Is logic normative for belief? A standard approach to answering this question has been to investigate bridge principles relating claims of logical consequence to norms for belief. Although the question is naturally an epistemic one, bridge principles have typically been investigated in isolation from epistemic debates over the correct norms for belief. In this paper we tackle the question of whether logic is normative for belief by proposing a Kripkean model theory accounting for the interaction between (...) logical, doxastic, epistemic and deontic notions and using this model theory to show which bridge principles are implied by epistemic norms that we have independent reason to accept, for example, the knowledge norm and the truth norm. We propose a preliminary theory of the interaction between logical, doxastic, epistemic and deontic notions that has among its commitments bridge principles expressing how logic is normative for belief. We also show how our framework suggests that logic is exceptionally normative. (shrink)

One explanation of rational peer disagreement is that agents find themselves in an epistemically permissive situation. In fact, some authors have suggested that, while evidence could be impermissive at the intrapersonal level, it is permissive at the interpersonal level. In this paper, I challenge such a claim. I will argue that, at least in cases of rational disagreement under full disclosure, there cannot be more interpersonal epistemically permissive situations than there are intrapersonal epistemically permissive situations. In other words, with respect (...) to cases of disagreement under full disclosure, I will argue that there is a necessary connection between interpersonal permissiveness and its intrapersonal counterpart. Specifically, I claim that a plausible principle of correct argumentation supports such a bridge. (shrink)

Fitch’s Paradox shows that if every truth is knowable, then every truth is known. Standard diagnoses identify the factivity/negative infallibility of the knowledge operator and Moorean contradictions as the root source of the result. This paper generalises Fitch’s result to show that such diagnoses are mistaken. In place of factivity/negative infallibility, the weaker assumption of any ‘level-bridging principle’ suffices. A consequence is that the result holds for some logics in which the “Moorean contradiction” commonly thought to underlie the result is (...) in fact consistent. This generalised result improves on the current understanding of Fitch’s result and widens the range of modalities of philosophical interest to which the result might be fruitfully applied. Along the way, we also consider a semantic explanation for Fitch’s result which answers a challenge raised by Kvanvig. (shrink)

How should we understand validity? A standard way to characterize validity is in terms of the preservation of truth (or truth in a model). But there are several problems facing such characterizations. An alternative approach is to characterize validity epistemically, for instance in terms of the preservation of an epistemic status. In this paper, I raise a problem for such views. First, I argue that if the relevant epistemic status is factive, such as being in a position to know or (...) having conclusive evidence for, then the account runs into trouble if we endorse certain familiar logical principles. Second, I argue that if the relevant epistemic status is non-factive, such as is rationally committed to or has justification for believing, then a similar problem arises if we endorse the logical principles as well as a sufficiently strong epistemic “level-bridging” principle. Finally, I argue that an analogous problem arises for the most natural characterization of validity in terms of rational credence. (shrink)

For smart cities, data-driven innovation promises societal benefits and increased well-being for residents and visitors. At the same time, the deployment of data-driven innovation poses significant ethical challenges. Although cities and other public-sector actors have increasingly adopted ethical principles, employing them in practice remains challenging. In this commentary, we use a virtue-based approach that bridges the gap between abstract principles and the daily work of practitioners who engage in and with data-driven innovation processes. Inspired by Aristotle, we describe (...) practices of data-driven innovation in a smart city applying the concepts of virtue and phronêsis, meaning good judgment of and sensitivity to ethical issues. We use a dialogic case-study approach to study two cases of data-driven innovation in the city of Helsinki. We then describe as an illustration of how our approach can help bridge the gap between concrete practices of data-driven innovation and high-level principles. Overall, we advance a theoretically grounded, virtue-based approach, which is practice oriented and linked to the daily work of data scientists and other practitioners of data-driven innovation. Further, this approach helps understand the need for and importance of individual application of phronêsis, which is particularly important in public-sector organizations that can experience gaps between principle and practice. This importance is further intensified in cases of data-driven innovation in which, by definition, novel and unknown contexts are explored. (shrink)

This essay examines an innovative cosmological hypothesis that proposes a connection between black holes and white holes via Einstein-Rosen bridges in the pre-Big Bang regime. Central to this proposal is a new "cosmic information preservation principle" that suggests observational limits are not constraints but essential features of our expanding cosmos. Drawing from observations of the unusual gamma-ray burst GRB 060614, early universe supermassive black holes, and cosmic microwave background radiation anomalies, the hypothesis offers a novel framework for understanding universe formation (...) and information preservation across cosmic boundaries. This work demonstrates how theoretical imagination, guided by observational phenomena, can advance our understanding of fundamental physics and cosmology. (shrink)

Recent literature has paid attention to a demarcation problem for evolutionary debunking arguments. This is the problem of asking in virtue of what regulative metaepistemic norm evolutionary considerations either render a belief justified, or debunk it as unjustified. I examine the so-called ‘Milvian Bridge principle’ A new science of religion, Routledge, New York, 2012; Sloan, McKenny, Eggelson Darwin in the 21st century: nature, humanity, and God, University Press, Notre Dame, 2015)), which offers exactly such a called for regulative metaepistemic (...) norm. The Milvian Bridge principle suggests that the metaepistemic norm is: adaptive reliability for truth of cognitive processes that the existence of corresponding truth-making facts evolutionary theory justifies. I argue that the Milvian Bridge principle is problematic on a number of counts, something that is shown via spiraling ‘companions in guilt arguments’. Finally, I consider ‘the core reductionist objection’ to the critique of the Milvian Bridge principle and offer a response. I conclude that the Milvian Bridge principle is destabilized. (shrink)

Efforts to bridge emotion theory with neurobiology can be facilitated by dynamic systems (DS) modeling. DS principles stipulate higher-order wholes emerging from lower-order constituents through bidirectional causal processes cognition relations. I then present a psychological model based on this reconceptualization, identifying trigger, self-amplification, and self-stabilization phases of emotion-appraisal states, leading to consolidating traits. The article goes on to describe neural structures and functions involved in appraisal and emotion, as well as DS mechanisms of integration by which they interact. (...) These mechanisms include nested feedback interactions, global effects of neuromodulation, vertical integration, action-monitoring, and synaptic plasticity, and they are modeled in terms of both functional integration and temporal synchronization. I end by elaborating the psychological model of emotion–appraisal states with reference to neural processes. (shrink)

