, people or language. This leads to the conclusion that the chôra does not exist, because all existence is a derivative of the chôra. Nor could the chôra be described, since it is a form of developing a space that is preceded by a lack of space characteristic of the chôra. Derrida intended the chôra to be an instance with an exceptional degree of transcendentalism, an anti-metaphysical instance, but also an a-theological one. However, this attempt failed, both in the field of secular philosophy and in the field of theology. Derrida’s characteristics of the chôra to strengthen its transcendentalism and negation of metaphysics had to be expressed in a language that immediately produces new concepts and a new metaphysics that reproduces the categories of the beginning, the origin or the foundation known from earlier philosophical traditions. All forms of criticism of metaphysics are also inspired by negative, apophatic and mystical theology. The undermining of many concepts of permanent meaning and the introduction of new concepts of unstable meaning, characteristic of the philosophy of deconstruction, had many features of originality, but it was directed towards problems whose solutions repeat, with the use of new vocabulary, the findings known in culture since Democritus. Thus, if apophatic philosophy can be regarded as deconstruction avant la lettre, then deconstruction itself in its late versions began to take on the features of a new religion. The exchange of inspiration between theology and deconstruction was manifested in a series of scientific conferences and publications in which Derrida’s philosophical concepts were interpreted within the scope of religious thought. Theological threads began to be found in such concepts of deconstruction as différance or the chôra, while at the same time Derrida himself undertook in his philosophy to study problems such as the Other (L’Autre) or the Impossible (Impossible), which belonged to newer theological traditions. As a consequence of the new problems, the deconstruction became closer to the features of a new religion. Philosophy, at least from Kant’s time, has tried to create a system that would take over from religion the tasks of setting moral and political goals. Similarly, Derrida has directed his interest towards the problems of democracy and ethics, which would enable their renewal. Attempts to create a new religion (cleared of old metaphors), a new community or a new democracy bring problems and threats which may be no less troublesome than the previous systems. All promises of freedom carry with them threats, the greater the more they strive for perfection. The renewal of existential orders, sometimes carried out by means of violent changes, is a certain repetitive feature of human cultures. Deep changes, however, do not protect against the return of both old gods and old demons. Tschumi and Derrida were shaped in their youth by the atmosphere of leftist rebellion against the moral and political limitations of ossified communities and the imperfections of democracy. The ethical theme distinguishes many of their works, including the Parc de La Villette. The opposition to the metaphysical traditions of philosophy and architecture contained in this park was prompted by specific political situations and resulted from bringing political issues to the level of philosophical considerations. Achievements made at the level of pure concepts were then subject to elevation, to a kind of sacralization, which made them religious concepts. The deconstruction reached for the status of the new religion especially when it found its followers and began to generate moral obligations. In the new situation, terms such as the chôra, l’Autre or the Impossible were absolutized and in relation to them a cult and attitude of adoration emerged. The Parc de La Villtette then gained new post-secular meanings, which allow it to be assigned the function of a Temple of Otherness (L’Autre) and Impossible. V In the traditional sense, a work of art creates an illustration of the outside world, or of a certain text or doctrine. Sometimes it is considered that such an illustration is not literal, but is an interpretation of what is visible, or an interpretation of a certain literary or ideological message. It can also be assumed that a work of art creates its own visual world, a separate story or a separate philosophical statement. Parc de La Villette represents the last of these possibilities: it is a philosophical statement that develops the premises derived from poststructuralist philosophies and the philosophy of deconstruction. The uniqueness of its being status, however, is that it does so not only at the level of the theoretical assumptions, but also through its functioning as an active philosophical work. This means that a park is a happening