Let T1 and T2 be two simple complete theories in disjoint languages. We prove that there is a simple complete theory which extends T1 ∪ T2 if T2 has a certain condition.

A longstanding philosophical premise perceives simplicity as a desirable attribute of scientific theories. One of several raised justifications for this notion is that simple theories are more likely to indicate the true makeup of natural systems. Qualitatively parsimonious hypotheses and theories keep to a minimum the number of different postulated entities within a system. Formulation of such ontologically simple working hypotheses proved to be useful in the experimental probing of narrowly defined bio systems. It is less certain, however, (...) whether qualitatively parsimonious theories are effective indicators of the true nature of complex biological systems. This paper assesses the success of ontologically simple theories in envisaging the makeup of three complex systems in bacteriology, immunology, and molecular biology. Evidence shows that parsimonious theories completely misconstrued the actual ontologically complex constitutions of the three examined systems. Since evolution and selective pressures typically produce ontologically intricate rather than simple bio systems, qualitatively parsimonious theories are mostly inapt indicators of the true nature of complex biological systems. (shrink)

An argument is offered that externalism can compromise the first‐person transparency of mental contents. The premises are John McDowell's view that experience is passively structured by concepts, and the Simple Theory of Colour advocated by John Campbell, according to which those properties that are the actual semantic values of colour concepts are just as they appear to normal observers under standard conditions. An example is offered to suggest that it must be an epistemic possibility that the semantic values (...) of such concepts, as externally determined, are not the properties the Simple Theory takes them to be. The possibility highlights a mismatch between the properties that the colour concepts present as their semantic values and their actual, externally determined semantic values. Such a mismatch is shown to induce an incoherence into colour concepts leaving them unfit passively to structure our colour experience. Under such circumstances, it would not be transparent to a subject on the basis of colour experience, whether those experiences are conceptually structured by concepts answering to the Simple Theory, or precisely what content they carry. (shrink)

Let T be a complete, superstable theory with fewer than ${2^{\aleph_{0}}}$ countable models. Assuming that generic types of infinite, simple groups definable in T eq are sufficiently non-isolated we prove that ω ω is the strict upper bound for the Lascar rank of T.

The notion of ecological rationality implies that the accuracy of a decision strategy depends on features of the information environment in which it is tested. We demonstrate that the performance of a group may be strongly affected by the decision strategies used by its individual members and specify how this effect is moderated by environmental features. Specifically, in a set of simulation studies, we systematically compared four decision strategies used by the individual group members: two linear, compensatory decision (...) strategies and two simple, noncompensatory heuristics. Individual decisions were aggregated by using a majority rule. To assess the ecological rationality of the strategies, we varied (a) the distribution of cue validities, (b) the quantity, and (c) the quality of shared information. Group performance strongly depended on the distribution of cue validities. When validities were linearly distributed, groups using a compensatory strategy achieved the highest accuracy. Conversely, when cue validities followed a J-shaped distribution, groups using a simple lexicographic heuristic performed best. While these effects were robust across different quantities of shared information, the quality of shared information exerted stronger effects on group performance. Consequences for prescriptive theories on group decision making are discussed. (shrink)

Much apprehension has been expressed by philosophers about the method of renormalisation in quantum field theory, as it apparently requires illegitimate procedure of infinite cancellation. This has lead to various speculations, in particular in Teller (1989). We examine Teller's discussion of perturbative renormalisation of quantum fields, and show why it is inadequate. To really approach the matter one needs to understand the ideas and results of the renormalisation group, so we give a simple but comprehensive account of (...) this topic. With this in hand, we explain how renormalisation can and should be understood. One thing that is revealed is that apparently very successful theories such as quantum electro-dynamics cannot be universally true; resolving the tension between success and falsity leads to a picture in which any theory may be viewed as irreducibly phenomenological. We explain how, and argue that the support for this view is tenuous at best. (shrink)

