Based on formal arguments from Zermelo–Fraenkel set theory we develop the environment for explaining and resolving certain fundamental problems in physics. By these formal tools we show that any quantum system defined by an infinite dimensional Hilbert space of states interferes with the spacetime structure M. M and the quantum system both gain additional degrees of freedom, given by models of Zermelo–Fraenkel set theory. In particular, M develops the ground state where classical gravity vanishes. Quantum mechanics distinguishes set-theoretic random forcing (...) such that M and gravitational degrees of freedom are parameterized by extended real line. The large scale smooth geometry compatible with the forcing extensions is one of exotic smoothness structures of \. The amoeba forcing makes the old real line to have Lebesgue measure zero in the extended one. We apply the entire procedure to the cosmological constant problem, especially to discard the zero-modes contributions to the gravitational vacuum density. Moreover, there exists certain exotic smooth \ from which one determines the realistic, agreeing with observation, small value of the vacuum energy density. (shrink)

Quantum mechanics (QM) predicts probabilities on the fundamental level which are, via Born probability law, connected to the formal randomness of infinite sequences of QM outcomes. Recently it has been shown that QM is algorithmic 1-random in the sense of Martin–Löf. We extend this result and demonstrate that QM is algorithmic $$\omega$$ -random and generic, precisely as described by the ’miniaturisation’ of the Solovay forcing to arithmetic. This is extended further to the result that QM becomes Zermelo–Fraenkel Solovay random on (...) infinite-dimensional Hilbert spaces. Moreover, it is more likely that there exists a standard transitive ZFC model M, where QM is expressed in reality, than in the universe V of sets. Then every generic quantum measurement adds to M the infinite sequence, i.e. random real $$r\in 2^{\omega }$$, and the model undergoes random forcing extensions M[r]. The entire process of forcing becomes the structural ingredient of QM and parallels similar constructions applied to spacetime in the quantum limit, therefore showing the structural resemblance of both in this limit. We discuss several questions regarding measurability and possible practical applications of the extended Solovay randomness of QM. The method applied is the formalization based on models of ZFC; however, this is particularly well-suited technique to recognising randomness questions of QM. When one works in a constant model of ZFC or in axiomatic ZFC itself, the issues considered here remain hidden to a great extent. (shrink)

We give an almost explicit presentation of exotic functions corresponding to some exotic smooth structure on topologically trivial R4. The construction relies on the model-theoretic tools from the previous paper. We can formulate unexpected, yet direct connection between ‘‘localized’’ exotic small R4’s and some noncommutative spaces. The formalism of QM can be interpreted in terms of exotic smooth R4’s localized in spacetime. A new way of looking at the problem of decoherence is suggested. The 4-dimensional spacetime itself has built-in means (...) which may enforce a kind of decoherence. (shrink)

A general duality connecting the level of a formal theory and of a metatheory is proposed. Because of the role of natural numbers in a metatheory the existence of a dual theory is conjectured, in which the natural numbers become formal in the theory but in formalizing non-formal natural numbers taken from the dual metatheory these numbers become nonstandard. For any formal theory there may be in principle a dual theory. The dual shape of the lattice of projections over separable (...) Hilbert space is exhibited. The crucial ingredient of this dual theory is set-theoretical (Cohen) forcing. Then, some attempts have been made to exhibit the dual shape of the exotic smooth (small) structures on topological ℝ4. There are striking similarities of both pictures. Nonstandard solutions of the equations of motion of 10-dimensional superstring of IIB type are described as a model theoretic extension of standard ones. Based on Brans conjecture one can predict the existence of sources of gravity in 4 dimensions. By their dual origins they carry quantum information as well. The generalized Maldacena conjecture appears naturally, which sheds light on a definition of background independent string theory. (shrink)

We consider consciousness attributed to systems in space-time which can be purely physical without biological background and focus on the mathematical understanding of the phenomenon. It is shown that the set theory based on sets in the foundations of mathematics, when switched to set theory based on ZFC models, is a very promising mathematical tool in explaining the brain/mind complex and the emergence of consciousness in natural and artificial systems. We formalise consciousness-supporting systems in physical space-time, but this is localised (...) in open domains of spatial regions and the result of this process is a family of different ZFC models. Random forcing, as in set theory, corresponds precisely to the random influence on the system of external stimuli, and the principles of reflection of set theory explain the conscious internal reaction of the system. We also develop the conscious Turing machines which have their external ZFC environment and the dynamics is encoded in the random forcing changing models of ZFC in which Turing machines with oracles are formulated. The construction is applied to cooperating families of conscious agents which, due to the reflection principle, can be reduced to the implementation of certain concurrent games with different levels of self-reflection. (shrink)

