According to the hierarchy of models (HoM) account of scientific experimentation developed by Patrick Suppes and elaborated by Deborah Mayo, theoretical considerations about the phenomena of interest are involved in an experiment through theoretical models that in turn relate to experimental data through data models, via the linkage of experimental models. In this paper, I dispute the HoM account in the context of present-day high-energy physics (HEP) experiments. I argue that even though the HoM account (...) aims to characterize experimentation as a model-based activity, it does not involve a modeling concept for the process of data acquisition, and it thus fails to provide a model-based characterization of the theory-experiment relationship underlying this process. In order to characterize the foregoing relationship, I propose the concept of a model of data acquisition and illustrate it in the case of the ATLAS experiment at CERN’s Large Hadron Collider, where the Higgs boson was discovered in 2012. I show that the process of data acquisition in the ATLAS experiment is performed according to a model of data acquisition that specifies and organizes the experimental procedures necessary to select the data according to a predetermined set of selection criteria. I also point out that this data acquisition model is theory-laden, in the sense that the underlying data selection criteria are determined by considering the testable predictions of the theoretical models that the ATLAS experiment is aimed to test. I take this sense of theory-ladenness to indicate that the relationship between the procedures of the ATLAS experiment and the theoretical models of the phenomena of interest is first established, prior to the formation of data models, through the data acquisition model of the experiment, thus not requiring the intermediary of other types of models as suggested by the HoM account. I therefore conclude that in the context of present-day HEP experiments, the HoM account does not consistently extend to the process of data acquisition so as to include models of data acquisition. (shrink)

According to the hierarchy of models account of scientific experimentation developed by Patrick Suppes and elaborated by Deborah Mayo, theoretical considerations about the phenomena of interest are involved in an experiment through theoretical models that in turn relate to experimental data through data models, via the linkage of experimental models. In this paper, I dispute the HoM account in the context of present-day high-energy physics experiments. I argue that even though the HoM account aims to (...) characterize experimentation as a model-based activity, it does not involve a modeling concept for the process of data acquisition, and it thus fails to provide a model-based characterization of the theory-experiment relationship underlying this process. In order to characterize the foregoing relationship, I propose the concept of a model of data acquisition and illustrate it in the case of the ATLAS experiment at CERN’s Large Hadron Collider, where the Higgs boson was discovered in 2012. I show that the process of data acquisition in the ATLAS experiment is performed according to a model of data acquisition that specifies and organizes the experimental procedures necessary to select the data according to a predetermined set of selection criteria. I also point out that this data acquisition model is theory-laden, in the sense that the underlying data selection criteria are determined by considering the testable predictions of the theoretical models that the ATLAS experiment is aimed to test. I take this sense of theory-ladenness to indicate that the relationship between the procedures of the ATLAS experiment and the theoretical models of the phenomena of interest is first established, prior to the formation of data models, through the data acquisition model of the experiment, thus not requiring the intermediary of other types of models as suggested by the HoM account. I therefore conclude that in the context of present-day HEP experiments, the HoM account does not consistently extend to the process of data acquisition so as to include models of data acquisition. (shrink)

Economics prefers complete explanations: general over partial equilibrium, microfoundational over aggregate. Similarly, probabilistic accounts of causation frequently prefer greater detail to less as in typical resolutions of Simpson’s paradox. Strategies of causal refinement equally aim to distinguish direct from indirect causes. Yet, there are countervailing practices in economics. Representative-agent models aim to capture economic motivation but not to reduce the level of aggregation. Small structural vector-autoregression and dynamic stochastic general-equilibrium models are practically preferred to larger ones. The distinction (...) between exogenous and endogenous variables suggests partitioning the world into distinct subsystems. The tension in these practices is addressed within a structural account of causation inspired by the work of Herbert Simon’s, which defines cause with reference to complete systems adapted to deal with incomplete systems and piecemeal evidence. The focus is on understanding the constraints that a structural account of causation places on the freedom to model complex or lower-order systems as simpler or higher-order systems and on to what degree piecemeal evidence can be incorporated into a structural account. (shrink)

