his paper is an excerpt from a larger project that aims to open a new pathway into Spinoza's Ethics by formally reconstructing an initial fragment of this text. The semantic backbone of the project is a custom-made Spinozian model theory that lays out some of the formal prerequisites for more ne-grained investigations into Spinoza's fundamental ontology and modal metaphysics. We implement Spinoza's theory of attributes using many-sorted models with a rich system of identity that allows us to (...) clarify the puzzling status of such logical principles as the Substitution of Identicals and Transitivity of Identity in Spinoza's thought. The intensional structure of our Spinozian models also captures his proposal that states of a airs can be necessitated or excluded by the essences of particular things, an essence-relative modality that should be of interest to philosophers who have sought to rehabilitate the concept of essence in contemporary analytic metaphysics. (shrink)

It is regrettably common for theorists to attempt to characterize the Humean dictum that one can’t get an ‘ought’ from an ‘is’ just in broadly logical terms. We here address an important new class of such approaches which appeal to model-theoretic machinery. Our complaint about these recent attempts is that they interfere with substantive debates about the nature of the ethical. This problem, developed in detail for Daniel Singer’s and Gillian Russell and Greg Restall’s accounts of Hume’s dictum, is (...) of a general type arising for the use of model-theoretic structures in cashing out substantive philosophical claims: the question of whether an abstract model-theoretic structure successfully interprets something often involves taking a stand on non-trivial issues surrounding the thing. In the particular case of Hume’s dictum, given reasonable conceptual or metaphysical claims about the ethical, Singer’s and Russell and Restall’s accounts treat obviously ethical claims as descriptive and vice versa. Consequently, their model-theoretic characterizations of Hume’s dictum are not metaethically neutral. This encourages skepticism about whether model-theoretic machinery suffices to provide an illuminating distinction between the ethical and the descriptive. (shrink)

We here make preliminary investigations into the model theory of DeMorgan logics. We demonstrate that Łoś's Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case study we examine the fate of Cantor's Theorem that the classical theory of dense linear orderings without endpoints is $\aleph_{0}$-categorical, and we show that the taking of ultraproducts commutes with respect to previously established methods of constructing nonclassical (...) structures, namely, Priest's Collapsing Lemma and Dunn's Theorem in 3-Valued Logic. (shrink)

In this paper, we introduce the basics of what we shall call "partial model theory", which is an extension of traditional model theory to partial structures. These are a specific kind of structure developed within the partial structures approach, which is a view constituting the semantic approach of theories. And together with other related semantical concepts, like the concept of quasi-truth, partial structures have been used in contemporary philosophy of science for several purposes. Nonetheless, those uses (...) presuppose certain technical results, or could be improved by resorting to certain technical notions and results, that have not been put forward so far. Thus, in the present work, we intend to introduce part of this particular technical apparatus that is still lacking especially in logic, throughout the development of partial model theory. We begin by extending traditional notions of model theory for partial structures, like the notions of substructure and homomorphism, and by proving some results concerning the notion of quasi-truth. Posteriorly, we show how the content introduced can be used to improve a particular application of partial structures and quasi-truth in the philosophy of science. (shrink)

The semantic view on theories has been much in vogue over four decades as the successor of the syntactic view. In the present paper, I take issue with this approach by arguing that theories and models must be separated and that a theory should be considered to be a linguistic systems consisting of a vocabulary and a set of rules for the use of that vocabulary.

Contingentism is the view that it is possible for there to be contingent existents. Timothy Williamson has argued that contingentists cannot provide a satisfactory interpretation of the possible-world semantics for modal logic. This paper aims to provide such an interpretation on behalf of contingentists.

Hilary Putnam’s BIV argument first occurred to him when ‘thinking about a theorem in modern logic, the “Skolem–Löwenheim Theorem”’ (Putnam 1981: 7). One of my aims in this paper is to explore the connection between the argument and the Theorem. But I also want to draw some further connections. In particular, I think that Putnam’s BIV argument provides us with an impressively versatile template for dealing with sceptical challenges. Indeed, this template allows us to unify some of Putnam’s most enduring (...) contributions to the realism/antirealism debate: his discussions of brains-in-vats, of Skolem’s Paradox, and of permutations. In all three cases, we have an argument which does not merely defeat the sceptic; it also shows us that we must reject some prima facie plausible philosophical picture. (shrink)

What would be an adequate theory of social understanding? In the last decade, the philosophical debate has focused on Theory Theory, Simulation Theory and Interaction Theory as the three possible candidates. In the following, we look carefully at each of these and describe its main advantages and disadvantages. Based on this critical analysis, we formulate the need for a new account of social understanding. We propose the Person Model Theory as an independent new (...) account which has greater explanatory power compared to the existing theories. (shrink)

This draft Chapter 4 of the book “In the Beginning was Chiasmus: On the Epistemology of Non-quantified Modelling, describes how Plato’s method of divisions and collections (diairesis) accommodates both linear hierarchal classification and combinatoric cross-classification. It presents Plato’s and the early Neoplatonists’ use of cross-classificatory (chiastic) modelling as an ancient prototype of contemporary typological and morphological modelling.