This paper examines an argument by Schaffer (2017) that aims to prove how, contrary to what many philosophers hold, there is no special explanatory gap occurring in the connection between the physical and the phenomenal. This is because a gap of the same kind can be found in every connection between a more fundamental and a less fundamental level of reality. These gaps lurk everywhere in nature. For Schaffer, they can be bridged by means of substantive metaphysical principles such (...) as grounding principles. He thus puts forward a version of grounding-based physicalism, which is supposed to provide this kind of substantive bridge principle. My main contention is as follows: even if Schaffer’s argument indeed proves the existence of a gap in every connection between fundamental and derivative entities, and such gaps can be bridged by means of grounding principles, a different gap remains open in the psycho-physical connection. (shrink)

We reflect on the nature of corporate codes of conduct is this article. Based on John Austin’s speech act theory, four characteristics of a performative concept of corporate codes will be introduced: 1) the existential self-performative of the firm identity, 2) which is demanded by and responsive to their stakeholders; 3) Because corporate codes are structurally threatened by the possibility of failure, 4) embracing the code not only consists in actual corporate responsible behaviour in light of the code, but in (...) the incessant recapturing of the code in the struggle of firms against the possible incongruence between their ethical principles and their actual responsible behaviour. A performative concept of corporate codes helps to bridge classical dichotomies like individualist versus collectivist approaches of moral agency and restrictive versus empowering ethics, and opens a new perspective on the interaction between individual ethical behaviour and the corporate institutionalisation of codes. (shrink)

A common view relating compositional semantics and the objects of assertion holds the following: Sentences φ and ψ expresses the same proposition iff φ and ψ have the same modal profile. Following Dummett, Evans, and Lewis, Stanley argues that this view is fundamentally mistaken. According to Dummett, we must distinguish the semantic contribution a sentence makes to more complex expressions in which it occurs from its assertoric content. Stojnić insists that views which distinguish the roles of content and semantic value (...) must nevertheless ensure a tight connection between the two. But, she contends, there is a crucial disanalogy between the views that follow Lewis and the views that follow Dummett. Stanley’s Dummettian view is argued to contain a fatal flaw: On such views, there is no way to secure an appropriate connection between semantic value and a theoretically motivated notion of assertoric content. I will review the background issues from Dummett, Evans, Lewis, and Stanley, and provide a principled way of bridging the gap between semantic value and a theoretically motivated notion of assertoric content. (shrink)

Ontological principles are needed in order to bridge the gap between medical and biological information in a robust and computable fashion. This is essential in order to draw inferences across the levels of granularity which span medicine and biology, an example of which include the understanding of the roles of tumor markers in the development and progress of carcinoma. Such information integration is also important for the integration of genomics information with the information contained in the electronic patient (...) records in such a way that real time conclusions can be drawn. In this paper we describe a large multi-granular datasource built by using ontological principles and focusing on the case of colon carcinoma. (shrink)

“Dialectic” has been a matter of growing interest in contemporary philosophy. The present article analyzes dialectical methods and positions them by reference to two paradigmatic texts of German idealism and analytic philosophy, i.e. J.G. Fichte’s Science of Knowing (1804) and J. McDowell’s Mind and World. Both dialectical approaches will be interpreted with regard to their contribution in the debate on reductionism and anti-reductionism: both Fichte and McDowell claim that philosophical positions and logical terms stand in a dualistic relationship to one (...) another, on the one hand, but are separated by a gulf, on the other. I will argue that for McDowell dialectic seems to be an alternative to one-sided reductionisms as well as to normal anti-reductionistic holism. Furthermore, for Fichte dialectic is an adequate method for describing the relationship of reductionism and anti-reductionism itself. Both see in dialectic a technique for bridging the gulf between binary opposite terms of logic as well as mutually exclusive positions, such as mind and world, subject and object, or idealism and realism. (shrink)

With the existing commitments to climate change mitigation, global warming is likely to exceed 2°C and to trigger irreversible and harmful threshold effects. The difference between the reductions necessary to keep the 2°C limit and those reductions countries have currently committed to is called the ‘emissions gap’. I argue that capable states not only have a moral duty to make voluntary contributions to bridge that gap, but that complying states ought to make up for the failures of some other (...) states to comply with this duty. While defecting or doing less than one’s fair share can be a good move in certain circumstances, it would be morally wrong in this situation. In order to bridge the emissions gap, willing states ought to take up the slack left by others. The paper will reject the unfairness-objection, namely that it is wrong to require agents to take on additional costs to discharge duties that are not primarily theirs. Sometimes what is morally right is simply unfair. (shrink)

This paper introduces Holistic Free Will (HFW), a transformative framework that reconceptualizes autonomy as a dynamic, relational, and ethically aspirational process embedded within structured realities. Distinct from traditional theories like libertarian free will and compatibilism, HFW integrates interdisciplinary insights from neuroscience, moral philosophy, and cultural traditions to provide a comprehensive understanding of free will that aligns individual agency with systemic and relational contexts. HFW emphasizes structured reality as comprising four dimensions—natural laws, human constructs, social norms, and personal histories—that act not (...) as constraints but as enablers of ethical autonomy and moral development. Central to the framework are mechanisms such as reflective veto, self-reflection, and virtue cultivation, which empower individuals to navigate deterministic influences and align actions with enduring ethical principles like justice, empathy, and humility. HFW’s practical applications across governance, education, and social systems, demonstrating its capacity to address global challenges such as social justice, environmental sustainability, and relational harmony. Case studies illustrate how structured realities foster personal and collective growth, positioning HFW as a tool for bridging theoretical insights and actionable strategies. By advancing autonomy as a relational and developmental process, HFW offers a groundbreaking model for ethical agency and societal transformation. (shrink)