philosophy. Its activity, however, does not refer only to the present tense, but is also an attempt to penetrate the future, all otherness and impossibility. This kind of activity assumes that the work, in a sense, does not yet fully exist, but is also still produced in the processes of its interpretation. The theoretical foundations of the park included texts by Tschumi, in which he questioned traditional ways of creating a work of architecture, postulating in return the use of a long series of negations, which were comparable to the crisis of metaphysics characteristic of contemporary philosophy. It is therefore no coincidence that the publication containing Tschumi’s theoretical text on Parc de La Villette was accompanied by an essay by Derrida developing some of the architect’s concepts. The next step in integrating philosophy into the process of park design was a series of discussions between Eisenman and Derrida, who completely moved the creation of the park into the world of thoughts, without accentuating the need for their realization in the material reality. The main topic of these discussions was the problem of the chôra, which was taken up by later commentators and used to interpret the park as a work in which the philosophy of the beginning is manifested relating to issues of politics, morality and religion. The park was therefore interpreted as a space of invention within the scope of creating new rules of functioning of the community and democracy. Thinking about the political future may, however, exceed the horizon of ordinary expectations. Although philosophical thought is always connected with contemporary problems and metaphysics sometimes intertwines with current politics, yet at the same time the customs of philosophy also include crossing horizons and thinking about absolute otherness and impossibility. Initially, the chôra, différance, absolute otherness (tout autre) and the Impossible were concepts of pure philosophy of atheistic character, but with the further development of the discussion, more and more theological motifs began to emerge. One of the reasons for this phenomenon was the fact that radical negations of all being, which were contemplated in contemporary philosophy (by Heidegger and Derrida, among others), had previously been manifested in negative and apophatic theologies (by Master Eckhart, among others).Also the category of the “Other”, taken from Emmanuel Levinas, was clearly connected with the thought about God. A further reason for connecting the chôra with the theological thought was the interest in the philosophy of deconstruction expressed by some theologians. John Caputo in particular managed to persuade Derrida to participate in discussions on the current status of religion. In the late period of Derrida’s writing, further statements on religious topics appeared. All these reasons led to posing a question about the identity of the chôra and God. Although there were no satisfactory conclusions on this issue, the discussion was also important to create an interpretation of the park as a place of worship. The chôra, representing, according to Plato, the preoriginal emptiness is the place of every beginning, but it turns out that it is not neutral to the being created in it. The chôra deposits itself in every being as an irremovable beginning that interferes with its stability. The chôra, therefore, forces us into a palintropical movement, but it also turns out to be a pure compulsion, an erring necessity and a fundamental force from which, in the human perception, motifs useful to the individual and to the community are extracted. All definitions of this force, including its anthropomorphisation, are formulated in such a way that they allow for building private and collective morality upon them. Such definitions are changed depending on variable political situations. It is difficult to determine whether in the processes of changes in the formulation of “God’s names” any essential value is retained, which is not subject to change. The current definitions of the chôra (God?), which can be found, for example, in the philosophy of Caputo, stress that she is a combination of various and contradictory forces. This characteristic inherits much of Plato’s concept, reminds us of Master Eckhart’s views on Gottheit and, at the same time, is not unfamiliar to Tschumi, whose essays were an apologia of contradictions. The current concept of chôra, transferred into the sphere of politics, is the praise of social diversity and the protection of the difference from the forces of order. In the Parc de La Villette, the future community and democracy were elevated as a system of safe existence of individuals in all their singularity. The park is a temple of a future community in which individual beings have nothing in common. (shrink)