Processes comparable in important respects to those underlying human conscious and non-conscious processing can be identified in a range of species and it is argued that these reflect evolutionary precursors of the human processes. A distinction is drawn between two types of processing: stimulus-based and higher-order. For ‘higher-order,’ in humans the operations of processing are themselves associated with conscious awareness. Conscious awareness sets the context for stimulus-based processing and its end-point is accessible to conscious awareness. However, the mechanics of the (...) translation between stimulus and response proceeds without conscious control. The paper argues that higher-order processing is an evolutionary addition to stimulus-based processing. The model’s value is shown for gaining insight into a range of phenomena and their link with consciousness. These include brain damage, learning, memory, development, vision, emotion, motor control, reasoning, the voluntary versus involuntary debate, and mental disorder. (shrink)

The studies of mysticism have traditionally emphasized a common core centered around experiences of ego dissolution and unity. However, this focus on a central set of experiences tends to downplay the non-central aspects, resulting in a limited understanding that may not encompass many other types of extraordinary experiences. This article proposes a layered hierarchy model of mysticism, which reverts to the fundamental definition of mysticism and resonates with the Jamesian characteristics of mysticism as noetic and ineffable. Consequently, an extended (...) definition is put forth to characterize mysticism as the transcendence of perceived reality and the transformation of the perceiver. Within this proposed model, four layers of mysticism are delineated. Monistic Mysticism is characterized by the perception of oneness in all existence and the dissolution of selfhood, exemplified by perennialist mystical unity. Nondualistic Mysticism involves the recognition of a higher reality beyond the mundane world and the subjugation of the ego to an idealized divine, exemplified by religious experiences. Dualistic Mysticism encompasses a world of spirits in contrast to human reality, where the self detaches from and interacts with spiritual beings, exemplified by psychedelic experiences and spiritism. Pluralistic Mysticism entails numerous coexisting realities, and the self is understood to have many facets and boundless potentials, exemplified by psychic phenomena and non-physicalism. This expanded framework broadens the scope of mysticism and makes it a versatile tool for studying a wide range of human experiences under a unified framework. (shrink)

In this paper we investigate composition models of incarnation, according to which Christ is a compound of qualitatively and numerically different constituents. We focus on three-part models, according to which Christ is composed of a divine mind, a human mind, and a human body. We consider four possible relational structures that the three components could form. We argue that a ‘hierarchy of natures’ model, in which the human mind and body are united to each other in the (...) normal way, and in which they are jointly related to the divine mind by the relation of co-action, is the most metaphysically plausible model. Finally, we consider the problem of how Christ can be a single person even when his components may be considered persons. We argue that an Aristotelian metaphysics, according to which identity is a matter of function, offers a plausible solution: Christ's components may acquire a radically new identity through being parts of the whole, which enables them to be reidentified as parts, not persons. (shrink)

In this paper we investigate composition models of incarnation, according to which Christ is a compound of qualitatively and numerically different constituents. We focus on three-part models, according to which Christ is composed of a divine mind, a human mind, and a human body. We consider four possible relational structures that the three components could form. We argue that a ’hierarchy of natures’ model, in which the human mind and body are united to each other in the (...) normal way, and in which they are jointly related to the divine mind by the relation of coaction, is the most metaphysically plausible model. Finally, we consider the problem of how Christ can be a single person even when his components may be considered persons. We argue that an Aristotelian metaphysics, according to which identity is a matter of function, offers a plausible solution: Christ’s components may acquire a radically new identity through being parts of the whole, which enables them to be reidentified as p. (shrink)

Assuming the existence of a measurable cardinal, we define a hierarchy of Ramsey cardinals and a hierarchy of normal filters. We study some combinatorial properties of this hierarchy. We show that this hierarchy is absolute with respect to the Dodd-Jensen core model, extending a result of Mitchell which says that being Ramsey is absolute with respect to the core model.