The main topic of this paper is the investigation of generalized amalgamation properties for simple theories. That is, we are trying to answer the question of when a simple theory has the property of n-dimensional amalgamation, where two-dimensional amalgamation is the Independence Theorem for simple theories. We develop the notions of strong n-simplicity and n-simplicity for 1≤n≤ω, where both “1-simple” and “strongly 1-simple” are the same as “simple”. For strong n-simplicity, we present examples (...) of simple unstable theories in each subclass and prove a characteristic property of strong n-simplicity in terms of strong n-dividing, a strengthening of the dependence relation called dividing in simple theories. We prove a strong three-dimensional amalgamation property for strongly 2-simple theories, and, under an additional assumption, a strong -dimensional amalgamation property for strongly n-simple theories. In the last section of the paper we comment on why strong n-simplicity is called strong. (shrink)

We identify complete fragments of the simple theory of types with infinity and Quine’s new foundations set theory. We show that TSTI decides every sentence ϕ in the language of type theory that is in one of the following forms: ϕ=∀x1r1⋯∀xkrk∃y1s1⋯∃ylslθ where the superscripts denote the types of the variables, s1>⋯>sl, and θ is quantifier-free, ϕ=∀x1r1⋯∀xkrk∃y1s⋯∃ylsθ where the superscripts denote the types of the variables and θ is quantifier-free. This shows that NF decides every stratified sentence (...) ϕ in the language of set theory that is in one of the following forms: ϕ=∀x1⋯∀xk∃y1⋯∃ylθ where θ is quantifier-free and ϕ admits a stratification that assigns distinct values to all of the variables y1,…,yl, ϕ=∀x1⋯∀xk∃y1⋯∃ylθ where θ is quantifier-free and ϕ admits a stratification that assigns the same value to all of the variables y1,…,yl. (shrink)

We show that a Kueker simple theory eliminates Ǝ∞ and densely interprets weakly minimal formulas. As part of the proof we generalize Hrushovski's dichotomy for almost complete formulas to simple theories. We conclude that in a unidimensional simple theory an almost-complete formula is either weakly minimal or trivially-almost-complete. We also observe that a small unidimensional simple theory is supersimple of finite SU-rank.

We lay down the groundwork for the treatment of almost hyperdefinable groups: notions from [5] are put into a natural hierarchy, and new notions, essential to the study to such groups, fit elegantly into this hierarchy. We show that "classical" properties of definable and hyperdefinable groups in simple theories can be generalised to this context. In particular, we prove the existence of stabilisers of Lascar strong types and of the connected and locally connected components of subgroups, and that in (...) a simple one-based theory an almost hyperdefinable group is bounded-by-abelian-by-bounded. (shrink)

A study of smooth classes whose generic structures have simple theory is carried out in a spirit similar to Hrushovski 147; Simplicity and the Lascar group, preprint, 1997) and Baldwin–Shi 1). We attach to a smooth class K0, of finite -structures a canonical inductive theory TNat, in an extension-by-definition of the language . Here TNat and the class of existentially closed models of =T+,EX, play an important role in description of the theory of the K0,-generic. (...) We show that if M is the K0,-generic then MEX. Furthermore, if this class is an elementary class then Th=Th). The investigations by Hrushovski and Pillay , provide a general theory for forking and simplicity for the nonelementary classes, and using these ideas, we show that if K0,, where {,*}, has the joint embedding property and is closed under the Independence Theorem Diagram then EX is simple. Moreover, we study cases where EX is an elementary class. We introduce the notion of semigenericity and show that if a K0,-semigeneric structure exists then EX is an elementary class and therefore the -theory of K0,-generic is near model complete. By this result we are able to give a new proof for a theorem of Baldwin and Shelah 1359). We conclude this paper by giving an example of a generic structure whose first-order theory is simple. (shrink)

In recent discussions of the Humean Theory of Motivation (HTM), several authors – not to mention other philosophers around the proverbial water cooler – have appealed to the simplicity of the theory to defend it. But the argument from simplicity has rarely been explicated or received much critical attention – until now. I begin by reconstructing the argument and then argue that it suffers from a number of problems. Most importantly, first, I argue that HTM is unlikely to (...) be simpler than even close competing theories, and second, it is unlikely that a plausible version of the theory will be very simple. Moreover, I argue that a convincing case for HTM is likely to have to show that it is more virtuous than defenders have done so far. (shrink)

The binding group theorem for stable theories is partially extended to the simple context. Some results concerning internality are proved. We also introduce a ‘small’ normal subgroup G0+ of the automorphism group and show that if p is Q-internal then it has a finite exponent and G/G0+ is interpretable.