Physics has been slowly and reluctantly beginning to address the role and fundamental basis of the ‘observer’ which has until now also been considered metaphysical and beyond the mandate empirical rigor. It is suggested that the fundamental premise of the currently dominant view of ‘Cognitive Theory’ - “Mind Equals Brain” is erroneous; and the associated belief that the ‘Planck scale, ‘the so-called basement level of reality’, as an appropriate arena from which to model psycho-physical bridging is also in error. In (...) this paper we delineate a simple, inexpensive experimental design to ‘crack the so-called cosmic egg’ thereby opening the door to largescale extra dimensions (LSXD) tantamount to the regime of the unified field and thus awareness. The methodology surmounts the quantum uncertainty principle in a manner violating Quantum Electrodynamics, (QED), a cornerstone of modern theoretical physics, by spectrographic analysis of newly theorized Tight-Bound State (TBS) Bohr orbits in ‘continuous-state’ transition frequencies of atomic hydrogen. If one wonders why QED violation in the spectra of atomic hydrogen relates to solving the mind-body (observer) problem; consider this a 1st wrench in a forthcoming tool box of Unified Field Mechanics, UF that will soon enough in retrospect cause the current tools of Classical and Quantum Mechanics to appear as stone axes. Max Planck is credited as the founder of quantum mechanics with his 1900 quantum hypothesis that energy is radiated and absorbed discretely by the formulation, E = hv. Empirically implementing this next paradigm shift utilizing parameters of the long sought associated ‘new physics’ of the 3rd regime (classical-quantum- unified) allows access to LSXD of space; thus pragmatically opening the domain of mental action for the 1st time in history. This rendering constitutes a massive paradigm shift to Unified Field Theory creating a challenge for both the writer and the reader! (shrink)

Unified Proof Set: Introducing the Next Paradigm of Understanding This set of interconnected papers collectively introduces a groundbreaking framework to achieve a Unified Field Theory (UFT), solving two of the Millennium Prize Problems (Riemann Hypothesis and Navier-Stokes Existence and Smoothness), and providing a comprehensive explanation for relational dynamics in science, ethics, and the cosmos. Papers in the Unified Proof Set 0. Introduction to the Unified Proof Set Abstract : This paper introduces the overarching purpose and framework of the Unified Proof (...) Set. It outlines the interconnected nature of the subsequent works, offering insights into their individual contributions while presenting a unified vision. 01. Relational Unity Equation of the Unified Field: Explained Abstract : A user-friendly breakdown of the Equation of Relational Unity, designed for both scientific and lay audiences. This paper provides an intuitive understanding of the mathematical framework that supports the Unified Field Theory. 1. Hyper-Conjugation: Achieving Unified Field Theory Abstract : Hyper-conjugation is introduced as the foundational mechanism enabling the mathematical representation of the Unified Field. By integrating relational dynamics and harmonic systems, this framework establishes a robust pathway to unify microcosmic and macrocosmic phenomena. 2. The Implicate Order: A New Paradigm for Universal Understanding Abstract : This work bridges the physical and metaphysical through a comprehensive exploration of the implicate order, synthesizing the relational coherence that emerges from entangled systems and their interplay within the unified field. 3. The Equation of Relational Unity Abstract : The centrepiece of the Unified Proof Set, this paper introduces the mathematical equation underpinning the Unified Field. The Equation of Relational Unity establishes a framework where harmonic coherence and energy flow govern all physical and relational dynamics across dimensions. 4. A Mathematical Proof for Ethics and Stability Abstract : Expanding on the implications of the Unified Field, this paper offers a mathematical proof for ethical behaviour as a stabilizing mechanism within dynamic systems. The work explores the relationship between coherence, intention, and the emergent harmonics of stability. 5. Resonance and Symmetry: A New Framework for the Riemann Hypothesis Abstract : This paper recontextualizes the Riemann Hypothesis through resonance and symmetry principles derived from the Unified Field Theory. The solution highlights the harmonic consistency within prime number distribution, offering a novel mathematical approach. 6. Unified Resonance in Fluid Dynamics: A Novel Proof for Navier-Stokes Existence and Smoothness Abstract : Building on the relational principles of the Unified Field, this work solves the Navier-Stokes Existence and Smoothness problem. The proof demonstrates how fluid motion remains stable through harmonic resonance, bridging chaos and coherence. Purpose of the Unified Proof Set The Unified Proof Set represents the culmination of decades of inquiry into the nature of existence. It seeks to bridge scientific, mathematical, ethical, and philosophical paradigms, providing a harmonious framework for future research and application. This work not only resolves significant open questions in mathematics and physics but also offers humanity a blueprint for sustainable, ethical, and innovative solutions to its most pressing challenges. Protection and Use Statement This work is published under the Creative Commons Attribution 4.0 International (CC BY 4.0) license, allowing for redistribution and adaptation, provided that proper attribution is given to the author. Any derivative works must explicitly credit the original creator and clearly distinguish modifications from the original content. The author asserts the originality and integrity of this work, intending it to be used ethically and for the advancement of science, knowledge, and humanity. Any misuse, misrepresentation, or unethical application of this work is strictly discouraged. For citation, acknowledgment, and further inquiries, please reference the DOI provided or contact the author directly. Eliahi Priest The Priest Group Pty Ltd AUSTRALIA. (shrink)

The aim of this paper is to begin a conversation about how we read and write about Nietzsche and, related to this, other figures in the history of philosophy. The principle of charity can appear to be a way to bridge two dif-ferent interpretative goals: getting the meaning of the text right and offering the best philosophy. I argue that the principle of charity is multiply ambiguous along three different dimensions, which I call “unit,” “mode,” and “strength”: consequently, it (...) is not a single, neutral or independent principle to which we can helpfully appeal and it cannot, in itself, perform this bridging function. Nietzsche, I suggest, is particularly ill suited to some forms of charitable reading. I compare charity to what I call “misreporting” a philosopher’s words, in order to highlight some problematic structural similarities. Finally, I assess what charity might be doing instead, if it is not intended to bridge meaning and best philosophy. (shrink)

In his “Bridging mainstream and formal ontology”, Augusto (2021) gives an excellent analysis of Dietrich von Freiberg’s idea of using causality as a partitioning principle for upper ontologies. For this Dietrich’s notion of extrinsic principles is crucial. The question whether causation can and indeed should be used as a partitioning principle for ontologies is discussed using mathematics and physics as examples.