Let CH be the class of compacta (i.e., compact Hausdorff spaces), with BS the subclass of Boolean spaces. For each ordinal α and pair $\langle K,L\rangle$ of subclasses of CH, we define Lev ≥α K,L), the class of maps of level at least α from spaces in K to spaces in L, in such a way that, for finite α, Lev ≥α (BS,BS) consists of the Stone duals of Boolean lattice embeddings that preserve all prenex first-order formulas of quantifier rank (...) α. Maps of level ≥ 0 are just the continuous surjections, and the maps of level ≥ 1 are the co-existential maps introduced in [8]. Co-elementary maps are of level ≥α for all ordinals α; of course in the Boolean context, the co-elementary maps coincide with the maps of level ≥ω. The results of this paper include: (i) every map of level ≥ω is co-elementary; (ii) the limit maps of an ω-indexed inverse system of maps of level ≥α are also of level ≥α; and (iii) if K is a co-elementary class, k ≥ k (K,K) = Lev ≥ k+1 (K,K), then Lev ≥ k (K,K) = Lev ≥ω (K,K). A space X ∈ K is co-existentially closed in K if Lev ≥ 0 (K, X) = Lev ≥ 1 (K, X). Adapting the technique of "adding roots," by which one builds algebraically closed extensions of fields (and, more generally, existentially closed extensions of models of universal-existential theories), we showed in [8] that every infinite member of a co-inductive co-elementary class (such as CH itself, BS, or the class CON of continua) is a continuous image of a space of the same weight that is co-existentially closed in that class. We show here that every compactum that is co-existentially closed in CON (a co-existentially closed continuum) is both indecomposable and of covering dimension one. (shrink)

For any n, we construct a model of in which each formula is equivalent to an formula.

A $\Sigma _{1}^{2}$ truth for λ is a pair 〈Q, ψ〉 so that Q ⊆ Hλ, ψ is a first order formula with one free variable, and there exists B ⊆ Hλ+ such that (Hλ+; ε, B) $(H_{\lambda +};\in ,B)\vDash \psi [Q]$ . A cardinal λ is $\Sigma _{1}^{2}$ indescribable just in case that for every $\Sigma _{1}^{2}$ truth 〈Q, ψ〉 for λ, there exists $\overline{\lambda}<\lambda $ so that $\overline{\lambda}$ is a cardinal and $\langle Q\cap H_{\overline{\lambda}},\psi \rangle $ is a (...) $\Sigma _{1}^{2}$ truth for $\overline{\lambda}$ . More generally, an interval of cardinals [κ, λ] with κ ≤ λ is $\Sigma _{1}^{2}$ indescribable if for every $\Sigma _{1}^{2}$ truth 〈Q, ψ〉 for λ, there exists $??\leq \overline{\lambda}<\kappa,??\subseteq H_{\overline{\lambda}}$ , and π: $H_{\overline{\lambda}}\rightarrow H_{\lambda}$ so that $??$ is a cardinal, $\langle ??,\psi \rangle $ is a $\Sigma _{1}^{2}$ truth for $??$ , and π is elementary from $(H_{\overline{\lambda}};\in,??,??)$ with $\pi \,|\,??={\rm id}$ . We prove that the restriction of the proper forcing axiom to c-linked posets requires a $\Sigma _{1}^{2}$ indescribable cardinal in L, and that the restriction of the proper forcing axiom to c⁺-linked posets, in a proper forcing extension of a fine structural model, requires a $\Sigma _{1}^{2}$ indescribable 1-gap [κ, κ⁺]. These results show that the respective forward directions obtained in " Hierarchies of Forcing Axioms I" by Neeman and Schimmerling are optimal. (shrink)

This paper connects information with computation and cognition via concept of agents that appear at variety of levels of organization of physical/chemical/cognitive systems – from elementary particles to atoms, molecules, life-like chemical systems, to cognitive systems starting with living cells, up to organisms and ecologies. In order to obtain this generalized framework, concepts of information, computation and cognition are generalized. In this framework, nature can be seen as informational structure with computational dynamics, where an (info-computational) agent is needed for the (...) potential information of the world to actualize. Starting from the definition of information as the difference in one physical system that makes a difference in another physical system – which combines Bateson and Hewitt’s definitions, the argument is advanced for natural computation as a computational model of the dynamics of the physical world, where information processing is constantly going on, on a variety of levels of organization. This setting helps us to elucidate the relationships between computation, information, agency and cognition, within the common conceptual framework, with special relevance for biology and robotics. (shrink)