We study model theory of fields with actions of a fixed finite group scheme. We prove the existence and simplicity of a model companion of the theory of such actions, which generalizes our previous results about truncated iterative Hasse–Schmidt derivations [13] and about Galois actions [14]. As an application of our methods, we obtain a new model complete theory of actions of a finite group on fields of finite imperfection degree.

We generalize tools and results from first order stable theories to groups inside a simple stable strongly homogeneous model.

An ω-categorical supersimple group is finite-by-abelian-by-finite, and has finite SU-rank. Every definable subgroup is commensurable with an acl( $\emptyset$ )-definable subgroup. Every finitely based regular type in a CM-trivial ω-categorical simple theory is non-orthogonal to a type of SU-rank 1. In particular, a supersimple ω-categorical CM-trivial theory has finite SU-rank.

_ Source: _Volume 29, Issue 1, pp 9 - 38 Hobbes tried to develop a strict version of the mechanical philosophy, in which all physical phenomena were explained only in terms of bodies in motion, and the only forces allowed were forces of collision or impact. This ambition puts Hobbes into a select group of original thinkers, alongside Galileo, Isaac Beeckman, and Descartes. No other early modern thinkers developed a strict version of the mechanical philosophy. Natural philosophies relying solely (...) on bodies in motion require a concept of inertial motion. Beeckman and Descartes assumed rectilinear motions were rectilinear, but Galileo adopted a theory which has been referred to as circular inertia. Hobbes’s natural philosophy depended to a large extent on what he called “simple circular motions.” In this paper, I argue that Hobbes’s simple circular motions derived from Galileo’s belief in circular inertia. The paper opens with a section outlining Galileo’s concept, the following section shows how Hobbes’s physics depended upon circular motions, which are held to continue indefinitely. A third section shows the difficulty Hobbes had in maintaining a strictly mechanistic philosophy, and the conclusion offers some speculations as to why Galileo’s circular inertia was never entertained as a serious rival to rectilinear inertia, except by Hobbes. (shrink)

It seems to be a widely shared view that any defensible desire-fulfillment theory of welfare must be framed not in terms of what an agent, in fact, desires but rather in terms of what an agent would desire under hypothetical conditions that include improved information. Unfortunately, though, such accounts are subject to serious criticisms. In this paper I show that in the face of these criticisms the best response is to jettison any appeal to idealized information conditions: the considerations (...) put forward in support of the appeal to what would be desired in hypothetical circumstances of improved information do not, in fact, give adequate reason to make that appeal. (shrink)

Let M be a smooth, compact manifold of dimension n ≥ 5 and sectional curvature | K | ≤ 1. Let Met (M) = Riem(M)/Diff(M) be the space of Riemannian metrics on M modulo isometries. Nabutovsky and Weinberger studied the connected components of sublevel sets (and local minima) for certain functions on Met (M) such as the diameter. They showed that for every Turing machine T e , e ∈ ω, there is a sequence (uniformly effective in e) of homology (...) n-spheres {P k e } k ∈ ω which are also hypersurfaces, such that P k e is diffeomorphic to the standard n-sphere S n (denoted P k e ≈ diff S n ) iff T e halts on input k, and in this case the connected sum N k e =M ♯ P k e ≈ diff M , so N k e ∈ Met(M), and N k e is associated with a local minimum of the diameter function on Met(M) whose depth is roughly equal to the settling time σ e (k) of T e on inputs y i } ∈ ω of c.e. sets so that for all i the settling time of the associated Turing machine for A i dominates that for A i + 1 , even when the latter is composed with an arbitrary computable function. From this, Nabutovsky and Weinberger showed that the basins exhibit a "fractal" like behavior with extremely big basins, and very much smaller basins coming off them, and so on. This reveals what Nabutovsky and Weinberger describe in their paper on fractals as "the astonishing richness of the space of Riemannian metrics on a smooth manifold, up to reparametrization." From the point of view of logic and computability, the Nabutovsky-Weinberger results are especially interesting because: (1) they use c.e. sets to prove structural complexity of the geometry and topology, not merely undecidability results as in the word problem for groups, Hilbert's Tenth Problem, or most other applications; (2) they use nontrivial information about c.e. sets, the Soare sequence {A i } i ∈ ω above, not merely G öodel's c.e. noncomputable set K of the 1930's; and (3) without using computability theory there is no known proof that local minima exist even for simple manifolds like the torus T 5 (see §). (shrink)