In Rahul Banerjee and Bikas K. Chakrabarti (eds.), Progress in Brain Research, 168: 215-246. Amsterdam: Elsevier. Electronic offprint available upon request.

Coherence and correspondence are classical contenders as theories of truth. In this paper we examine them instead as interacting factors in the dynamics of belief across epistemic networks. We construct an agent-based model of network contact in which agents are characterized not in terms of single beliefs but in terms of internal belief suites. Individuals update elements of their belief suites on input from other agents in order both to maximize internal belief coherence and to incorporate ‘trickled in’ elements (...) of truth as correspondence. Results, though often intuitive, prove more complex than in simpler models (Hegselmann & Krause 2002, 2006; Grim, Singer, Reade & Fisher 2015). The optimistic finding is that pressures toward internal coherence can exploit and expand on small elements of truth as correspondence is introduced into epistemic networks. Less optimistic results show that pressures for coherence can also work directly against the incorporation of truth, particularly when coherence is established first and new data is introduced later. (shrink)

I provide a theory of causation within the causal modeling framework. In contrast to most of its predecessors, this theory is model-invariant in the following sense: if the theory says that C caused (didn't cause) E in a causal model, M, then it will continue to say that C caused (didn't cause) E once we've removed an inessential variable from M. I suggest that, if this theory is true, then we should understand a cause (...) as something which transmits deviant or non-inertial behavior to its effect. (shrink)

Experiments in particle physics have hitherto failed to produce any significant evidence for the many explicit models of physics beyond the Standard Model (BSM) that had been proposed over the past decades. As a result, physicists have increasingly turned to model-independent strategies as tools in searching for a wide range of possible BSM effects. In this paper, we describe the Standard Model Effective Field Theory (SM-EFT) and analyse it in the context of the philosophical discussions about (...) models, theories, and (bottom-up) effective field theories. We find that while the SM-EFT is a quantum field theory, assisting experimentalists in searching for deviations from the SM, in its general form it lacks some of the characteristic features of models. Those features only come into play if put in by hand or prompted by empirical evidence for deviations. Employing different philosophical approaches to models, we argue that the case study suggests not to take a view on models that is overly permissive because it blurs the lines between the different stages of the SM-EFT research strategies and glosses over particle physicists' motivations for undertaking this bottom-up approach in the first place. Looking at EFTs from the perspective of modelling does not require taking a stance on some specific brand of realism or taking sides in the debate between reduction and emergence into which EFTs have recently been embedded. (shrink)

Three metascientific concepts that have been object of philosophical analysis are the concepts oflaw, model and theory. The aim ofthis article is to present the explication of these concepts, and of their relationships, made within the framework of Sneedean or Metatheoretical Structuralism (Balzer et al. 1987), and of their application to a case from the realm of biology: Population Dynamics. The analysis carried out will make it possible to support, contrary to what some philosophers of science in general (...) and of biology in particular hold, the following claims: a) there are "laws" in biological sciences, b) many of the heterogeneous and different "models" of biology can be accommodated under some "theory", and c) this is exactly what confers great unifying power to biological theories. (shrink)

Discussing theories at length, including their origin, development, and replacement by other theories, can help students in understanding of both objective and subjective aspects of the scientific process. Presenting theories in the form of- models helps in this undertaking, and the history of science provides a number of suitable models. The paper describes specific examples that have been used in in-service courses for science teachers.

Numerous societal issues, from climate change to pandemics, require public engagement with scientific research. Such engagement reveals challenges that can arise when experts communicate with laypeople. One of the most common frameworks for framing these communicative interactions is the deficit model of science communication, which holds that laypeople lack scientific knowledge and/or positive attitudes towards science, and that imparting knowledge will fill knowledge gaps, lead to desirable attitude/behavior changes, and increase trust in science. §1 introduces the deficit model (...) in more detail and shows that adhering to this model often fails to achieve its aims, which motivates the main question of this chapter: how can Ludwik Fleck’s theory of thinking collectives address the persistent problem of deficit approaches in science communication? I suggest that it can do so by exposing the deficit model’s implicit assumption of an expert-lay divide. Accordingly, §2 lays out Fleck’s theory and §3 contrasts it with contemporary debates about science communication. Following this descriptive work, §4 draws on Fleck’s ideas to make four concrete suggestions for further questioning the expert-lay divide. (shrink)

Because formal systems of symbolic logic inherently express and represent the deductive inference model formal proofs to theorem consequences can be understood to represent sound deductive inference to deductive conclusions without any need for other representations.