The analytic hierarchy process (AHP) can be used to determine co-author responsibility for a scientific paper describing collaborative research. The objective is to deter scientific fraud by holding co-authors accountable for their individual contributions. A hiearchical model of the research presented in a paper can be created by dividing it into primary and secondary elements. The co-authors then determine the contributions of the primary and secondary elements to the work as a whole as well as their own individual contributions. (...) They can use the results to determine authorship order. (shrink)

Several models of macromolecular arrangements in eukaryotic chromosomes have been proposed during the past fifteen years. Many of the models are consistent with physical and chemical data on the molecular components of chromosomes, and a few have the appearance of meeting the requirements for cytological organization in chromosomes. However, one of the most frustrating problems in developing a working model is to provide a scheme that fits genetic function while satisfying the structural parameters. This has not yet been (...) achieved.Although emphasis in this review has been placed on uninemic and polynemic models, alternatives, such as a bineme, for example, remain. It is clear, moreover, that the issue can be resolved only through continued efforts to make direct observations of chromosomes with light and electron microscopy coupled with the additional tools ofX-ray analysis and analytical biochemistry. A recent analysis byWray andStubblefield has led to a rather innovative model of the chromosome, and exemplifies the kind of approach needed to clarify the phenomenon. Furthermore, analyses of meiotic chromosomes may provide valuable insight for relating organization to genetic function . Of particular interest are mutation events as related to subchromatid organization, and the reorganization of chromosomal fibrils during early meiotic stages. At present, and as a generalization, the evidence points more strongly toward at least a binemic arrangement of chromosomal subunits than toward a uninemic one. (shrink)

The sense of self has always been a topic of high interest in both psychoanalysis and most recently in neuroscience. Nowadays, there is an agreement in psychoanalysis that the self emerges from the relationship with the other (e.g., the caregiver) in terms of his/her capacity to attune, regulate, and synchronize with the emergent self of the infant. The outcome of this relational/intersubjective synchronization is the development of the sense of self and its regulatory processes both in dynamic psychology and neuroscience. (...) In this work, we propose that synchrony is a fundamental biobehavioral factor in these dialectical processes between self and others which shapes the brain–body–mind system of the individuals, including their sense of self. Recently in neuroscience, it has been proposed by the research group around Northoff that the self is constituted by a brain-based nested hierarchical three-layer structure, including interoceptive, proprio-exteroceptive, and mental layers of self. This may be disrupted, though, when traumatic experiences occur. Following the three levels of trauma theorized by Mucci, we here suggest how different levels of traumatic experiences might have an enduring effect in yielding a trauma-based topographic and dynamic re-organization of the nested model of self featured by dissociation. In conclusion, we propose that different levels and degrees of traumatic experience are related to corresponding disruptions in the topography and dynamic of the brain-based three-layer hierarchical structure of the self. (shrink)

Large scale experiments at CERN’s Large Hadron Collider rely heavily on computer simulations, a fact that has recently caught philosophers’ attention. CSs obviously require appropriate modeling, and it is a common assumption among philosophers that the relevant models can be ordered into hierarchical structures. Focusing on LHC’s ATLAS experiment, we will establish three central results here: with some distinct modifications, individual components of ATLAS’ overall simulation infrastructure can be ordered into hierarchical structures. Hence, to a good degree of approximation, (...) hierarchical accounts remain valid at least as descriptive accounts of initial modeling steps. In order to perform the epistemic function Winsberg Model-based reasoning in scientific discovery. Kluwer Academic/plenum Publishers, New York, pp 255–269, 1999) assigns to models in simulation—generate knowledge through a sequence of skillful but non-deductive transformations—ATLAS’ simulation models have to be considered part of a network rather than a hierarchy, in turn making the associated simulation modeling messy rather than motley. Deriving knowledge-claims from this ‘mess’ requires two sources of justification: holistic validation :253–262, 2010; in Carrier M, Nordmann A Science in the context of application. Springer, Berlin, pp 115–130, 2011), and model coherence. As it turns out, the degree of model coherence sets HEP apart from other messy, simulation-intensive disciplines such as climate science, and the reasons for this are to be sought in the historical, empirical and theoretical foundations of the respective discipline. (shrink)