One of the criteria to a strong principle in natural sciences is simplicity. The conventional view holds that the world is provided with natural laws that must be simple. This common-sense approach is a modern rewording of the medieval philosophical/theological concept of the Multiple arising from (and generated by) the One. Humans need to pursue unifying frameworks, classificatory criteria and theories of everything. Still, the fact that our cognitive abilities tend towards simplification and groupings does not necessarily entail that (...) this is the way the world works. Here we ask: what if singularity does not pave the way to multiplicity? How will we be sure if the Ockham’s razor holds in real life? We will show in the sequel that the propensity to reduce to simplicity the relationships among the events leads to misleading interpretations of scientific issues. We are not going to take a full sceptic turn: we will engage in active outreach, suggesting examples from biology and physics to demonstrate how a novel methodological antiunitary approach might help to improve our scientific attitude towards world affairs. We will provide examples from aggregation of SARS-Cov-2 particles, unclassified extinct creatures, pathological brain stiffness. Further, we will describe how antiunitary strategies, plagiarising medieval concepts from William od Ockham and Gregory of Rimini, help to explain novel relational approaches to quantum mechanics and the epistemological role of our mind in building the real world. (shrink)

Dissipative structures exist at all scales, systems, and at different levels of complexity. A thermodynamic theory integrating simple and complex DS is introduced, which addresses existence of growing/decaying DS based on their entropy analysis. Two entropy-based dimensionless ratios are introduced, which explain negentropy-debt payment and existence of DS with growth or decay. It is shown that excess negentropy debt payment is needed and beneficial for growing DS; but for decaying DS, it hastens its approach to perish and is (...) counter-productive. Growing complex DS tend to pay lower negentropy debt to their surroundings, due to involvement in other activities enabled by complexity; e.g. mediation for survival that is linked to their mortality. Hence, disorder of complex DS increases, due to which, their growth can be un-sustained, leading to entry in decay-phase in spite of availability of adequate mass-energy in-flows. Proper handling or reduction of complexity enables growth in the direction of ideal growth, which is limited only by availability of adequate mass-energy in-flows. (shrink)

The main aim is to extend the range of logics which solve the set-theoretic paradoxes, over and above what was achieved by earlier work in the area. In doing this, the paper also provides a link between metacomplete logics and those that solve the paradoxes, by finally establishing that all M1-metacomplete logics can be used as a basis for naive set theory. In doing so, we manage to reach logics that are very close in their axiomatization to that of (...) the logic R of relevant implication. A further aim is the use of metavaluations in a new context, expanding the range of application of this novel technique, already used in the context of negation and arithmetic, thus providing an alternative to traditional model theoretic approaches. (shrink)

We present a cut-elimination proof for simple type theory with an axiom of choice formulated in the language with an epsilon-symbol. The proof is modeled after Takahashi's proof of cut-elimination for simple type theory with extensionality. The same proof works when types are restricted, for example for second-order classical logic with an axiom of choice.

After leading to a new axiomatic derivation of quantum theory, the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles, the automata theory is quantum ab-initio, and does not assume Lorentz (...) covariance and mechanical notions. Being discrete it can describe localized states and measurements, solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (shrink)

It is sometimes claimed that string theory posits a fundamental ontology including extended mereological simples, either in the form of minimum-sized regions of space or of the strings themselves. But there is very little in the actual theory to support this claim, and much that suggests it is false. Extant string theories treat space as a continuum, and strings do not behave like simples.

The standard account of counterfactuals that most philosophers endorse—Lewis's 'Analysis 1' — is wrong. The correct theory is one invented by Jonathan Bennett in 1984 which he called 'The Simple Theory'. Bennett later argued himself out of that theory and went on to champion the standard account. But those arguments fail. The Simple Theory has been right all along.