The logic of indicative conditionals remains the topic of deep and intractable philosophical disagreement. I show that two influential epistemic norms—the Lockean theory of belief and the Ramsey test for conditional belief—are jointly sufficient to ground a powerful new argument for a particular conception of the logic of indicative conditionals. Specifically, the argument demonstrates, contrary to the received historical narrative, that there is a real sense in which Stalnaker’s semantics for the indicative did succeed in capturing the logic (...) of the Ramseyan indicative conditional. (shrink)

The aim of this paper was to prove that reduction of social, cultural and spiritual explanation of religion, to the purely biological one, is unattainable, and what is more, that such efforts are redundant and give threat to the quality of science, as well as to the quality of religious beliefs. With regard to elementary methodological scientific criteria, the examples of limitation in biological investigating and explaining of religion was shown. Subsequently, the paper presents a few important logical (...) mistakes (pseudoarguments) as examples of ontological underinterpretation of scientific facts. Finally, the discourse concentrates on the threats (to science and religion) that are associated with biological investigation of religion. (shrink)

In this paper, I examine Quine's views on the epistemology of logic. According to Quine's influential holistic account, logic is central in the “web of belief” that comprises our overall theory of the world. Because of this, revisions to logic would have devastating systematic consequences, and this explains why we are loath to make such revisions. In section1, I clarify this idea and thereby show that Quine actually takes the web of belief to have asymmetrical internal structure. This (...) raises two puzzles. First, as I show in section 2, Quine's mature thoroughly naturalized view has it that logic is simply obvious, and this is explains why we do not typically consider revising it. While Quine presents this naturalized view as a way to make good on his earlier metaphor of centrality in a web of belief, I argue that the resources of Quine's naturalized epistemology cannot adequately explain why we are reluctant to revise logic. And, Quine seems to recognize this point himself. In light of this, I explain in section 3 how Quine can allow that our overall scientific theory has systematic structure in a way that is consistent with his naturalistic strictures. Second, the asymmetrical internal structure of the web of belief seems to be inconsistent with its being a holistic web at all. I defuse this problem in section 4 by showing how Quine distinguishes between structural and confirmational considerations. I close by using this distinction to show how Quine's view can evade Michael Friedman’s criticisms, and allow for important methodological distinctions between areas of the web of belief. (shrink)

Hegel attacks Kantian morality most often without stating an opposing moral theory, tending to subsequently take up discussion of religion or the state. Commentators have variously suggested the logical consequence of Hegel's position is "the dissolution of ethics in sociology" without "room for personal morality of any kind" or that Hegel's argument is against Kantian <i>Moralitat</i>, which allows the private individual to appeal beyond social mores to universal moral standards, with Hegel insisting that concrete values come instead from <i>Sittlichkeit</i>, (...) the social order. If thinking of morality as a purely private matter of the individual's conscience seems too abstract, the Hegelian criticisms should show that moral reflections are vacuous unless they take account of the social world in which they will be realized as concrete actions. From the Hegelian's perspective on morality as seen from the more inclusive context of <i>Sittlichkeit</i>, social action that is also moral will not need to be analyzed in terms of Kant's metaphysical dualisms between reason and inclination, intentions and consequences, or the sensible and the intelligible realms. Whereas Kant thinks moral theory leads directly to religious and metaphysical postulates, Hegel deliberately leads it in another direction. He can be understood historically as going beyond Kant's effort to secularize moral philosophy. Kant begins this process by grounding moral philosophy in reason alone, not in religion. Religious postulates may follow from moral beliefs, says Kant, but morality is not derived from religious premisses. In going from private moral conscience not to religious beliefs but to social, political, and historical considerations (which could include religion seen as a social institution), Hegel extends the process of secularizing moral philosophy." Marcuse and Knox could thus both be right, since Hegel's goal is not to replace Kant's moral philosophy with another, competing moral philosophy, but to accept it, while recognizing its limitations, as a special case of a larger theory of social action. In the Hegelian jargon, from a standpoint recognizing Sittlichkeit, Moralitdt is thus <i>aufgehoben</i>, that is, Kant's formal procedures will be both "negated" (criticized for their limitations) and "preserved" (embedded in a more inclusive philosophy). (shrink)

This paper takes two tasks. The one is elaborating on the relationship of inductive logic with decision theory to which later Carnap planned to apply his system (§§1-7); this is a surveying side of this article. The other is revealing the property of our prediction of the future, subjectivity (§§8-11); this is its philosophical aspect. They are both discussed under the name of belief in causation. Belief in causation is a kind of “degree of belief” born about (...) the causal effect of the action. As such, it admits of the analysis by inductive logic. (shrink)

In researching presuppositions dealing with logic and dynamic of belief we distinguish two related parts. The first part refers to presuppositions and logic, which is not necessarily involved with intentional operators. We are primarily concerned with classical, free and presuppositonal logic. Here, we practice a well known Strawson’s approach to the problem of presupposition in relation to classical logic. Further on in this work, free logic is used, especially Van Fraassen’s research of the role of presupposition in supervaluations (...) class='Hi'>logical systems. At the end of the first part, presuppositional logic, advocated by S.K. Thomason, is taken into consideration. The second part refers to the presuppositions in relation to the logic of the dynamics of belief. Here the logic of belief change is taken into consideration and other epistemic notions with immanent mechanism for the presentation of the dynamics. Three representative and dominant approaches are evaluated. First, we deal with new, less classical, situation semantics. Besides Strawson’s theory, the second theory is the theory of the belief change, developed by Alchourron, Gärdenfors, and Makinson (AGM theory). At the end, the oldest, universal, and dominant approach is used, recognized as Hintikka’s approach to the analysis of epistemic notions. (shrink)

