Abstract Can physical reality be fully captured by an algorithmic Theory of Everything? We argue not. Gödelian incompleteness shows that no sound, recursively axiomatizable formalism proves all truths of a sufficiently rich domain, while Tarskian undefinability shows that no such formalism defines its own truth predicate. This combined obstruction is not merely epistemic: undecidability in quantum logic, quantum measurement, and spectral gap problems demonstrates the existence of physically determinate questions that no algorithm can decide. We distinguish the Mental Lucas-Penrose (MLP) argument, concerning human cognition, from the Real Lucas-Penrose (RLP) argument introduced here, which transfers the Gödel-Tarski obstruction to the ontology of the physical world. Since truth for sufficiently rich domains is necessarily external, and spacetime is emergent from deeper formal structure, a non-algorithmic semantic layer prior to spacetime is required. Standard objections to MLP do not apply to RLP. A non-algorithmic truth principle is therefore foundational to physics.
Abstract Humean accounts of causality deny the existence of any causal factor that imparts regularity to empirical data. According to the cosmic fluke objection, this makes Humeanism very unlikely, since it must attribute the extensive regularities that we observe to mere chance. In defence of Humeanism, I argue that this objection equivocates between two senses of regularity. Both science and everyday cognition rely not on global, residue-free compressions of data (whole-string regularities), but on component patterns that appear together with nonzero noise (two-part regularities). Any data set, even one that is algorithmically random, can be decomposed into such patterns and noise. Consequently, the existence of such regularities in empirical data is not surprising, even in the absence of a mechanism devoted to making data regular.
This paper examines the parallels between Marya Schechtman's (2014. Staying Alive: Personal Identity, Practical Concerns, and the Unity of a Life. Oxford: Oxford University Press) 'Person Life View' (PLV) and Conventionalism regarding personal identity. PLV contends that personal identity hinges on recognition by others and societal institutions, while Conventionalism argues that personhood is influenced by social conventions. Schechtman argues against Conventionalism and in favour of PLV on the grounds that changing conventions could undermine personhood. However, this paper argues that PLV is a form of Conventionalism. By analysing the roles of conventions, desires, and behaviours in both theories this paper demonstrates their fundamental similarities. In particular, PLV's reliance on the notion of 'acceptance into the person-space' aligns with Conventionalism. Ultimately, this analysis suggests that Schechtman's distinctions between her theory and Conventionalism may be artificial, showing how her criticism of Conventionalism is based on misunderstanding of the theory rather than genuine critiques.
In book Gamma of the Metaphysics Aristotle defends what is known as the principle of non-contradiction (PNC). He highlights how the proclivity of early thinkers to determine the nature or metaphysical identity of something according to sensation leads them to propose contradictions and ultimately deny PNC. This presocratic error can be aptly thought of as a kind of essentialism since the early philosophers generally assign the fundamental nature of a thing, what Aristotle would call essence, to its sensible properties. The paper focusses on what this error entails for the Heracliteans, arguing that the Heracliteans identify a thing as a static collection of properties - what Aristotle would call accidents. This leads to a metaphysics of change in which a subject in a state of change has no diachronic identity, contrasting with Aristotle's replacement model of change in which a subject retains its essence through accidental change.
Realism about metaphysics states that metaphysics seeks, and can sometimes succeed in discovering, valuable truths. One version of realism about metaphysics, which I call Structural Realism, holds that although many ordinary truths about the world seem to require the existence of certain things with particular properties, we cannot actually draw metaphysical conclusions from these truths because they are not stated in a way that "matches" or represents the intrinsic structure of reality (they do not "carve at the joints" of nature). In this paper, I clarify this view and distinguish two forms of it. I show that the more extreme version cannot be correct because a constitutive aim of language use is communication; I argue for this using a novel, teleological account of constitutive aims. I then critique the more moderate version of the theory on the grounds that it would render metaphysics irrelevant to other areas of philosophy.