In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to (...) applications. Firstly, it is argued that, since ITL is truly intensional, it can be used to model ascriptions of propositional attitude without predicting logical omniscience. In order to illustrate this a small fragment of English is defined and provided with an ITL semantics. Secondly, it is shown that ITL models contain certain objects that can be identified with possible worlds. Essential elements of modal logic become available within classical type theory once the axiom of Extensionality is given up. (shrink)

Boolean-valued models of set theory were independently introduced by Scott, Solovay and Vopěnka in 1965, offering a natural and rich alternative for describing forcing. The original method was adapted by Takeuti, Titani, Kozawa and Ozawa to lattice-valued models of set theory. After this, Löwe and Tarafder proposed a class of algebras based on a certain kind of implication which satisfy several axioms of ZF. From this class, they found a specific 3-valued model called PS3 which satisfies all (...) the axioms of ZF, and can be expanded with a paraconsistent negation *, thus obtaining a paraconsistent model of ZF. The logic (PS3 ,*) coincides (up to language) with da Costa and D'Ottaviano logic J3, a 3-valued paraconsistent logic that have been proposed independently in the literature by several authors and with different motivations such as CluNs, LFI1 and MPT. We propose in this paper a family of algebraic models of ZFC based on LPT0, another linguistic variant of J3 introduced by us in 2016. The semantics of LPT0, as well as of its first-order version QLPT0, is given by twist structures defined over Boolean agebras. From this, it is possible to adapt the standard Boolean-valued models of (classical) ZFC to twist-valued models of an expansion of ZFC by adding a paraconsistent negation. We argue that the implication operator of LPT0 is more suitable for a paraconsistent set theory than the implication of PS3, since it allows for genuinely inconsistent sets w such that [(w = w)] = 1/2 . This implication is not a 'reasonable implication' as defined by Löwe and Tarafder. This suggests that 'reasonable implication algebras' are just one way to define a paraconsistent set theory. Our twist-valued models are adapted to provide a class of twist-valued models for (PS3,*), thus generalizing Löwe and Tarafder result. It is shown that they are in fact models of ZFC (not only of ZF). (shrink)

The primary aim of this paper is to critically evaluate the deductive model of ethical applications, which is based on normative ethical theories like deontology and consequentialism, and to show why a number of models have failed to furnish appropriate resolutions to practical moral problems. Here, for the deductive model, I want to call it a “Linear Mechanical Model” because the basic assumption of this model is that if a normative theory is sacrosanct, then the (...) case is as it is. The conclusion derived from the case will also be correct, true and acceptable. However, traditional ethicists used to apply their ethical theories, but they did not know which moral theory was effective on the ground level of reality. The study will show readers how ethical theories are in conflict with each other in the case of euthanasia. In more precise words, “which ethical theories are said to be applied, meta-ethical or normative, or both for the resolution of ethical problems? If normative theories are said to be applied, how the application can take place when it is contrary to our experience, that (then) in a situation of moral crises, no one really applies a theory?” For that, my argument is the linear model has failed because it is rigid, often ignores the agents’ intrinsic values, and has no space to amend it, no matter how bizarre the consequence is. Its alternative is the Inductive model. For that, the paper will take three moral principles (autonomy, beneficence including maleficence, and justice) of Beauchamp & Childress. This suggests us for resolving value-laden moral problems, we should consider some steps such as a) recognising moral issues to start with; b) developing the moral imagination; c) sharpening analytical/critical skills; d) testing out disagreements; e) effecting decisions and behavior; and f) implementation, closure, and process are of vital importance, in other words, it starts with the free and informed consensus of all interested parties, but this model also has been failed because the model could not give a systematic organization to their way of resolution. Here, my argument is that the inductive model provides resolution of the practical problem but ignores what is ethically obligatory, permissible, or wrong in that situation, and there are no appropriate suggestions in the case of a moral crisis. (shrink)

This article argues that common intuitions regarding (a) the specialness of ‘use-novel’ data for confirmation and (b) that this specialness implies the ‘no-double-counting rule’, which says that data used in ‘constructing’ (calibrating) a model cannot also play a role in confirming the model’s predictions, are too crude. The intuitions in question are pertinent in all the sciences, but we appeal to a climate science case study to illustrate what is at stake. Our strategy is to analyse the intuitive (...) claims in light of prominent accounts of confirmation of model predictions. We show that on the Bayesian account of confirmation, and also on the standard classical hypothesis-testing account, claims (a) and (b) are not generally true; but for some select cases, it is possible to distinguish data used for calibration from use-novel data, where only the latter confirm. The more specialized classical model-selection methods, on the other hand, uphold a nuanced version of claim (a), but this comes apart from (b), which must be rejected in favour of a more refined account of the relationship between calibration and confirmation. Thus, depending on the framework of confirmation, either the scope or the simplicity of the intuitive position must be revised. (shrink)