In artificial intelligence (AI), responses generated by machine-learning models (most often large language models) may be unfactual information presented as a fact. For example, a chatbot might state that the Mona Lisa was painted in 1815. Such phenomenon is called AI hallucinations, seeking inspiration from human psychology, with a great difference of AI ones being connected to unjustified beliefs (that is, AI “beliefs”) rather than perceptual failures). -/- AI hallucinations may have their source in the data itself, that is, the (...) source content, or in the training procedure, i.e. the way the knowledge was encoded in the model’s parameters, so that errors in encoding and decoding textual and non-textual representations can cause hallucinations. In this paper, we will observe how such errors come to life and how they might be mitigated. For this purpose, we will analyze the usability of justification logics, to behave as a proof checker for validating the correctness of large language models’ (LLM) responses. Justification logic was developed by S. Artemov, and later on mostly by Artemov and M. Fitting, deriving its main idea from the logic of proofs (LP): knowledge and belief modalities are seen as justification terms, i.e. t:X stands for t is a (proper) justification for X. Justification logic originated from attempts to create semantics for intuitionistic logic where proofs were the most proper justifications, but in further development, justification logic could be applied to different kinds of justifications). With the recent attempts to mitigate incorrect LLM responses, we will analyze various guardrails that are currently used for LLM responses, and see how the logic of justification may provide its benefits as an AI safety layer against false data. (shrink)

The paper surveys the currently available axiomatizations of common belief (CB) and common knowledge (CK) by means of modal propositional logics. (Throughout, knowledge- whether individual or common- is defined as true belief.) Section 1 introduces the formal method of axiomatization followed by epistemic logicians, especially the syntax-semantics distinction, and the notion of a soundness and completeness theorem. Section 2 explains the syntactical concepts, while briefly discussing their motivations. Two standard semantic constructions, Kripke structures and neighbourhood structures, are introduced (...) in Sections 3 and 4, respectively. It is recalled that Aumann's partitional model of CK is a particular case of a definition in terms of Kripke structures. The paper also restates the well-known fact that Kripke structures can be regarded as particular cases of neighbourhood structures. Section 3 reviews the soundness and completeness theorems proved w.r.t. the former structures by Fagin, Halpern, Moses and Vardi, as well as related results by Lismont. Section 4 reviews the corresponding theorems derived w.r.t. the latter structures by Lismont and Mongin. A general conclusion of the paper is that the axiomatization of CB does not require as strong systems of individual belief as was originally thought- only monotonicity has thusfar proved indispensable. Section 5 explains another consequence of general relevance: despite the "infinitary" nature of CB, the axiom systems of this paper admit of effective decision procedures, i.e., they are decidable in the logician's sense. (shrink)

We consider a basic logic with two primitive uni-modal operators: one for certainty and the other for plausibility. The former is assumed to be a normal operator, while the latter is merely a classical operator. We then define belief, interpreted as “maximally plausible possibility”, in terms of these two notions: the agent believes \ if she cannot rule out \ ), she judges \ to be plausible and she does not judge \ to be plausible. We consider four interaction (...) properties between certainty and plausibility and study how these properties translate into properties of belief. We then prove that all the logics considered are minimal logics for the highlighted theorems. We also consider a number of possible interpretations of plausibility, identify the corresponding logics and show that some notions considered in the literature are special cases of our framework. (shrink)