In this article we investigate infinitary propositional logics from the perspective of their completeness properties in abstract algebraic logic. It is well-known that every finitary logic is complete with respect to its relatively subdirectly irreducible models. We identify two syntactical notions formulated in terms of intersection-prime theories that follow from finitarity and are sufficient conditions for the aforementioned completeness properties. We construct all the necessary counterexamples to show that all these properties define pairwise different classes of logics. Consequently, we (...) obtain a new hierarchy of logics going beyond the scope of finitarity. (shrink)

This article seeks to reconcile a historicist sensitivity to how intellectually virtuous behavior is shaped by historical contexts with a non-relativist account of historical scholarship. To that end, it distinguishes between hierarchies of intellectual virtues and hierarchies of intellectual goods . The first hierarchy rejects a one-size-fits-all model of historical virtuousness in favor of a model that allows for significant varieties between the relative weight that historians must assign to intellectual virtues in order to acquire justified historical understanding. It (...) grounds such differences, not on the historians’ interests or preferences, but on their historiographical situations, so that hierarchies of virtues are a function of the demands that historiographical situations (defined as interplays of genre, research question, and state of scholarship) make upon historians. Likewise, the second hierarchy allows for the pursuit of various intellectual goods, but banishes the specter of relativism by treating historical understanding as an intellectual good that is constitutive of historical scholarship and therefore deserves priority over alternative goods. The position that emerges from this is classified as a form of weak historicism. (shrink)

In this paper I propose a type-hierarchy approach to provide an intersubjective framework for the evaluation of evolutionary analogies. This approach develops David Hull’s and others’ attempts to provide full generalisation for selection processes, in order to show that sociocultural development and, particularly, scientific change can be considered as an instance of Darwinian selection. I argue that the recent work by Eileen Cornell Way on type hierarchies can offer the kind of generalisation needed to solve the main problems that (...) still affect Hull’s theory and to show that the evolutionary analogy is, after all, only a particular way of grouping phenomena together. If Hull’s main objective is a unified theory of selection, which supports the idea that science selection and natural selection obey the same laws, I also argue that the type hierarchy approach to models shows that this objective is unsustainable as it stands, and is in need of further development. I will firstly introduce the general outline of the type hierarchy approach to models. Then, after a brief recapitulation of Hull’s main points and difficulties, I will try and construct a hierarchy for a general abstraction of selection processes. Finally I will introduce the main criticisms that Hull’s work has faced from philosophers and scientists, and show how they compare with my proposal. (shrink)

We give a sufficient condition for the inexpressibility of the k-th extended vectorization of a generalized quantifier $\sf Q$ in ${\rm FO}({\vec Q}_k)$ , the extension of first-order logic by all k-ary quantifiers. The condition is based on a model construction which, given two ${\rm FO}({\vec Q}_1)$ -equivalent models with certain additional structure, yields a pair of ${\rm FO}({\vec Q}_k)$ -equivalent models. We also consider some applications of this condition to quantifiers that correspond to graph properties, such as (...) connectivity and planarity. (shrink)

We consider ω n -automatic structures which are relational structures whose domain and relations are accepted by automata reading ordinal words of length ω n for some integer n ≥ 1. We show that all these structures are ω-tree-automatic structures presentable by Muller or Rabin tree automata. We prove that the isomorphism relation for ω 2 -automatic (resp. ω n -automatic for n > 2) boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups) is not (...) determined by the axiomatic system ZFC. We infer from the proof of the above result that the isomorphism problem for ω n -automatic boolean algebras, n ≥ 2, (respectively, rings, commutative rings, non commutative rings, non commutative groups) is neither a ${\mathrm{\Sigma }}_{2}^{1}-\mathrm{s}\mathrm{e}\mathrm{t}$ nor a ${\mathrm{\Pi }}_{2}^{1}-\mathrm{s}\mathrm{e}\mathrm{t}$ . We obtain that there exist infinitely many ω n -automatic, hence also ω-tree-automatic, atomless boolean algebras $\mathcal{B}_{n}$ , n ≥ 1, which are pairwise isomorphic under the continuum hypothesis CH and pairwise non isomorphic under an alternate axiom AT, strengthening a result of [14]. (shrink)