Evolutionary anthropologists and archaeologists have been considerably successful in modelling the cumulative evolution of culture, of technological skills and knowledge in particular. Recently, one of these models has been introduced in the philosophy of science by De Cruz and De Smedt (Philos Stud 157:411–429, 2012), in an attempt to demonstrate that scientists may collectively come to hold more truth-approximating beliefs, despite the cognitive biases which they individually are known to be subject to. Here we identify a major shortcoming in that (...) attempt: De Cruz & De Smedt’s mathematical model makes one particularly strong tractability assumption that causes the model to largely miss its target (namely, truth accumulation in science), and that moreover conflicts with empirical observations. The second, more constructive part of the paper presents an alternative, agent-based model, which allows one to much better examine the conditions for scientific progress and decline. (shrink)

The purpose of this article is to present several immediate consequences of the introduction of a new constant called Lambda in order to represent the object ``nothing" or ``void" into a standard set theory. The use of Lambda will appear natural thanks to its role of condition of possibility of sets. On a conceptual level, the use of Lambda leads to a legitimation of the empty set and to a redefinition of the notion of set. It lets also clearly (...) appear the distinction between the empty set, the nothing and the ur-elements. On a technical level, we introduce the notion of pre-element and we suggest a formal definition of the nothing distinct of that of the null-class. Among other results, we get a relative resolution of the anomaly of the intersection of a family free of sets and the possibility of building the empty set from ``nothing". The theory is presented with equi-consistency results . On both conceptual and technical levels, the introduction of Lambda leads to a resolution of the Russell's puzzle of the null-class. (shrink)

Schaffner’s model of theory reduction has played an important role in philosophy of science and philosophy of biology. Here, the model is found to be problematic because of an internal tension. Indeed, standard antireductionist external criticisms concerning reduction functions and laws in biology do not provide a full picture of the limits of Schaffner’s model. However, despite the internal tension, his model usefully highlights the importance of regulative ideals associated with the search for derivational, and (...) embedding, deductive relations among mathematical structures in theoretical biology. A reconstructed Schaffnerian model could therefore shed light on mathematical theory development in the biological sciences and on the epistemology of mathematical practices more generally. *Received November 2006; revised March 2009. †To contact the author, please write to: Philosophy Department, University of California, Santa Cruz, 1156 High St., Santa Cruz, CA 95064; e‐mail: [email protected]. (shrink)

On entend généralement par « théorie des modèles » autant la métamathématique (ou sémantique formelle) que la sémantique des modèles des sciences non formelles. Cet article a pour objet la théorie des modèles scientifiques que Mario Bunge a développée dans Method, Models and Matter (1973). J’y analyse l’intégration théorique qu’opère Bunge des sciences formelles et des sciences expérimentales ou observationnelles, laquelle prend appui sur sa philosophie des sciences. Je la compare sommairement à la théorie des modèles de Gilles-Gaston Granger dans (...) le but évident d’en dégager les ressemblances et les dissimilitudes, mais aussi leur commun point d’achoppement : l’une comme l’autre usent en effet d’un concept non analysé dont la fonction épistémologique est pourtant capitale et produit les mêmes effets. Au centre de la théorie des modèles de Bunge se trouve le concept de simulation que je comparerai à celui qui est en usage dans les sciences de l’ordinateur et qui est de nos jours largement appliqué à diverses sciences, tant sociales que naturelles. Je conclurai sur les conséquences méthodologiques et métaphysiques de la théorie bungéenne des modèles. (shrink)

In recent decades, philosophers of science have devoted considerable efforts to understand what models represent. One popular position is that models represent fictional situations. Another position states that, though models often involve fictional elements, they represent real objects or scenarios. Though these two positions may seem to be incompatible, I believe it is possible to reconcile them. Using a threefold distinction between different signs proposed by Peirce, I develop an argument based on a proposal recently made by Kralemann and Lattman (...) (in Synthese 190:3397–3420, 2013) that shows that the two aforementioned positions can be reconciled by distinguishing different ways in which a model representation can be used. In particular, on the basis of Peirce’s distinction between icons, indices and symbols, I argue that models can sometimes function as icons, sometimes as indexes and sometimes as symbols, depending on the context in which they are considered and the use that they are developed for because they all have iconic, indexical and symbolic features. In addition, I show that conceiving models as signs enables us to develop an account of scientific representation that meets the main desiderata that Shech (in Synthese 192:3463–3485, 2015) presents. (shrink)

Political theory as a discipline has long been skeptical of computational methods. In this paper, I argue that it is time for theory to make a perspectival shift on these methods. Specifically, we should consider integrating recently developed generative large language models like GPT-4 as tools to support our creative work as theorists. Ultimately, I suggest that political theorists should embrace this technology as a method of supporting our capacity for creativity—but that we should do so in a (...) way that is mindful of the content and value of theorizing, the technical constraints of the models, and the ethical questions that the technology raises. (shrink)