Darwiche and Pearl’s seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. Most suggestions have resulted in a form of ‘reductionism’ that identifies belief states with orderings of worlds. However, this position has recently been criticised as being unacceptably strong. Other proposals, such as the popular principle (P), aka ‘Independence’, characteristic of ‘admissible’ operators, remain commendably more modest. (...) In this paper, we supplement the DP postulates and (P) with a number of novel conditions. While the DP postulates constrain the relation between a prior and a posterior conditional belief set, our new principles notably govern the relation between two posterior conditional belief sets obtained from a common prior by different revisions. We show that operators from the resulting family, which subsumes both lexicographic and restrained revision, can be represented as relating belief states associated with a ‘proper ordinal interval’ (POI) assignment, a structure more fine-grained than a simple ordering of worlds. We close the paper by noting that these operators satisfy iterated versions of many AGM era postulates, including Superexpansion, that are not sound for admissible operators in general. (shrink)

A lean hylomorphism stands as a metaphysical holy grail. An embarrassing feature of traditional hylomorphic ontologies is prime matter. Prime matter is both so basic that it cannot be examined (in principle) and its engagement with the other hylomorphic elements is far from clear. One particular problem posed by prime matter is how it is to be understood both as a principle of individuation for material substances and as pure potency. I present Thomas Aquinas’s way of squeezing some intelligibility out (...) of prime matter by modeling it on the idea of logical genus. Such a modeling provides insight into understanding prime matter as substratum, as maximally indeterminate, and as ontologically vague. One of the unusual but exciting things that fall out from this analysis of prime matter is the Entirety Thesis: “For any substance x, if x has prime matter then the prime matter of x is the same* as x,” where ‘same*’ is understood as “indeterminately identical.”. (shrink)

JOHN CORCORAN AND WAGNER SANZ, Disbelief Logic Complements Belief Logic. Philosophy, University at Buffalo, Buffalo, NY 14260-4150 USA E-mail: [email protected] Filosofia, Universidade Federal de Goiás, Goiás, GO 74001-970 Brazil E-mail: [email protected] -/- Consider two doxastic states belief and disbelief. Belief is taking a proposition to be true and disbelief taking it to be false. Judging also dichotomizes: accepting a proposition results in belief and rejecting in disbelief. Stating follows suit: asserting a proposition conveys belief and (...) denying conveys disbelief. Traditional logic implicitly focused on logical relations and processes needed in expanding and organizing systems of beliefs. Deducing a conclusion from beliefs results in belief of the conclusion. Deduction presupposes consequence: one proposition is a consequence of a set of a propositions if the latter logically implies the former. The role of consequence depends on its being truth-preserving: every consequence of a set of truths is true. This paper, which builds on previous work by the second author, explores roles of logic in expanding and organizing systems of disbeliefs. Aducing a conclusion from disbeliefs results in disbelief of the conclusion. Aduction presupposes contrequence: one proposition is a contrequence of a set of propositions if the set of negations or contradictory opposites of the latter logically implies that of the former. The role of contrequence depends on its being falsity-preserving: every contrequence of a set of falsehoods is false. A system of aductions that includes, for every contrequence of a given set, an aduction of the contrequence from the set is said to be complete. Historical and philosophical discussion is illustrated and enriched by presenting complete systems of aductions constructed by the second author. One such, a natural aduction system for Aristotelian categorical propositions, is based on a natural deduction system attributed to Aristotle by the first author and others. ADDED NOTE: Wagner Sanz reconstructed Aristotle’s logic the way it would have been had Aristole focused on constructing “anti-sciences” instead of sciences: more generally, on systems of disbeliefs. (shrink)

Logical reasoning is not only a component of religious faith (cf., for instance, the "Golden rule"), but, in addition, the religious faith itself can be conceived as a logical pragmatic function applied to sentences and their meanings. Pragmatic role of religious faith is shown on the examples of the analogy of seed and spoken word (e.g., Mt 13:3-23) and on the degrees of faith described in the episode about Nicodemus (John 3). Pragmatics adds (different grades of) perseverance to (...) the correctness of reasoning and to the truth-preservation of the consequence relation. Correspondingly, religious faith is described by formally defined model and satisfaction relation, which are applied to and examined on the text of John 3. (shrink)