With recent advancements in systems engineering and artificial intelligence, autonomous agents are increasingly being called upon to execute tasks that have normative relevance. These are tasks that directly—and potentially adversely—affect human well-being and demand of the agent a degree of normative-sensitivity and -compliance. Such norms and normative principles are typically of a social, legal, ethical, empathetic, or cultural nature. Whereas norms of this type are often framed in the abstract, or as high-level principles, addressing normative concerns in concrete (...) applications of autonomous agents requires the refinement of normative principles into explicitly formulated practical rules. This paper develops a process for deriving specification rules from a set of high-level norms, thereby bridging the gap between normative principles and operational practice. This enables autonomous agents to select and execute the most normatively favourable action in the intended context premised on a range of underlying relevant normative principles. In the translation and reduction of normative principles to SLEEC rules, we present an iterative process that uncovers normative principles, addresses SLEEC concerns, identifies and resolves SLEEC conflicts, and generates both preliminary and complex normatively-relevant rules, thereby guiding the development of autonomous agents and better positioning them as normatively SLEEC-sensitive or SLEEC-compliant. (shrink)

Two goals - improving replicability and accountability of Machine Learning research respectively, have accrued much attention from the AI ethics and the Machine Learning community. Despite sharing the measures of improving transparency, the two goals are discussed in different registers - replicability registers with scientific reasoning whereas accountability registers with ethical reasoning. Given the existing challenge of the Responsibility Gap - holding Machine Learning scientists accountable for Machine Learning harms due to them being far from sites of application, this paper (...) posits that reconceptualizing replicability can help bridge the gap. Through a shift from model performance replicability to claim replicability, Machine Learning scientists can be held accountable for producing non-replicable claims that are prone to eliciting harm due to misuse and misinterpretation. In this paper, I make the following contributions. First, I define and distinguish two forms of replicability for ML research that can aid constructive conversations around replicability. Second, I formulate an argument for claim-replicability's advantage over model performance replicability in justifying assigning accountability to Machine Learning scientists for producing non-replicable claims and show how it enacts a sense of responsibility that is actionable. In addition, I characterize the implementation of claim replicability as more of a social project than a technical one by discussing its competing epistemological principles, practical implications on Circulating Reference, Interpretative Labor, and research communication. (shrink)

This paper examines a paradigm case of allegedly successful reductive explanation, viz. the explanation of the fact that water boils at 100°C based on facts about H2O. The case figures prominently in Joseph Levine’s explanatory gap argument against physicalism. The paper studies the way the argument evolved in the writings of Levine, focusing especially on the question how the reductive explanation of boiling water figures in the argument. It will turn out that there are two versions of the explanatory gap (...) argument to be found in Levine’s writings. The earlier version relies heavily on conceptual analysis and construes reductive explanation as a process of deduction. The later version makes do without conceptual analysis and understands reductive explanations as based on theoretic reductions that are justified by explanatory power. Along the way will be shown that the bridge principles — which are being neglected in the explanatory gap literature — play a crucial role in the explanatory gap argument. (shrink)

The 5P, an acronym for the five principles, was proposed precisely to bridge the gap between scientific progress and societal acceptance, particularly in interdisciplinary scientific research on sustainability.

The article presents the reasons for which the issue of providing housing to low-income citizens has been a real challenge in Addis Ababa during the recent years and will continue to be, given that its population is growing extremely fast. It examines the tensions between the universal aspirations and the local realities in the case of some of Ethiopia’s most ambitious mass pro-poor housing schemes, such as the “Addis Ababa Grand Housing Program” (AAGHP), which was launched in 2004 and was (...) integrated in the “Integrated Housing Development Program” (IHDP) in 2006. The article argues that the quotidian practices of communities and their socio-economic and cultural characteristics are related to the spatial attributes of co-housing practices. Drawing upon the idea that there is a mutual correspondence between social and spatial structures, it places particular emphasis on the analysis of the IHDP and aims to show that to shape strategies that take into account the social and cultural aspects of daily life of the poor citizens of Addis Ababa, it is pivotal to invite them to take part in the decision-making processes regarding their resettlement. Departing from the fact that a large percentage of the housing supply in Addis Ababa consists of informal unplanned housing, the article also compares the commoning practices in kebele houses and condominium units. The former refers to the legal informal housing units owned by the government and rented to their dwellers, whereas the latter concerns the housing blocks built in the framework of the IHDP for the resettlement of the kebele dwellers. The article analyzes these processes of resettlement, shedding light of the fact that kebele houses were located at the inner city, whereas the condominiums are located in the suburbs. Despite the fact that the living conditions in the condominium units are of a much higher quality than those in the kebele houses, their design underestimated or even neglected the role of the commoning practices. The article highlights the advantages of commoning practices in architecture and urban planning, and how the implementation of participation-oriented solutions can respond to the difficulties of providing housing. It argues that understanding the significance of the endeavors that take into account the opinions of dwellers during the phase of decision-making goes hand in hand with considering commoning practices as a source of architecture and urban planning frameworks for low-cost housing in this specific context. The key argument of the article is that urban planning and architecture solutions in Addis Ababa should be based on the principles of the so-called “negotiated planning” approach, which implies a close analysis of the interconnections between planning, infrastructure, and land. (shrink)

Psychoanalytic self-psychology as outlined by such depth psychologists as Jung, Fordham, Winnicott and Kohut provide a framework for conceptualizing a relationship of complementarity between psychic and immune defence as well as loss of bodily and self integration in disease. Physicist Erwin Schrödinger’s thesis that the so-called “arrow of time” does not necessarily deal a mortal blow to its creator is reminiscent of the concept of timeless dimensions of the unconscious mind and the Self in Analytical Psychology, manifest for instance, in (...) dream content and archetypal symbols. These notions are not only consistent with the concepts of timelessness and meaningful coincidence (synchronicity) in psychoanalysis. They are also implicitly spiritual with intimations of a numinous dimension of the evolutionary process in which humanity participates. This includes the idea that an evolving God becomes conscious through and is completed by humankind in a process (Incarnational) theology which regards the numinous as both immanent and transcendent. And concepts of mind which transcend the individual in a transpersonal sense. The treatment of the psychophysical problem by depth psychologist Carl Jung and physicist Wolfgang Pauli with their notion of the unconscious archetypes as timeless, cosmic ordering and regulating principles creating a bridge between mind and matter in a relationship of complementarity is compatible with such a perspective on the numinous which might in turn be useful for contemporary theology and spirituality. (shrink)

Is logic normative for reasoning? In the wake of work by Gilbert Harman and John MacFarlane, this question has been reduced to: are there any adequate bridge principles which link logical facts to normative constraints on reasoning? Hitherto, defenders of the normativity of logic have exclusively focussed on identifying adequate validity bridge principles: principles linking validity facts—facts of the form 'gamma entails phi'—to normative constraints on reasoning. This paper argues for two claims. First, for the (...) time being at least, Harman’s challenge cannot be surmounted by articulating validity bridge principles. Second, Harman’s challenge can be met by articulating invalidity bridge principles: principles linking invalidity facts of the form 'gamma does not entail phi' to normative constraints on reasoning. In doing so, I provide a novel defence of the normativity of logic. (shrink)