In recent years, apparently the Big Bang as described by the Lambda CDM-Standard Model Cosmology has become widely accepted by majority of physics and cosmology communities. Even some people have concluded that it has no serious alternative in horizon. Is that true? First, as we argued elsewhere, Big Bang story relies on singularity. In other words, when we are able to describe the observed data without invoking singularity, then Big Bang model is no longer required. Therefore, here we (...) explore a few alternative stories other than Big Bang story, which most cosmologists believe it is the nearest to Biblical account of creation. We would argue that re-reading of Genesis 1:2 will lead us to another viable story, albeit the alternative has not been developed rigorously as LCDM theories. We also briefly discuss a fluid Maxwell equations of Prof. Tsutomu Kambe based on vortex sound theory. (shrink)

I put forward an externalist theory of social understanding. On this view, psychological sense making takes place in environments that contain both agent and interpreter. The spatial structure of such environments is social, in the sense that its occupants locate its objects by an exercise in triangulation relative to each of their standpoints. This triangulation is achieved in intersubjective interaction and gives rise to a triadic model of the social mind. This model can then be used to (...) make sense of others’ observed actions. Its possession plays a vital role in the development of the capacity for false belief reasoning. The view offers an integrated account of the development of social cognition from primary intersubjectivity to level-2 perspective taking. It incorporates insights from interactionism and mindreading theories of social cognition and thus offers a way out of the stalemate between defenders of the two views. Because psychological sense making is perspectival, the frame problem does not arise for social reasoners: the perspective they bring to bear on the action that is to be interpreted constrains the information they can select to make sense of what others do. (shrink)

The purpose of this paper is to show that the Elementary Process Theory (EPT) agrees with the knowledge of the physical world obtained from the successful predictions of Special Relativity (SR). For that matter, a recently developed method is applied: a categorical model of the EPT that incorporates SR is fully specified. Ultimate constituents of the universe of the EPT are modeled as point-particles, gamma-rays, or time-like strings, all represented by integrable hyperreal functions on Minkowski space. This proves (...) that the EPT agrees with SR. -/- Edit: this preprint differs significantly from the published chapter. (shrink)

A new non-Archimedean approach to interacted quantum fields is presented. In proposed approach, a field operator φ(x,t) no longer a standard tempered operator-valued distribution, but a non-classical operator-valued function. We prove using this novel approach that the quantum field theory with Hamiltonian P(φ)_4 exists and that the corresponding C^*­ algebra of bounded observables satisfies all the Haag-Kastler axioms except Lorentz covariance. We prove that the λ(φ^2n )_4,n≥2 quantum field theory models are Lorentz covariant.

There is a complex interplay between the models in dark matter detection experiments that have led to a difficulty in interpreting the results of the experiments and ascertain whether we have detected the particle or not. The aim of this paper is to categorise and explore the different models used in said experiments, by emphasizing the distinctions and dependencies among different types of models used in this field. With a background theory, models are categorised into four distinct types: background (...) theory, theoretical, phenomenological, experimental and data. This taxonomy highlights how each model serves a unique purpose and operates under varying degrees of independence from their respective frameworks. A key focus is on the experimental model, which is shown to rely on constraints from both data and phenomenological ones. The article argues that while theoretical models provide a backdrop for understanding the nature of dark matter, the experimental models must stand independently, particularly in their methodological approaches. This is done via a discussion of the inherent challenges in dark matter detection, such as inconsistent results and difficulties in cross-comparison, stemming from the diverse modelling approaches. (shrink)

The incompleteness of set theory ZF C leads one to look for natural nonconservative extensions of ZF C in which one can prove statements independent of ZF C which appear to be “true”. One approach has been to add large cardinal axioms.Or, one can investigate second-order expansions like Kelley-Morse class theory, KM or Tarski-Grothendieck set theory T G or It is a nonconservative extension of ZF C and is obtained from other axiomatic set theories by the inclusion (...) of Tarski’s axiom which implies the existence of inaccessible cardinals. See also related set theory with a filter quantifier ZF (aa). In this paper we look at a set theory NC# ∞# , based on bivalent gyper infinitary logic with restricted Modus Ponens Rule In this paper we deal with set theory NC# ∞# based on bivalent gyper infinitary logic with Restricted Modus Ponens Rule. Nonconservative extensions of the canonical internal set theories IST and HST are proposed. (shrink)

Ecological neutral theory has been controversial as an alternative to niche theory for explaining community structure. Neutral theory, which explains community structure in terms of ecological drift, is frequently charged with being unrealistic, but commentators have usually not provided an account of theory or model realism. In this paper, I propose a framework for comparing the “realism” or accuracy of alternative theories within a domain with respect to the extent to which the theories abstract and (...) idealize. Using this framework I argue, contrary to most previous commentators, that neutral and niche theories are similarly realistic. Realism cannot provide a basis for accepting or rejecting either type of theory; instead, community ecologists should continue working with a plurality of models. While theoretical unification may become possible, we should treat a plurality of complementary, partial models as the expected situation within community ecology. (shrink)