The work reported here is of two sorts. One the one hand, we attempt to consolidate a lot of recent work on situation theory into a workable version, one that researchers can use and add to in ways that might be suitable for various applications. On the other, we attempt to solve a representational problem with situation theory: how can we represent complicated situation-theoretic objects in a way that is perspicuous. Our way in to the latter problem comes (...) from an on-going project aimed at bringing insights from Discourse Representation Theory and Situation Theory to bear on one another. In terms of this project, this paper represents a rather modest contribution. Our goal is to design a language for representing situationtheoretic objects that is based on Kamp's discourse representation structures. This was where we started but we found that working on the notation and its semantics led us to clari cations of various aspects of situation theory. A major part of the clari cation in the theory comes from our use of the work on parameters and abstraError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapction by Aczel and Lunnon AL]. (shrink)

Prioritized bases, i.e., weakly ordered sets of sentences, have been used for specifying an agent’s ‘basic’ or ‘explicit’ beliefs, or alternatively for compactly encoding an agent’s belief state without the claim that the elements of a base are in any sense basic. This paper focuses on the second interpretation and shows how a shifting of priorities in prioritized bases can be used for a simple, constructive and intuitive way of representing a large variety of methods for the change of (...) belief states—methods that have usually been characterized semantically by a system-of-spheres modeling. Among the methods represented are ‘radical’, ‘conservative’ and ‘moderate’ revision, ‘revision by comparison’ in its raising and lowering variants, as well as various constructions for belief expansion and contraction. Importantly, none of these methods makes any use of numbers. (shrink)

On one level, the idea here is simple: organise people into small groups and see how they react to different ways of doing politics. On another, it is more challenging: evaluate different political principles by seeing how people behave when they have to work with them. Do they, for example, become more or less engaged as we alter the number of chairing roles, debates, and votes? Do they stick around longer in-person or online? Do they come back more or (...) less often when key powers are distributed by lottery? There is then a focus here, not on the decisions participants make, as found in ‘X-Phi’ and deliberative-democracy experiments, but rather on the process by which they came to make those decisions. We want to know how they found that process as a way of doing politics. Or, more precisely, how they reacted to the institutions and in turn principles those processes represent, because, if we know that, we also know something fundamental about the value of those principles. (shrink)

There are a number of key data-centric questions that must be answered when developing classifiers for operator functional states. “Should a supervised or unsupervised learning approach be used? What degree of labeling and transformation must be performed on the data? What are the trade-offs between algorithm flexibility and model interpretability, as generally these features are at odds?” Here, we focus exclusively on the labeling of cognitive load data for supervised learning. We explored three methods of labeling cognitive states for three-state (...) classification. The first method labels states derived from a tertiary split of trial difficulty during a spatial memory task. The second method was more adaptive; it employed a mixed-effects stress–strain curve and estimated an individual’s performance asymptotes with respect to the same spatial memory task. The final method was similar to the second approach; however, it employed a mixed-effects Rasch model to estimate individual capacity limits within the context of item response theory for the spatial memory task. To assess the strength of each of these labeling approaches, we compared the area under the curve (AUC) for receiver operating curves (ROCs) from elastic net and random forest classifiers. We chose these classifiers based on a combination of interpretability, flexibility, and past modeling success. We tested these techniques across two groups of individuals and two tasks to test the effects of different labeling techniques on cross-person and cross-task transfer. Overall, we observed that the Rasch model labeling paired with a random forest classifier led to the best model fits and showed evidence of both cross-person and cross-task transfer. (shrink)

Robert Stalnaker recently proposed a simple theory of propositions using the notion of a set of propositions being consistent, and conjectured that this theory is equivalent to the claim that propositions form a complete atomic Boolean algebra. This paper clarifies and confirms this conjecture. Stalnaker also noted that some of the principles of his theory may be given up, depending on the intended notion of proposition. This paper therefore also investigates weakened constraints on consistency and the (...) corresponding classes of Boolean algebras. (shrink)

"We prove that any variety of relation algebras which contains an algebra with infinitely many elements below the identity, or which contains the full group relation algebra on some infinite group (or on arbitrarily large finite groups), must have an undecidable equational theory. Then we construct an embedding of the lattice of all subsets of the natural numbers into the lattice of varieties of relation algebras such that the variety correlated with a set [italic capital]X of natural (...) numbers has a decidable equational theory if and only if [italic capital]X is a decidable (i.e., recursive) set. Finally, we construct an example of an infinite, finitely generated, simple, representable relation algebra that has a decidable equational theory.'' -- Abstract. (shrink)