How does logic relate to rational belief? Is logic normative for belief, as some say? What, if anything, do facts about logical consequence tell us about norms of doxastic rationality? In this paper, we consider a range of putative logic-rationality bridge principles. These purport to relate facts about logical consequence to norms that govern the rationality of our beliefs and credences. To investigate these principles, we deploy a novel approach, namely, epistemic utility theory. That is, we assume (...) that doxastic attitudes have different epistemic value depending on how accurately they represent the world. We then use the principles of decision theory to determine which of the putative logic-rationality bridge principles we can derive from considerations of epistemic utility. (shrink)

While it is generally believed that justification is a fallible guide to the truth, there might be interesting exceptions to this general rule. In recent work on bridge-principles, an increasing number of authors have argued that truths about what a subject ought to do are truths we stand in some privileged epistemic relation to and that our justified normative beliefs are beliefs that will not lead us astray. If these bridge-principles hold, it suggests that justification might (...) play an interesting role in our normative theories. In turn, this might help us understand the value of justification, a value that's notoriously difficult to understand if we think of justification as but a fallible means to a desired end. We will argue that these bridge-principles will be incredibly difficult to defend. While we do not think that normative facts necessarily stand in any interesting relationship to our justified beliefs about them, there might well be a way of defending the idea that our justified beliefs about what to do won't lead us astray. In turn, this might help us understand the value of justification, but this way of thinking about justification and its value comes with costs few would be willing to pay. (shrink)

An organizing theme of the dissertation is the issue of how to make philosophical theories useful for scientific purposes. An argument for the contention is presented that it doesn’t suffice merely to theoretically motivate one’s theories, and make them compatible with existing data, but that philosophers having this aim should ideally contribute to identifying unique and hard to vary predictions of their theories. This methodological recommendation is applied to the ranking-theoretic approach to conditionals, which emphasizes the epistemic relevance and the (...) expression of reason relations as part of the semantics of the natural language conditional. As a first step, this approach is theoretically motivated in a comparative discussion of other alternatives in psychology of reasoning, like the suppositional theory of conditionals, and novel approaches to the problems of compositionality and accounting for the objective purport of indicative conditionals are presented. In a second step, a formal model is formulated, which allows us to derive quantitative predictions from the ranking-theoretic approach, and it is investigated which novel avenues of empirical research that this model opens up for. Finally, a treatment is given of the problem of logical omniscience as it concerns the issue of whether ranking theory (and other similar approaches) makes too idealized assumptions about rationality to allow for interesting applications in psychology of reasoning. Building on the work of Robert Brandom, a novel solution to this problem is presented, which both opens up for new perspectives in psychology of reasoning and appears to be capable of satisfying a range of constraints on bridge principles between logic and norms of reasoning, which would otherwise stand in a tension. (shrink)

What is it to base a belief on reasons? Existing attempts to give an account of the basing relation encounter a dilemma: either one appeals to some kind of neutral process that does not adequately reflect the way basing is a content‐sensitive first‐personal activity, or one appeals to linking or bridge principles that over‐intellectualize and threaten regress. We explain why this dilemma arises, and diagnose the commitments that are key obstacles to providing a satisfactory account. We explain why (...) they should be rejected anyway, and then offer a new, knowledge‐first virtue epistemological theory of the basing relation that shows how we can substantially theorize about mental processes without these commitments. The resulting view plausibly captures the way in which basing is an inherently mental and content‐sensitive process. (shrink)

It is now common to distinguish Metaphysical from Epistemological Disjunctivism. It is equally common to suggest that it is at least not obvious that the latter requires a commitment to the former: at the very least, a suitable bridge principle will need to be identified which takes one from the latter to the former. This paper identifies a plausible-looking bridge principle that takes one from the version of Epistemological Disjunctivism defended by John McDowell and Duncan Pritchard, which I (...) label Reflective Epistemological Disjunctivism, or (RED), to Metaphysical Disjunctivism. Moreover, it identifies a modification the proponent of (RED) could, and should, make to the Internalist component of their theory, and argues that the commitment to Metaphysical Disjunctivism remains, even if such a modification is made. The upshot is that the commitment to Metaphysical Disjunctivism on the part of (RED) is shown to be particularly robust. (shrink)

There is a widespread view that in order to be rational we must mostly know what we believe. In the probabilistic tradition this is defended by arguments that a person who failed to have this knowledge would be vulnerable to sure loss, or probabilistically incoherent. I argue that even gross failure to know one's own beliefs need not expose one to sure loss, and does not if we follow a generalization of the standard bridge principle between first-order and second-order (...) beliefs. This makes it possible for a subject to use probabilistic decision theory to manage in a rational way cases of potential failure of this self-knowledge, as we find in implicit bias. Through such cases I argue that it is possible for uncertainty about what our beliefs are to be not only rationally permissible but advantageous. (shrink)

Kant's formulae ought to effectively produce the same result when applied to the moral validity of any particular maxim; further, no valid maxim produces contradictory results when applied against Kant's Universal Law and Humanity formulae. Where one uses all formulae in the assessment of a maxim, one gains a more complete understanding of the moral law, thereby bridging principles of reason with intuition within the agent who has undertaken to evaluate the morality of a particular action. These formulae command (...) without regard to any particular interests, but are instead unconditional; further, these formulae effectively limit choice of action and therefore give rise to duty. Kant implies that the structure of all maxims requires different formulae of the same moral law, i.e., all maxims have a ‘form’ and a ‘matter’, which prompt reconfiguring of the categorical imperative into different formulae in order to test the morality of a maxim. (shrink)

In this paper, I argue that perception justifies belief about the external world in virtue of its phenomenal character together with its relations to the external world. But I argue that perceptual relations to the external world impact on the justifying role of perception only by virtue of their impact on its representational content. Epistemic level-bridging principles provide a principled rationale for avoiding more radically externalist theories of perceptual justification.