Pettit (2012) presents a model of popular control over government, according to which it consists in the government being subject to those policy-making norms that everyone accepts. In this paper, I provide a formal statement of this interpretation of popular control, which illuminates its relationship to other interpretations of the idea with which it is easily conflated, and which gives rise to a theorem, similar to the famous Gibbard-Satterthwaite theorem. The theorem states that if government policy is subject to (...) popular control, as Pettit interprets it, and policy responds positively to changes in citizens' normative attitudes, then there is a single individual whose normative attitudes unilaterally determine policy. I use the model and theorem as an illustrative example to discuss the role of mathematics in normative political theory. (shrink)

A comprehensible model is proposed aimed at an analysis of the reasons for theory change in science. According to the model the origins of scientific revolutions lie not in a clash of fundamental theories with facts, but of “old” fundamental theories with each other, leading to contradictions that can only be eliminated in a more general theory. The model is illustrated with reference to physics in the early 20th century, the three “old” theories in this (...) case being Maxwellian electrodynamics, statistical mechanics and thermodynamics. Modern example, referring to general relativity and quantum field theory fusion, is highlighted. Key words: Popper, Kuhn, Lakatos, Feyerabend, Stepin, Bransky,Mamchur, mature theory, structure, Einstein, Lorentz, , Boltzmann, Planck, Hawking, De Witt. (shrink)

I argue that dimensional analysis provides an answer to a skeptical challenge to the theory of model mediated measurement. The problem arises when considering the task of calibrating a novel measurement procedure, with greater range, to the results of a prior measurement procedure. The skeptical worry is that the agreement of the novel and prior measurement procedures in their shared range may only be apparent due to the emergence of systematic error in the exclusive range of the novel (...) measurement procedure. Alternatively: what if the two measurement procedures are not in fact measuring the same quantity? The theory of model mediated measurement can only say that we _assume_ that there is a common quantity. In contrast, I show that the satisfaction of dimensional homogeneity across the metrological extension is independent evidence for the so-called assumption. This is illustrated by the use of dimensional analysis in high pressure experiments. This results in an extension of the theory of model mediated measurement, in which a common quantity in metrological extension is no longer assumed, but hypothesized. (shrink)

A practical viewpoint links reality, representation, and language to calculation by the concept of Turing (1936) machine being the mathematical model of our computers. After the Gödel incompleteness theorems (1931) or the insolvability of the so-called halting problem (Turing 1936; Church 1936) as to a classical machine of Turing, one of the simplest hypotheses is completeness to be suggested for two ones. That is consistent with the provability of completeness by means of two independent Peano arithmetics discussed in Section (...) I. Many modifications of Turing machines cum quantum ones are researched in Section II for the Halting problem and completeness, and the model of two independent Turing machines seems to generalize them. Then, that pair can be postulated as the formal definition of reality therefore being complete unlike any of them standalone, remaining incomplete without its complementary counterpart. Representation is formal defined as a one-to-one mapping between the two Turing machines, and the set of all those mappings can be considered as “language” therefore including metaphors as mappings different than representation. Section III investigates that formal relation of “reality”, “representation”, and “language” modeled by (at least two) Turing machines. The independence of (two) Turing machines is interpreted by means of game theory and especially of the Nash equilibrium in Section IV. Choice and information as the quantity of choices are involved. That approach seems to be equivalent to that based on set theory and the concept of actual infinity in mathematics and allowing of practical implementations. (shrink)

Sora from Open AI has shown exceptional performance, yet it faces scrutiny over whether its technological prowess equates to an authentic comprehension of reality. Critics contend that it lacks a foundational grasp of the world, a deficiency V-JEPA from Meta aims to amend with its joint embedding approach. This debate is vital for steering the future direction of Artificial General Intelligence(AGI). We enrich this debate by developing a theory of productive imagination that generates a coherent world model based (...) on Kantian philosophy. We identify three indispensable components in the coherent world model that enable genuine world understanding: latent representations of isolated objects, an a priori law of change across space and time, and Kantian categories. Our analysis reveals that Sora is limited because of its oversight of the a priori law of change and Kantian categories, flaws that are not rectifiable through scaling up the training. V-JEPA learns the context-dependent aspect of the a priori law of change. Yet it fails to fully comprehend Kantian categories and incorporate experience, leading us to conclude that neither system currently achieves a comprehensive world understanding. Nevertheless, each system has developed components essential to advancing an integrated AI productive imagination-understanding engine. Finally, we propose an innovative training framework for an AI productive imagination-understanding engine, centered around a joint embedding system designed to transform disordered perceptual input into a structured, coherent world model. Our philosophical analysis pinpoints critical challenges within contemporary video AI technologies and a pathway toward achieving an AI system capable of genuine world understanding, such that it can be applied for reasoning and planning in the future. (shrink)