Recent studies indicate that indicative conditionals like "If people wear masks, the spread of Covid-19 will be diminished" require a probabilistic dependency between their antecedents and consequents to be acceptable (Skovgaard-Olsen et al., 2016). But it is easy to make the slip from this claim to the thesis that indicative conditionals are acceptable only if this probabilistic dependency results from a causal relation between antecedent and consequent. According to Pearl (2009), understanding a causal relation involves multiple, hierarchically organized conceptual dimensions: (...) prediction, intervention, and counterfactual dependence. In a series of experiments, we test the hypothesis that these conceptual dimensions are differentially encoded in indicative and counterfactual conditionals. If this hypothesis holds, then there are limits as to how much of a causal relation is captured by indicative conditionals alone. Our results show that the acceptance of indicative and counterfactual conditionals can become dissociated. Furthermore, it is found that the acceptance of both is needed for accepting a causal relation between two co-occurring events. The implications that these findings have for the hypothesis above, and for recent debates at the intersection of the psychology of reasoning and causal judgment, are critically discussed. Our findings are consistent with viewing indicative conditionals as answering predictive queries requiring evidential relevance (even in the absence of direct causal relations). Counterfactual conditionals in contrast target causal relevance, specifically. Finally, we discuss the implications our results have for the yet unsolved question of how reasoners succeed in constructing causal models from verbal descriptions. (shrink)

We prove that the logics of Magidor-Malitz and their generalization by Rubin are distinct even for PC classes. Let $M \models Q^nx_1 \cdots x_n \varphi(x_1 \cdots x_n)$ mean that there is an uncountable subset A of |M| such that for every $a_1, \ldots, a_n \in A, M \models \varphi\lbrack a_1, \ldots, a_n\rbrack$ . Theorem 1.1 (Shelah) $(\diamond_{\aleph_1})$ . For every n ∈ ω the class $K_{n + 1} = \{\langle A, R\rangle \mid \langle A, R\rangle \models \neg (...) Q^{n + 1} x_1 \cdots x_{n + 1} R(x_1, \ldots, x_{n + 1})\}$ is not an ℵ 0 -PC-class in the logic L n , obtained by closing first order logic under Q 1 , ..., Q n . I.e. for no countable L n -theory T, is K n + 1 the class of reducts of the models of T. Theorem 1.2 (Rubin) $(\diamond_{\aleph_1}).^3$ . Let $M \models Q^E x y\varphi(x, y)$ mean that there is $A \subseteq |M|$ such that $E_{A, \varphi} = \{\langle a, b \rangle \mid a, b \in A$ and $M \models \varphi\lbrack a, b\rbrack\}$ is an equivalence relation on A with uncountably many equivalence classes, and such that each equivalence class is uncountable. Let $K^E = \{\langle A, R\rangle\mid \langle A, R\rangle\models \neg Q^Exy R(x, y)\}$ . Then K E is not an ℵ 0 -PC-class in the logic gotten by closing first order logic under the set of quantifiers {Q n ∣ n ∈ ω} which were defined in Theorem 1.1. (shrink)

Computational modeling of the brain holds great promise as a bridge from brain to behavior. To fulfill this promise, however, it is not enough for models to be 'biologically plausible': models must be structurally accurate. Here, we analyze what this entails for so-called psychobiological models, models that address behavior as well as brain function in some detail. Structural accuracy may be supported by (1) a model's a priori plausibility, which comes from a reliance on evidence-based assumptions, (...) (2) fitting existing data, and (3) the derivation of new predictions. All three sources of support require modelers to be explicit about the ontology of the model, and require the existence of data constraining the modeling. For situations in which such data are only sparsely available, we suggest a new approach. If several models are constructed that together form a hierarchy of models, higher-level models can be constrained by lower-level models, and low-level models can be constrained by behavioral features of the higher-level models. Modeling the same substrate at different levels of representation, as proposed here, thus has benefits that exceed the merits of each model in the hierarchy on its own. (shrink)