Hume seems to contend that you can’t get an ought from an is. Searle professed to prove otherwise, deriving a conclusion about obligations from a premise about promises. Since (as Schurz and I have shown) you can’t derive a substantive ought from an is by logic alone, Searle is best construed as claiming that there are analytic bridge principles linking premises about promises to conclusions about obligations. But we can no more derive a moral obligation to pay up (...) from the fact that a promise has been made than we can derive a duty to fight a duel from the fact that a challenge has been issued – just conclusions about what we ought to do according to the rules of the relevant games. Hume suggests bridge principles that would take us from the rules of the games to conclusions about duties, but these principles are false. My argument features an obstreperous earl, an anarchist philosopher and a dueling Prime Minister. (shrink)

I defend the claim that physicalism is not committed to the view that non-phenomenal macrophysical truths are a priori entailed by the conjunction of microphysical truths , basic indexical facts , and a 'that's all' claim . I do so by showing that Chalmers and Jackson's most popular and influential argument in support of the claim that PIT ⊃ M is a priori, where 'M' stands for any ordinary, non-phenomenal, macroscopic truth, falls short of establishing its conclusion. My objection to (...) Chalmers and Jackson's argument takes the form of a nested dilemma. Let 'Conceptual Competence Principle ' stand for the following claim: for any complete microphysical description D of a world w, a subject who is in possession of and competent with a macrophysical concept C is capable of determining a priori the extension of C. Either Jackson and Chalmers accept CCP or not. If the latter, then they cannot demonstrate that the conditional PIT ⊃ M is a priori. If the former, then they have a choice: they can either cite reasons that support the principle or argue that the principle should be taken for granted since it is entailed by the very notion of conceptual competence. But both alternatives are problematic. In regard to the first horn of this latter dilemma, I show not only that there are no good reasons to support the principle, but that there are also reasons to reject it. In regard to the second horn, I show that it cannot be the case that CCP is part of the very notion of conceptual competence. The conceptual capacity expressed by CCP requires that certain bridge principles or conditionals, which link the microphysical level to the macroscopic level, are either implicitly or explicitly given to the subject. But, as I argue, Chalmers and Jackson have no way of accounting for these bridge principles or conditionals in a manner that does not trivialize their position. (shrink)

In "How to Speak of the Colors", Mark Johnston’s claims that eliminativism would require us to jettison colour discourse. In this paper, I challenge Johnston’s claim. I argue that a particular version of eliminativism, i.e., prescriptive colour fictionalism, allows us to continue employing colour discourse as we have thus far in the absence of colours. In doing so, it employs statistical models in its base discourse to derive high-level statistical constructs that can be linked to the fiction via bridge (...) principles. (shrink)

The Barcan formula (BF) is commonly paraphrased as the schematic conditional that if it is possible that there be a phi then something or other is possibly a phi. It is validated by the most straightforward systems of quantified modal logic. It is also widely considered to pose a threat to the commonsensical metaphysical view that there are no non-actual (or ‘merely possible’) things. I show how BF can be cleared of such a charge by construing it as a (...) class='Hi'>bridge principle connecting modality de dicto and modality de re while retaining a Russellian robust sense of reality in modal matters. (shrink)

In an earlier discussion, I argued that Kant's moral theory satisfies some of the basic criteria for being a genuine theory: it includes testable hypotheses, nomological higher-and lower-level laws, theoretical constructs, internal principles, and bridge principles. I tried to show that Kant's moral theory is an ideal, descriptive deductive-nomological theory that explains the behavior of a fully rational being and generates testable hypotheses about the moral behavior of actual agents whom we initially assume to conform to its (...) theoretical constructs. I argued that the moral "ought" is best understood as the "ought" of tentative prediction expressed in the range of uses of the German sollen; and that the degree to which such a theory is well-confirmed is a function of the degree to which we actually judge individual human agents, on a case-by-case basis, to be motivated by rationality, stupidity, or moral corruption in their actions. I assume that a similar case could be made for other major contenders, such as Utilitarianism or Aristotelianism. But there still remains unanswered the question of which of these theories is the best among the available alternatives. To answer this question, further criteria of selection must be invoked. Among these are structural elegance and explanatory simplicity, but even these do not exhaust the desiderata for an adequate moral theory. More pressing in the case of moral theory is the requirement that the theory enable us to understand all the available data of moral experience; that the theory be sufficiently inclusive that in the formulation of its descriptive laws and practical principles, it be capable of identifying as morally significant all the behavior to which moral praise, condemnation, or acquittal is a relevant and appropriate response. (shrink)

This is a commentary on Adrian Heathcote’s interesting paper ‘Hume’s Master Argument’. Heathcote contends that No-Ought-From-Is is primarily a logical thesis, a ban on Is/Ought inferences which Hume derives from the logic of Ockham. NOFI is thus a variation on what Heathcote calls ‘Hume’s Master Argument’, which he also deploys to prove that conclusions about the future (and therefore a-temporal generalizations) cannot be derived by reason from premises about the past, and that conclusions about external objects or other minds cannot (...) be derived by reason from premises about impressions. Heathcote raises an important question. Having (apparently) argued that our inductive inferences are not justified by reason, Hume puts them down to Custom, and seems to suggest that we OUGHT to indulge this propensity but NOt the superstitious propensities that lead to religious belief. (Query: Why is it right to indulge one non-rational propensity but not the others?) Finally Heathcote argues that just as there are valid, but not formally valid, arguments taking us from claims about inferential relations to claims about what we ought to believe, so there may be valid, but not formally valid, arguments taking us from factual claims about some situation to claims about what we ought to do. -/- I reply that Hume does indeed have a Master Argument and that it does rely on logical principles but not on the logic of Ockham which had been largely forgotten by Hume’s day. Instead Hume relies on the idea widely believed in the 18th Century and taught to Hume at Edinburgh by his logic Professor Colin Drummond, that in a logically valid argument the conclusion is contained in the premises. I reconstruct Hume’s Master Argument using this principle. I draw a careful distinction between two theses: 1) that we cannot get from non-moral premises to moral conclusions with the aid of logic alone and 2) that we cannot get from non-moral premises to moral conclusions with aid of analytic bridge principles. Hume believed the first but not the second. What then is the role of NOFI in the larger argument of the Treatise? To show that the truths of ethics cannot be derived via logic from self-evident truths of some other kind and thus that they are not demonstrable. How can we make sense of Hume’s apparent belief that it is sometimes right to transcend reason and sometimes not? In the case of Custom, we live in a world governed by causal regularities, and, in such a world, induction is in fact a fairly reliable belief-forming mechanism. Thus a suitably qualified spectator (one aware of the kind of world we live in) would tend to approve of indulging it, even if it cannot be justified by reason. However, our superstitious propensities are (and can be known to be) unreliable, since they produce different and inconsistent results in different people. Thus it is it is wrong (something a suitably qualified spectator would disapprove of) to indulge the faculty of Superstition. I also take issue with Heathcote’s penchant for valid, but not formally valid, inferences. I supply the missing premises for Heathcote’s Is/Ought inferences and argue that they are either not true or not necessary. (shrink)