A model-theoretic realist account of science places linguistic systems and their corresponding non-linguistic structures at different stages or different levels of abstraction of the scientific process. Apart from the obvious problem of underdetermination of theories by data, philosophers of science are also faced with the inverse (and very real) problem of overdetermination of theories by their empirical models, which is what this article will focus on. I acknowledge the contingency of the factors determining the nature – and choice – (...) of a certain model at a certain time, but in my terms, this is a matter about which we can talk and whose structure we can formalise. In this article a mechanism for tracing "empirical choices" and their particularized observational-theoretical entanglements will be offered in the form of Yoav Shoham's version of non-monotonic logic. Such an analysis of the structure of scientific theories may clarify the motivations underlying choices in favor of certain empirical models (and not others) in a way that shows that "disentangling" theoretical and observation terms is more deeply model-specific than theory-specific. This kind of analysis offers a method for getting an articulable grip on the overdetermination of theories by their models – implied by empirical equivalence – which Kuipers' structuralist analysis of the structure of theories does not offer. (shrink)

I explain why model theory is unsatisfactory as a semantic theory and has drawbacks as a tool for proofs on logic systems. I then motivate and develop an alternative, the truth-valuational substitutional approach (TVS), and prove with it the soundness and completeness of the first order Predicate Calculus with identity and of Modal Propositional Calculus. Modal logic is developed without recourse to possible worlds. Along the way I answer a variety of difficulties that have been raised against (...) TVS and show that, as applied to several central questions, model-theoretic semantics can be considered TVS in disguise. The conclusion is that the truth-valuational substitutional approach is an adequate tool for many of our logic inquiries, conceptually preferable over model-theoretic semantics. Another conclusion is that formal logic is independent of semantics, apart from its use of the notion of truth, but that even with respect to it its assumptions are minimal. (shrink)

This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or toy model of quantum mechanics over sets (QM/sets). There have been several previous attempts to develop a quantum-like model with the base field of ℂ replaced by ℤ₂. Since there are no inner products on vector spaces over finite fields, the problem is to define the Dirac brackets and the probability calculus. (...) The previous attempts all required the brackets to take values in ℤ₂. But the usual QM brackets <ψ|ϕ> give the "overlap" between states ψ and ϕ, so for subsets S,T⊆U, the natural definition is <S|T>=|S∩T| (taking values in the natural numbers). This allows QM/sets to be developed with a full probability calculus that turns out to be a non-commutative extension of classical Laplace-Boole finite probability theory. The pedagogical model is illustrated by giving simple treatments of the indeterminacy principle, the double-slit experiment, Bell's Theorem, and identical particles in QM/Sets. A more technical appendix explains the mathematics behind carrying some vector space structures between QM over ℂ and QM/Sets over ℤ₂. (shrink)

The Fundamental Interrelationships Model – An Alternative Approach to the Theory of Everything, Part 4 Subtitle: The Nature of Beauty and Fundamental Interrelationships -/- Abstract: This article is Chapter 21, titled The Nature of Beauty and the Fundamental Interrelationships, from the book Behind Civilization. It posits that the nature of beauty is rooted in one of the fundamental interrelationships: order. Beauty is perceived as a response in the human brain to this fundamental interrelationship. This article provides evidence that (...) the order theory uniquely explains all forms of beauty and reaffirms the IRM's ability to offer a comprehensive framework for the Theory of Everything. (shrink)

This paper proposes a novel model for understanding consciousness by envisioning Brahman—the ultimate, universal consciousness in Vedanta—as an infinitely layered JSON (JavaScript Object Notation) structure. In this model, each aspect of reality, from individual thoughts to timelines and entire universes, is represented as a property within this universal JSON object. By integrating the Vedantic concepts of Atman (individual self) and Brahman (universal consciousness) with ideas from quantum mechanics and information theory, this model suggests that all possible (...) experiences, thoughts, and realities exist within Brahman, ready to be accessed by individual consciousness. This framework offers a fresh way to think about reality, creativity, and free will, proposing that every possible thought or action already exists as a “node” within Brahman’s JSON, and that we simply “select” which part to experience. (shrink)

A comprehensible model is proposed aimed at an analysis of the reasons for theory change in science. According to model the origins of scientific revolutions lie not in a clash of fundamental theories with facts, but of “old” fundamental theories with each other, leading to contradictions that can only be eliminated in a more general theory. The model is illustrated with reference to physics in the early 20th century, the three “old” theories in this case (...) being Maxwellian electrodynamics, statistical mechanics and thermodynamics. Modern example, referring to general relativity and quantum field theory, is considered. Key words: Popper, Kuhn, Stepin, Einstein . (shrink)