All known structural extensions of the substructural logic $\textbf{FL}_{\textbf{e}}$, the Full Lambek calculus with exchange/commutativity (corresponding to subvarieties of commutative residuated lattices axiomatized by $\{\vee, \cdot, 1\}$ -equations), have decidable theoremhood; in particular all the ones defined by knotted axioms enjoy strong decidability properties (such as the finite embeddability property). We provide infinitely many such extensions that have undecidable theoremhood, by encoding machines with undecidable halting problem. An even bigger class of extensions is shown to have undecidable deducibility problem (the (...) corresponding varieties of residuated lattices have undecidable word problem); actually with very few exceptions, such as the knotted axioms and the other prespinal axioms, we prove that undecidability is ubiquitous. Known undecidability results for non-commutative extensions use an encoding that fails in the presence of commutativity, so and-branching counter machines are employed. Even these machines provide encodings that fail to capture proper extensions of commutativity, therefore we introduce a new variant that works on an exponential scale. The correctness of the encoding is established by employing the theory of residuated frames. (shrink)

This paper presents an account of what it is for a property or relation (or ‘attribute’ for short) to be logically simple. Based on this account, it is shown, among other things, that the logically simple attributes are in at least one important way sparse. This in turn lends support to the view that the concept of a logically simple attribute can be regarded as a promising substitute for Lewis’s concept of a perfectly natural attribute. At least (...) in part, the advantage of using the former concept lies in the fact that it is amenable to analysis, where that analysis—i.e., the account put forward in this paper—requires the adoption neither of an Armstrongian theory of universals nor of a primitive notion of naturalness, fundamentality, or grounding. (shrink)

1 A particular may have other particulars as parts, but according to the bundle theory its ultimate constituents are confined to universals. Parts are different from constituents or components. A part is a type of constituent, but there are constituents that are not parts. Parts belong to the same general category as the whole: if a concrete particular has parts, those parts will themselves be concrete particulars. This is not always the case with constituents: the constituents of a fact (...) do not have to be facts and the constituents (or members) of a set do not have to be sets. The relation of “being a part of” is also transitive, whereas the relation of “being a constituent of” is not always transitive. If a particular has parts, such as atoms, then its constituents include its intrinsic properties, its atoms, and the arrangement relation. If an atom has parts, such as subatomic particles, then the constituents of the atom include its properties, the subatomic particles, and the arrangement universal. If it is like this all the way down without any termination (no bedrock), then the bundle theory says that at each stage there are only universals and ordinary particulars with parts, in other words there are no bare particulars. This approach should also work if there were arbitrary undetached parts that are real entities. The alternative to no bedrock is metaphysical atomism. There are two ways that metaphysical atomism could be true in classical mechanics: (1) if the ultimate constituents of matter are point particles — perhaps electrons are point particles, (2) if matter is continuously divisible and arbitrary undetached parts are not real entities or real parts. But it would be rash to say that these were the only two options for all theories. Point particles are a convenient kind of particular to think about when discussing the bundle theory. There could be just three properties bundled together, a certain mass, a certain charge, and the property of being point like.. (shrink)

We develop the theory of germs of generic functions in simple theories. Starting with an algebraic quadrangle (or other similar hypotheses), we obtain an "almost" generic group chunk, where the product is denned up to a bounded number of possible values. This is the first step towards the proof of the group configuration theorem for simple theories, which is completed in [3].

We examine the conditions under which we can keep simplicity or categoricity after adding a Skolem function to the theory.

Both extended simples and unextended complexes have been extensively discussed and widely used in metaphysics and philosophy of physics. However, the characterizations of such notions are not entirely satisfactory inasmuch as they rely on a mereological notion of extension that is too simplistic. According to such a mereological notion, being extended boils down to having a mereologically complex exact location. In this paper, I make a detailed plea to supplement this notion of extension with a different one that is phrased (...) in terms of measure theory. This proposal has significant philosophical payoffs. I provide new characterizations of both extended simples and unextended complexes, that help re-evaluating the question of whether such entities are metaphysically possible. Finally, I advance several suggestions as to how different notions of extension relate, first, to one another and, second, to mereological structure. (shrink)

The classical Ulm theory provides a complete set of invariants for countable abelian p-groups, and hence also for countable torsion abelian groups. These invariants involve countable ordinals. One can read off many simple structural properties of such groups directly from the Ulm theory. We carry out a reverse mathematics analysis of several such properties. In many cases, we reverse to ATR0, thereby demonstrating a kind of necessary use of Ulm theory.