When some P implies some Q, this should have some impact on what attitudes we take to P and Q. In other words: logical consequence has a normative import. I use this idea, recently explored by a number of scholars, as a stepping stone to a bolder view: that relations of logical consequence can be identified with norms on our propositional attitudes, or at least that our talk of logical consequence can be explained in terms of such norms. I investigate (...) the prospects of such a cognitive norm account of logical consequence. I go over the challenges involved in finding a plausible bridge principle connecting logical consequence to cognitive norms, in particular a biconditional principle that gives us not only necessary but sufficient conditions for logical consequence in terms of norms on propositional attitudes. Then, on the assumption that an adequate norm can be found, I consider what the philosophical merits of such a cognitive norm account would be, and what theoretical commitments it would generate. (shrink)

This dissertation proposes and defends a hybrid view I call Hybrid Impermissivism, which combines the following two theses: Moderate Uniqueness and Credal Permissivism. Moderate Uniqueness says that no evidence could justify both believing a proposition and its negation. However, on Moderate Uniqueness, evidence could justify both believing and suspending judgement on a proposition (hence the adjective “Moderate”). And Credal Permissivism says that more than one credal attitude could be justified on the evidence. Hybrid Impermissisim is developed into a precise theory (...) by using normative bridge principles on how rational belief and credence ought to interact. My overall conclusion is that Hybrid Impermissivism is a coherent, plausible, and conciliatory position and provides a correct characterisation of the requirements of evidence on doxastic attitudes . (shrink)

On at least one of its uses, ‘higher-order evidence’ refers to evidence about what opinions are rationalized by your evidence. This chapter surveys the foundational epistemological questions raised by such evidence, the methods that have proven useful for answering them, and the potential consequences and applications of such answers.

Abstract** This paper illuminates the journey of discovery in understanding universal interconnectedness, examining how seemingly complex relationships between quantum and cosmic phenomena become elegantly simple once properly understood. Following Galileo's insight that truth, once discovered, reveals its inherent simplicity, we explore how the connection between universes via quantum-classical bridges might represent such a fundamental truth—one that, once grasped, transforms our understanding of consciousness, reality, and human existence. This work charts both the path of discovery and the resulting clarity it brings (...) to our comprehension of cosmic relationships. (shrink)

The Self-Evidencing Agent offers a unique method for addressing difficult philosophical questions. Self-evidencing occurs when an agent uses their model of the world and of themselves to explain what they observe in the world and in themselves, such that those observations become evidence for their model – the more agents explain, the more they self-evidence. This book argues that there is good reason to cast an agent’s existence itself in terms of self-evidencing, and that if we begin from this as (...) a first principle, then we can make better sense of who and what we are, of how we engage in diverse ways with the world, and what matters to us. Self-evidencing can help situate attention, action, and perception. It also furnishes compelling approaches to decision-making and rationality, the self, of preferences and values. It can build bridges to consciousness, and even on to free will, and to meaning and wisdom. (shrink)

A series of recent developments points towards auditing as a promising mechanism to bridge the gap between principles and practice in AI ethics. Building on ongoing discussions concerning ethics-based auditing, we offer three contributions. First, we argue that ethics-based auditing can improve the quality of decision making, increase user satisfaction, unlock growth potential, enable law-making, and relieve human suffering. Second, we highlight current best practices to support the design and implementation of ethics-based auditing: To be feasible and effective, (...) ethics-based auditing should take the form of a continuous and constructive process, approach ethical alignment from a system perspective, and be aligned with public policies and incentives for ethically desirable behaviour. Third, we identify and discuss the constraints associated with ethics-based auditing. Only by understanding and accounting for these constraints can ethics-based auditing facilitate ethical alignment of AI, while enabling society to reap the full economic and social benefits of automation. (shrink)

Book Description (Blurb): Cognitive Design for Artificial Minds explains the crucial role that human cognition research plays in the design and realization of artificial intelligence systems, illustrating the steps necessary for the design of artificial models of cognition. It bridges the gap between the theoretical, experimental and technological issues addressed in the context of AI of cognitive inspiration and computational cognitive science. -/- Beginning with an overview of the historical, methodological and technical issues in the field of Cognitively-Inspired Artificial Intelligence, (...) Lieto illustrates how the cognitive design approach has an important role to play in the development of intelligent AI technologies and plausible computational models of cognition. Introducing a unique perspective that draws upon Cybernetics and early AI principles, Lieto emphasizes the need for an equivalence between cognitive processes and implemented AI procedures, in order to realise biologically and cognitively inspired artificial minds. He also introduces the Minimal Cognitive Grid, a pragmatic method to rank the different degrees of biologically and cognitive accuracy of artificial systems in order project and predict their explanatory power with respect to the natural systems taken as source of inspiration. -/- Providing a comprehensive overview of cognitive design principles in constructing artificial minds, this text will be essential reading for students and researchers of artificial intelligence and cognitive science. (shrink)

In the Groundwork and all three Critiques, Kant expresses the hope of eventually unifying theoretical and practical reason in one system, with a principle common to both. But he never clarifies what this principle is, leaving scholars to advance different possibilities. I advance a new response to this problem: I claim that Kant begins to refer to what he calls the ‘autonomy of ideas of reason’ in his final decade, enabling a new approach to finally bridging the theoretical and the (...) practical. This concept of autonomy, however, is no longer equivalent to the moral autonomy attributed to the self-legislating will, nor does it refer to the spontaneity of theoretical reason. Instead, it corresponds to the autonomy ascribed to reflective judgment in representing both theoretical and practical ideas of reason. Thus, this conception furnishes a principle, the principle of purposiveness, which I propose as the unifying principle Kant had been seeking. (shrink)