We show, under the assumption that factoring is hard, that a model of PV exists in which the polynomial hierarchy does not collapse to the linear hierarchy; that a model of S21 exists in which NP is not in the second level of the linear hierarchy; and that a model of S21 exists in which the polynomial hierarchy collapses to the linear hierarchy. Our methods are model-theoretic. We use the assumption about factoring to get a (...) model in which the weak pigeonhole principle fails in a certain way, and then work with this failure to obtain our results. As a corollary of one of the proofs, we also show that in S21 the failure of WPHP (for Σb1 definable relations) implies that the strict version of PH does not collapse to a finite level. (shrink)

We review Evolution and the Levels of Selection by Samir Okasha. This important book provides a cohesive philosophical framework for understanding levels-of-selections problems in biology. Concerning evolutionary transitions, Okasha proposes that three stages characterize the shift from a lower level of selection to a higher one. We discuss the application of Okasha’s three-stage concept to the evolutionary transition from unicellularity to multicellularity in the volvocine green algae. Okasha’s concepts are a provocative step towards a more general understanding of the major (...) evolutionary transitions; however, the application of certain ideas to the volvocine model system is not straightforward. (shrink)

We introduce and study certain classes of optimization problems over the real numbers. The classes are defined by logical means, relying on metafinite model theory for so called R-structures . More precisely, based on a real analogue of Fagin's theorem [12] we deal with two classes MAX-NPR and MIN-NPR of maximization and minimization problems, respectively, and figure out their intrinsic logical structure. It is proven that MAX-NPR decomposes into four natural subclasses, whereas MIN-NPR decomposes into two. This gives a real (...) number analogue of a result by Kolaitis and Thakur [13] in the Turing model. Our proofs mainly use techniques from [17]. Finally, approximation issues are briefly discussed. (shrink)

A probabilistic Chomsky–Schützenberger hierarchy of grammars is introduced and studied, with the aim of understanding the expressive power of generative models. We offer characterizations of the distributions definable at each level of the hierarchy, including probabilistic regular, context-free, (linear) indexed, context-sensitive, and unrestricted grammars, each corresponding to familiar probabilistic machine classes. Special attention is given to distributions on (unary notations for) positive integers. Unlike in the classical case where the "semi-linear" languages all collapse into the regular languages, (...) using analytic tools adapted from the classical setting we show there is no collapse in the probabilistic hierarchy: more distributions become definable at each level. We also address related issues such as closure under probabilistic conditioning. (shrink)

Based on Kolchinsky and Wolpert’s work on the semantics of autonomous agents, I propose an application of Mathematical Logic and Probability to model cognitive processes. In this work, I will follow Bateson’s insights on the hierarchy of learning in complex organisms and formalize his idea of applying Russell’s Type Theory. Following Weaver’s three levels for the communication problem, I link the Kolchinsky–Wolpert model to Bateson’s insights, and I reach a semantic and conceptual hierarchy in living systems as an (...) explicative model of some adaptive constraints. Due to the generality of Kolchinsky and Wolpert’s hypotheses, I highlight some fundamental gaps between the results in current Artificial Intelligence and the semantic structures in human beings. In light of the consequences of my model, I conclude the paper by proposing a general definition of knowledge in probabilistic terms, overturning de Finetti’s Subjectivist Definition of Probability. (shrink)

We investigate the set S 2 of "quickly sharped" reals: \begin{align*}S_2 &= \{x \mid x \in M, M \text{the} <^\ast-\text{least mouse} \not\in L\lbrack x\rbrack\} \\ &= \{x \mid L\lbrack x\rbrack \models "V = K"\},\\ \end{align*} in the manner of [K] defining a natural hierarchy and quasi-hierarchy of constructibility degrees and identifying their termination points.