What is the connection between modelling thought and modelling the brain? In a model (as understood here), we strip away from the modelled system some non-essential features and retain some essential ones. What are the essential features of thought that are to be re- tained in the model, and conversely, what are its inessential features, that may be stripped away in the model? According to a prevalent view in contemporary science and philoso- phy, thought is a computation, (...) and therefore its essential features are its computational features. A necessary part of the computational view of thought is the idea that the same computation can be realised by, or implemented in, physically heterogeneous systems, an idea known as “Multiple Realizability” of the computational features or properties by the physical ones. I will describe why the very idea of Multiple Realizability, especially in the case of mental computation, entails mind-body dualism, and explore some implications of this conclusion concerning the question of which are the essential features of thought to be retained in modeling it. (shrink)

This paper proposes a novel model for understanding consciousness by envisioning Brahman—the ultimate, universal consciousness in Vedanta—as an infinitely layered JSON (JavaScript Object Notation) structure. In this model, each aspect of reality, from individual thoughts to timelines and entire universes, is represented as a property within this universal JSON object. By integrating the Vedantic concepts of Atman (individual self) and Brahman (universal consciousness) with ideas from quantum mechanics and information theory, this model suggests that all possible (...) experiences, thoughts, and realities exist within Brahman, ready to be accessed by individual consciousness. This framework offers a fresh way to think about reality, creativity, and free will, proposing that every possible thought or action already exists as a “node” within Brahman’s JSON, and that we simply “select” which part to experience. (shrink)

Currently there are at least four sizeable projects going on to establish the gravitational acceleration of massive antiparticles on earth. While general relativity and modern quantum theories strictly forbid any repulsive gravity, it has not yet been established experimentally that gravity is attraction only. With that in mind, the Elementary Process Theory (EPT) is a rather abstract theory that has been developed from the hypothesis that massive antiparticles are repulsed by the gravitational field of a body of ordinary (...) matter: the EPT essentially describes the elementary processes by which the smallest massive systems have to interact with their environments for repulsive gravity to exist. In this paper we model a nonrelativistic, one-component massive system that evolves in time by the processes as described by the EPT in an environment described by classical fields: the main result is a semi-classical model of a process at Planck scale by which a non-relativistic onecomponent system interacts with its environment, such that the interaction has both gravitational and electromagnetic aspects. Some worked-out examples are provided, among which the repulsion of an antineutron by the gravitational field of the earth. The general conclusion is that the semi-classical model of the EPT corresponds to non-relativistic classical mechanics. Further research is aimed at demonstrating that the EPT has a model that reproduces the successful predictions of general relativity. (shrink)

The philosophy of mathematics has been accused of paying insufficient attention to mathematical practice: one way to cope with the problem, the one we will follow in this paper on extensive magnitudes, is to combine the `history of ideas' and the `philosophy of models' in a logical and epistemological perspective. The history of ideas allows the reconstruction of the theory of extensive magnitudes as a theory of ordered algebraic structures; the philosophy of models allows an investigation into the (...) way epistemology might affect relevant mathematical notions. The article takes two historical examples as a starting point for the investigation of the role of numerical models in the construction of a system of non-Archimedean magnitudes. A brief exposition of the theories developed by Giuseppe Veronese and by Rodolfo Bettazzi at the end of the 19th century will throw new light on the role played by magnitudes and numbers in the development of the concept of a non-Archimedean order. Different ways of introducing non-Archimedean models will be compared and the influence of epistemological models will be evaluated. Particular attention will be devoted to the comparison between the models that oriented Veronese's and Bettazzi's works and the mathematical theories they developed, but also to the analysis of the way epistemological beliefs affected the concepts of continuity and measurement. (shrink)

In this paper I apply the concept of _inter-Model Inconsistency in Set Theory_ (MIST), introduced by Carolin Antos (this volume), to select positions in the current universe-multiverse debate in philosophy of set theory: I reinterpret H. Woodin’s _Ultimate L_, J. D. Hamkins’ multiverse, S.-D. Friedman’s hyperuniverse and the algebraic multiverse as normative strategies to deal with the situation of de facto inconsistency toleration in set theory as described by MIST. In particular, my aim is to situate these (...) positions on the spectrum from inconsistency avoidance to inconsistency toleration. By doing so, I connect a debate in philosophy of set theory with a debate in philosophy of science about the role of inconsistencies in the natural sciences. While there are important differences, like the lack of threatening explosive inferences, I show how specific philosophical positions in the philosophy of set theory can be interpreted as reactions to a state of inconsistency similar to analogous reactions studied in the philosophy of science literature. My hope is that this transfer operation from philosophy of science to mathematics sheds a new light on the current discussion in philosophy of set theory; and that it can help to bring philosophy of mathematics and philosophy of science closer together. (shrink)