This paper completes the proof of the group configuration theorem for simple theories started in [1]. We introduce the notion of an almost hyperdefinable structure, and show that it has a reasonable model theory. We then construct an almost hyperdefinable group from a polygroup chunk.

In the present paper we shall prove that countable ω-categorical simple CM-trivial theories and countable ω-categorical simple theories with strong stable forking are low. In addition, we observe that simple theories of bounded finite weight are low.

With the present paper I maintain that the group field theory (GFT) approach to quantum gravity can help us clarify and distinguish the problems of spacetime emergence from the questions about the nature of the quanta of space. I will show that the mechanism of phase transition suggests a form of indifference between scales (or phases) and that such an indifference allows us to black-box questions about the nature of the ontology of the fundamental levels of the (...) class='Hi'>theory. I consider the GFT approach to quantum gravity which derives spacetime as an emergent property from abstract non-geometrical tetrahedra through a processes of phase transition. Because the physical interpretation of the tetrahedra is problematic in view of their (non)-spatiotemporal nature, I will apply the considerations about phase transitions to GFT and conclude that the fundamental ontology of the theory and the mechanism of spacetime emergence can and should be treated separately. (shrink)

In conclusion, then, we have tried to show that Drug actions can be predicted and described best on a probabilistic basis and information theory offers a suitable framework for such predictions. Drug actions are fundamentally of the all-or-none type involving the choice between two alternatives and these choises are therefore measurable by binary digits. Drug actions are not absolutely but only relatively specific and such specificity can be measured on the basis of information theory by an array of (...) suitable correlation data. Synergisms and antagonisms can best be explained and measured by considering them as intersymbol influences in communications. A theory of drug action based on information theory is more comprehensive and simpler than any theory based on the principles of classical physics and chemistry.However, these conclusions provide only the general basis for future detailed studies of various drug groups which will probably require the collaboration of chemists and pharmacologists as well as biological mathematicians to produce practical results.Der Verfasser bespricht die verschiedenen Probleme der Drogenwirkung und der Reizwirkung im allgemeinen und kommt zu den folgenden Schlussfolgerungen: Die Wirkung der Drogen kann am besten auf Grundlage der Wahrscheinlichkeitstheorie vorhergesagt und beschrieben werden und die mathematische Informationstheorie bietet einen befriedigenden Rahmen für solche Voraussagungen. Drogenwirkungen beruhen im Grunde genommen auf dem „Alles oder Nichts Prinzip”, d.h. sie beruhen auf einer Wahl zwischen zwei Alternativen und diese Wahlen sind als Logarithmen mit der Basis 2 messbar. Drogenwirkungen sind nicht absolut sondern nur relativ spezifisch und diese SpezifizitÄt kann auf Grundlage der Informationstheorie durch eine Matrize gernessen werden die eine Anordnung passender Korrelationsdaten enthÄlt. Synergismen und Antagonismen zwischen verschiedenen Substanzen können am besten dadurch erklÄrt und gemessen werden, dass man sie als gegenseitige Beeinflussung zwischen den eine Mitteilung bildenden Symbolen auffasst. Eine Theorie der Drogenwirkung auf der Informationstheorie basiert, ist umfassender und einfacher als irgend eine andere der die Prinzipien der klassischen Physik und Chemie zugrunde liegen.Jedoch bieten diese Schlussfolgerungen nur die allgemeine Grundlage für zukünftige detaillierte Studien der verschiedenen Drogenklassen und diese Studien werden die Mitarbeit der Chemiker, der Pharmakologen und der mathematisch eingestellten Biologen erfordern.L'auteur discute les divers aspects de l'action des drogues et des stimulus en général et arrive aux conclusions suivantes: La meilleure manière de prédire et de décrire l'action des drogues est celle qui se base sur la théorie des probabilités, et la théorie mathématique des informations et communications offre un cadre satisfaisant pour de telles prédictions. L'action des drogues est essentiellement du type „tout ou rien”, c'es-à-dire qu'un choix entre deux alternatives prend place et ces choix peuvent Être mesurés par des digits binaires. L'action des drogues est charactérisée non pas par une specificité absolue mais seulement relative et cette specificité peut Être mesurée sur base de la théorie des informations par une matrice contenant des données corrélatives convenables. Les synergismes et les antagonismes des substances agissant simultanément peuvent Être expliqués et mesurés en les considérant comme des influences, existantes entre les symboles constituant une communication. Une théorie pharmacodynamique basée sur la théorie des informations est plus compréhensive et plus simple qu'une théorie basée sur les principes de la physique et de la chimie classiques.Toutefois, ces conclusions ne fournissent que la base générale pour des études futures détaillées des diverses classes de substances pharmacologiques, et ces études demanderont la collaboration des chimistes, des pharmacologistes ainsi que des biologistes mathématiciens. (shrink)