Clonal disease is often regarded as almost synonymous with cancer. However, it is becoming increasingly clear that our bodies harbor numerous mutant clones that are not tumors, and mostly give rise to no disease at all. Here we discuss three somatic mutations arising within the hematopoietic system: BCR‐ABL, characteristic of chronic myeloid leukemia; mutations of the PIG‐A gene, characteristic of paroxysmal nocturnal hemoglobinuria; the V617F mutation in the JAK2 gene, characteristic of myeloproliferative diseases. The population frequencies of these three blood (...) disorders fit well with a hierarchical model of hematopoiesis. The fate of any mutant clone will depend on the target cell and on the fitness advantage, if any, that the mutation confers on the cell. In general, we can expect that only a mutation in a hematopoietic stem cell will give long‐term disease; the same mutation taking place in a cell located more downstream may produce just a ripple in the hematopoietic ocean. (shrink)

We give a sufficient condition for a countable model M of PA to be expandable to an ω-model of AST with absolute Ω-orderings. The condition is in terms of saturation schemes or, equivalently, in terms of the ability of the model to code sequences which have some kind of definition in (M, ω). We also show that a weaker scheme of saturation leads to the existence of wellorderings of the model with nice properties. Finally, we answer affirmatively the question of (...) whether the intersection of all β-expansions of a β-expandable model M is the set RA(M, ω)--the ramified analytical hierarchy over (M, ω). The results are based on forcing constructions. (shrink)

In the 1960s, theoretical biologist Richard Levins criticised modellers in his own discipline of population biology for pursuing the “brute force” strategy of building hyper-realistic models. Instead of exclusively chasing complexity, Levins advocated for the use of multiple different kinds of complementary models, including much simpler ones. In this paper, I argue that the epistemic challenges Levins attributed to the brute force strategy still apply to state-of-the-art climate models today: they have big appetites for unattainable data, they (...) are limited by computational tractability, and they are incomprehensible to the human modeller. Along the lines Levins described, this uncertainty generates a trade-off between realistic, precise models with predictive power and simple, highly idealised models that facilitate understanding. In addition to building ensembles of highly complex dynamical models, climate modellers can address model uncertainty by comparing models of different types, such as dynamical and data-driven models, and by systematically comparing models at different levels of what climate modellers call the model hierarchy. Despite its age, Levins’ paper remains incredibly insightful and should be considered an important entry into the philosophy of computational modelling. (shrink)

While game theory has been transformative for decision making, the assumptions made can be overly restrictive in certain instances. In this work, we investigate some of the underlying assumptions of rationality, such as mutual consistency and best response, and consider ways to relax these assumptions using concepts from level-k reasoning and quantal response equilibrium (QRE) respectively. Specifically, we propose an information-theoretic two-parameter model called the quantal hierarchy model, which can relax both mutual consistency and best response while still approximating (...) level-k, QRE, or typical Nash equilibrium behavior in the limiting cases. The model is based on a recursive form of the variational free energy principle, representing higher-order reasoning as (pseudo) sequential decision-making in extensive-form game tree. This representation enables us to treat simultaneous games in a similar manner to sequential games, where reasoning resources deplete throughout the game-tree. Bounds in player processing abilities are captured as information costs, where future branches of reasoning are discounted, implying a hierarchy of players where lower-level players have fewer processing resources. We demonstrate the effectiveness of the quantal hierarchy model in several canonical economic games, both simultaneous and sequential, using out-of-sample modelling. (shrink)

For each ordinal α it is given a model for Skala's set theory using the well-known cumulative type hierarchy.

Computational models of memory are often expressed as hierarchic sequence models, but the hierarchies in these models are typically fairly shallow, reflecting the tendency for memories of superordinate sequence states to become increasingly conflated. This article describes a broad-coverage probabilistic sentence processing model that uses a variant of a left-corner parsing strategy to flatten sentence processing operations in parsing into a similarly shallow hierarchy of learned sequences. The main result of this article is that a broad-coverage (...) model with constraints on hierarchy depth can process large newspaper corpora with the same accuracy as a state-of-the-art parser not defined in terms of sequential working memory operations. (shrink)