The relationship between the One and the Multiple in mystic philosophy is a profound and central theme that explores the nature of existence, the cosmos, and the divine. This theme is present in various mystical traditions, including those of the East and West, and it addresses the paradoxical coexistence of the unity and multiplicity of all things. -/- In mystic philosophy, the **One** often represents the ultimate reality, the source from which all things emanate and to which all things return. (...) It is the absolute, the infinite, and the unchanging. The One is beyond all attributes and is often associated with the divine or the absolute truth. -/- The **Multiple**, on the other hand, represents the manifest world, the diversity of forms, and the realm of change and plurality. It is the world we experience through our senses, the domain of time and space, where differentiation and individuality are apparent. -/- The relationship between the One and the Multiple is not one of opposition but of emanation and unity. The Multiple is seen as a reflection, expression, or manifestation of the One. In this sense, the diversity of the world doesn’t contradict the unity of the One but rather demonstrates it in a myriad of forms. -/- Mystics seek to understand and experience this relationship through various practices and insights. They aim to transcend the illusion of separation and duality to experience the non-dual reality where the One and the Multiple are recognized as inseparable. -/- This concept can be illustrated by the metaphor of the ocean and its waves. The ocean represents the One—vast, deep, and all-encompassing—while the waves represent the Multiple—distinct, diverse, and ever-changing. Each wave is unique, yet it is not separate from the ocean. The wave’s existence is dependent on and made of the same substance as the ocean. In the same way, each individual entity in the Multiple is an expression of the One. -/- In summary, the relationship between the One and the Multiple in mystic philosophy is a dynamic interplay that challenges the conventional understanding of separation. It invites a deeper exploration of reality, where the apparent multiplicity of the world is a direct expression of the singular, underlying essence of all that is. -/- The relationship between the One and the Multiple in the context of mathematical philosophy is a profound topic that touches upon the very foundations of existence and knowledge. It’s a theme that has been explored by philosophers and mathematicians alike, often leading to the contemplation of unity and diversity within the structures of reality. -/- In mathematics, the concept of the One can be seen as the basis of unity from which all numbers derive. It’s the identity element in multiplication, the starting point in counting, and the foundation of dimension in geometry. The One is often associated with the concept of monism in philosophy, which posits that there is a single, underlying substance or principle that constitutes reality. -/- On the other hand, the Multiple represents the infinite variety and diversity of forms and numbers that arise from the One. It’s the embodiment of plurality and the complex interplay of different entities that mathematics seeks to understand and describe. This reflects the philosophical stance of pluralism, which acknowledges the existence of multiple realities or truths. -/- The interplay between the One and the Multiple can be seen in the mathematical concept of sets. A set can be thought of as a unity, a whole composed of distinct elements. Yet, each element within the set also retains its individuality, contributing to the diversity of the set’s composition. This duality is mirrored in the philosophical exploration of the universal and the particular, where the universal represents the One, and the particulars represent the Multiple. -/- In the realm of mathematical philosophy, this relationship often leads to questions about the nature of mathematical objects: Are they discovered as part of an objective reality (the One), or are they constructed by the human mind from a multitude of experiences (the Multiple)? This debate resonates with the philosophical inquiry into the nature of truth and reality. -/- Reflecting on the One and the Multiple can also lead to a deeper understanding of the self and the cosmos. Just as the number one is integral to the existence of all other numbers, the individual self can be seen as a unique expression of the universal whole. Similarly, the cosmos can be viewed as a grand unity composed of a multiplicity of forms and phenomena. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers⁴. -/- The **first incompleteness theorem** reveals that within any such consistent system, there are propositions that are true but cannot be proven within the system itself. This reflects the idea of the Multiple in that there is an abundance of mathematical truths, a multiplicity that exceeds the unifying framework of any one system. It suggests that the realm of mathematical truth is more extensive than any single formal system can fully capture. -/- The **second incompleteness theorem** extends this by showing that a system cannot prove its own consistency. This relates to the concept of the One, as it implies that a system’s complete self-understanding, its unity and coherence, is unattainable from within. It must look beyond itself, to an external vantage point, to ascertain its consistency. -/- In the context of the One and the Multiple, Gödel’s theorems imply that the One (a consistent formal system) is inherently incomplete and cannot encompass the Multiple (the totality of mathematical truths). This resonates with philosophical discussions about the relationship between unity and plurality. Just as a single philosophical system cannot capture the entirety of truth, a single formal mathematical system cannot encapsulate all mathematical truths. -/- Moreover, Gödel’s work suggests that the pursuit of a single, unified theory of everything in mathematics—a One that encompasses all Multiples—is an inherently Sisyphean task. There will always be more truths (Multiples) than can be derived from any given set of axioms (the One). -/- In essence, Gödel’s incompleteness theorems provide a formal underpinning to the philosophical notion that the One cannot exist without the Multiple, and vice versa. They are interdependent, with the One giving rise to the Multiple, and the Multiple necessitating the One for its expression and comprehension. This interplay is a dance of limitations and possibilities, where the boundaries of logic, mathematics, and philosophy blur into one another. -/- The relationship between the One and the Multiple in the context of the mathematics of zero is a deeply philosophical inquiry that bridges the abstract world of numbers with the existential questions of being and non-being. -/- Zero, in mathematics, is a symbol of absence, a representation of nothingness, yet it holds a pivotal position as a number. It is the void from which all things emerge and to which they return. In the philosophy of mathematics, zero is the paradoxical junction where the One and the Multiple converge and diverge. -/- From the perspective of the One, zero can be seen as the origin—the singular point that precedes the existence of numbers. It is the empty set, the foundation upon which the edifice of mathematics is constructed. As the identity element in addition, zero maintains the integrity of numbers, for adding zero to any number leaves it unchanged, reflecting the immutable nature of the One. -/- Conversely, when we consider the Multiple, zero represents the infinite potentiality of creation. It is the canvas upon which the integers, both positive and negative, express their multitude. Zero is the balance point, the fulcrum around which the symphony of numbers dances. It embodies the plurality of possibilities, the beginning of the number line that stretches infinitely in both directions. -/- Philosophically, zero challenges our understanding of existence. It is both something and nothing—a number that quantifies the absence of quantity. This duality echoes the philosophical struggle to comprehend how the One gives rise to the Multiple. How does the unity of being manifest the diversity of the cosmos? Zero offers a mathematical metaphor for this mystery, as it encapsulates the transition from non-existence to existence, from the undifferentiated One to the differentiated Multiple. -/- In the realm of set theory, zero corresponds to the empty set—a set with no elements. This set is unique in that it is the only set that contains nothing, yet it is the foundation upon which all other sets are built. The empty set is the mathematical embodiment of the One, and all other sets, containing multiple elements, arise from it. -/- Reflecting on zero in the context of Gödel’s incompleteness theorems, we find a resonance with the idea that the One (a consistent formal system) cannot capture the entirety of the Multiple (the totality of mathematical truths). Zero, as the foundation of numbers, similarly suggests that from the nothingness of the One, the infinite complexity of the Multiple emerges—yet it can never be fully encompassed or expressed by any single system. -/- In conclusion, the mathematics of zero offers a profound reflection on the relationship between the One and the Multiple. It serves as a bridge between the abstract and the concrete, the known and the unknowable, challenging us to ponder the origins of existence and the nature of reality itself. -/- . (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)