The mechanism of laser-induced gas ionization is analyzed in the context of the theories presently available, namely multiphoton and cascade theory, and their predictions are shown to be in serious divergence from experimentation. A novel hypothesis is then formulated which considers the classical photon energy expression ε=hν as the limit of a general expression ε=hν/[1−βν f(I)],f(I) being a function of light intensity and βν a coefficient such that βν f(I) significantly differs from zero only for high-intensity laser light. Starting (...) from the new formulation of the photon energy expression, a theory is developed for the laser ionization phenomenon and a few simple relations are found. The successful use of these relations in the verification of the experimental results suggests that the new photon energy expression has a real physical meaning rather than an empirical significance, and some considerations on the physical meaning are presented. (shrink)

Inertial frames and Lorentz transformations have a preferred status in the special theory of relativity (STR). Lorentz transformations, in turn, embody Einstein's convention that the velocity of light is isotropic, a convention that is necessary for the establishment of a standard signal synchrony. If the preferred status of Lorentz transformations in STR is not due to some particular bias introduced by a convention on signal synchronism, but to the fact that the Lorentz transformation group is the symmetry (...) class='Hi'>group of the theory, then the signal synchronism is not a matter of convention but rather a matter of fact. In order to explore the conventionalist thesis, that within the frame of STR isotropy in the velocity of light and, hence, signal synchronism is a matter of convention, we need a generalized Lorentz transformation group that does not embody Einstein's isotropy convention, and upon which STR can be based. We present here a new approach to the resulting search for a generalized STR, which is well suited for establishing some well-known results of Winnie as well as some new results. (shrink)

In his testamentary letter to Auguste Chevalier, Évariste Galois states that, in modern terminology, the smallest simple group has order 60. No proof of this statement survives in his papers, and it has been suggested that a proof would have been impossible using the methods available at the time. We argue that this assertion is unduly pessimistic. Moreover, one fragmentary document, dismissed as a triviality and misunderstood, looks suspiciously like cryptic notes related to this result. We give an (...) elementary proof of Galois’s statement, explain why it is likely that he would have been aware of the methods involved, and discuss the potential relevance of the fragment. (shrink)

The difficulties of relativistic particle theories formulated by means of canonical quantization, such as those of Klein–Gordon and Dirac, ultimately led theoretical physicists to turn to quantum field theory to model elementary particle physics. In order to overcome these difficulties, the theories of the present approach are developed deductively from the physical principles that specify the system, without making use of canonical quantization. For a free particle these starting assumptions are invariance of the theory and covariance of position (...) with respect to Poincaré transformations. In pursuing the approach, the effectiveness of group theoretical methods is exploited. The coherent development of our program has shown that robust classes of representations of the Poincaré group, discarded by the known particle theories, can in fact be taken as bases for perfectly consistent theories. For massive spin zero particles, six inequivalent theories have been determined, two of which do not correspond to any of the current ones; all of these theories overcome the difficulties of Klein–Gordon one. The present lack of the explicit transformation properties of position with respect to boosts prevents the complete determination of non zero spin particle theories. In the past a particular form of these transformation properties was adopted by Jordan and Mukunda. We check its consistency within the present approach and find that for spin \ particles there is only one consistent theory, which is unitarily related to Dirac’s; yet, once again, it requires classes of irreducible representations previously discarded. (shrink)

We completely characterize the simple majority weighted voting game achievable hierarchies, and, in doing so, show that a problem about representative government, noted by J. Banzhaf [Rutgers Law Review 58, 317–343 (1965)] cannot be resolved using the simple majority quota. We also demonstrate that all hierarchies achievable by any quota can be achieved if the simple majority quota is simply incremented by one.

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