Abstract. Gettier’s famous examples intended to show that knowledge cannot always be equated with justified true belief. The Gettier problem can also be considered as a problem for topological epistemic logic: If knowledge and justified belief are conceived as topological operators K and B on topological spaces (to be considered as universes of possible worlds), one may ask whether it happens that there is a proposition A such that KA ≠ A & BA or not. If this is (...) the case, the epistemological logic defined by the topological operators K and B may be said to be non-traditional since there is for them a “Gettier proposition” where knowledge does not coincide with justified true belief. As far as we know, for the first time, this topological Gettier problem is discussed in Steinvold’s PhD dissertation (Steinsvold 2012). In Baltag, Bezhanishvili, Özgün, and Smets (2013), Steinvold’s co-derived set account is criticized since it can be easily “Gettierized”. Baltag et alii claim (without proof) that their topological account of Stalnaker’s logic KB of knowledge and belief does not have this flaw. In the following we will give some topological conditions that determine whether a topological KB model does or does not cope with the Gettier challenge. First, it will be shown that every KB model defines a (topologically slightly simplified) model that is rather similar to it but a is a model of traditional JTB (knowledge = justified true belief) logic of knowledge and belief. The existence of such doppelgangers of all KB models may be read as a qualified and partial topological rehabilitation of traditional JTB epistemology. Second, we consider the Gettier problem for a special class of models of Stalnaker’s combined logic of knowledge and belief KB, namely, for T0 Alexandroff spaces. We prove that, that almost all Alexandroff spaces do not face Gettier counterexamples. Third, we prove that the Stone spaces of Boolean algebras of regular closed subsets of Hausdorff (or T2) spaces X do not face Gettier counterexamples if the X are not pseu–docompact, and these Stone spaces do face Gettier counterexamples for compact spaces X. Succinctly formulated, Stalnaker’s KB logic of knowledge and belief can avoid Gettier problems for some models, while it falls back to traditional pre-Gettier JTB epistemology for other models. In contrast, co-derived set semantics is doomed to fail always in the sense that its models always fall prey to Gettier counterexamples. (shrink)

As George Boole saw it, the laws of logic are the laws of thought, and by this he meant, not that human thought is actually governed by the laws of logic, but, rather, that it should be. Boole’s view that the laws of logic have normative implications for how we ought to think is anything but an outlier. The idea that violating the laws of logic involves epistemic impropriety has seemed to many to be just obvious. It has seemed especially (...) obvious to those who see propositional justification as more fundamental than doxastic justification. Whatever other principles are required for defining propositional justification, the laws of logic seem indispensable. The idea that violation of the laws of logic involves some sort of epistemic impropriety—whatever the peculiarities of our psychology may be—has served as a fixed point around which defenders of the fundamentality of propositional justification are united, whatever their other differences. This paper challenges that common thread in defenses of the fundamentality of propositional justification. It is argued that the laws of logic have no bearing whatever on epistemic justification. Once we see why this should be so, the way is paved for seeing why it is that doxastic justification is more fundamental than propositional justification. (shrink)

In this paper we distinguish between various kinds of doxastic theories. One distinction is between informal and formal doxastic theories. AGM-type theories of belief change are of the former kind, while Hintikka’s logic of knowledge and belief is of the latter. Then we distinguish between static theories that study the unchanging beliefs of a certain agent and dynamic theories that investigate not only the constraints that can reasonably be imposed on the doxastic states of a rational agent but (...) also rationality constraints on the changes of doxastic state that may occur in such agents. An additional distinction is that between non-introspective theories and introspective ones. Non-introspective theories investigate agents that have opinions about the external world but no higher-order opinions about their own doxasticnstates. Standard AGM-type theories as well as the currently existing versions of Segerberg’s dynamic doxastic logic (DDL) are non-introspective. Hintikka-style doxastic logic is of course introspective but it is a static theory. Thus, the challenge remains to devise doxastic theories that are both dynamic and introspective. We outline the semantics for truly introspective dynamic doxastic logic, i.e., a dynamic doxastic logic that allows us to describe agents who have both the ability to form higher-order beliefs and to reflect upon and change their minds about their own (higher-order) beliefs. This extension of DDL demands that we give up the Preservation condition on revision. We make some suggestions as to how such a non-preservative revision operation can be constructed. We also consider extending DDL with conditionals satisfying the Ramsey test and show that Gärdenfors’ well-known impossibility result applies to such a framework. Also in this case, Preservation has to be given up. (shrink)