We show that in 4-spacetime modified at very short distances due to the weakening of classical logic, the higher dimensions emerge. We analyse the case of some smooth topoi, and the case of some class of pointless topoi. The pointless topoi raise the dimensionality due to the forcing adding “string” objects and thus replacing classical points in spacetime. Turning to strings would be something fundamental and connected with set theoretical forcing. The field theory/strings dualities originate at the set theoretical level (...) of the theories. It is argued that this fundamental level can help solving some difficulties of the physical dualities. (shrink)

We build a topological model, based on intuitionistic logic, for multi-agent biological systems (such as _Physarum polycephalum_, bacterial colonies or any other swarm), reacting to external nourishment stimuli. Our construction follows the topological description of brain activity, where particles (neurons) are activated by an external environment, represented by a topological space _X_ with an open cover \(\{U_i:i\in I\}\). The brain builds the model of this external space via the nerve (trace) of a topological space _X_. Here the body of _Physarum (...) polycephalum_ or a swarm made of networks of tubular structures represents a nerve (trace) of _X_ also which means that _Physarum polycephalum_ or a swarm gains orientation in the space of external stimuli even in the absence of any neural system. The logic of living organisms is based on open subsets of _X_ and thus can be represented by Heyting algebra (i.e. intuitionistically). We also consider the generalisation of the nerve construction to a categorical context, where the category is determined by the network structures of multi-agent biological system. This model can be generalised up to simulating the behaviour of any swarm by means of intuitionistic logic. (shrink)

Even though the description of the universe in cosmology is known to be given by a smooth 4-dimensional Lorentz manifold for energies below Planck scale, one still can ask about the origins of this phenomenon. In this paper we show that mathematics used for description of quantum systems at micro scale determines smoothness of spacetime at large cosmological scales and indicates the dimension 4 as the only possible dimension for spacetime.

Even though the description of the universe in cosmology is known to be given by a smooth 4-dimensional Lorentz manifold for energies below Planck scale, one still can ask about the origins of this phenomenon. In this paper we show that mathematics used for description of quantum systems at micro scale determines smoothness of spacetime at large cosmological scales and indicates the dimension 4 as the only possible dimension for spacetime.

Recently the cosmological evolution of the universe has been considered where 3-dimensional spatial topology undergone drastic changes. The process can explain, among others, the observed smallness of the neutrino masses and the speed of inflation. However, the entire evolution is perfectly smooth from 4-dimensional point of view. Thus the raison d’être for such topology changes is the existence of certain non-standard 4-smoothness on R4 already at very early stages of the universe. We show that the existence of such smoothness can (...) be understood as a byproduct of the quantumness of the origins of the universe. Our analysis is based on certain formal aspects of the quantum mechanical lattice of projections of infinite dimensional Hilbert spaces where formalization reaches the level of models of axiomatic set theory. (shrink)

We analyse the proposition that the spacetime structure is modified at short distances or at high energies due to weakening of classical logic. The logic assigned to the regions of spacetime is intuitionistic logic of some topoi. Several cases of special topoi are considered. The quantum mechanical effects can be generated by such semi-classical spacetimes. The issues of: background independence and general relativity covariance, field theoretic renormalization of divergent expressions, the existence and definition of path integral measures, are briefly discussed (...) in the proposal. The connection with some problems in foundations of mathematics and differential topology are also discussed. (shrink)

This book examines the fundamental issues in neuroscience from methodological and philosophical perspectives. The reader will learn about the methodological difficulties connected with the use of neuroscientific experiments in philosophical argumentation and about the nature of scientific explanation in neuroscience. In addition, the book includes case studies of several issues lying at the intersection of neuroscience and philosophy, such as theory of mind, self-consciousness, self-deception, depression, and morality.

Resumo Este artigo analisa, as recentes versões, da objecção à existência de um fluxo do tempo, com base na pergunta: “Com que velocidade flui o tempo?”. O autor mostra que as soluções existentes para o problema não são plausíveis e, que em vez disso, a resolução deve ser encontrada numa nova concepção de fluxo temporal, que evite tais dificuldades. A teoria metafísica proposta desenvolve as ideias de Broad e Prior sob um novo enquadramento, que invalida a objecção resultante da questão (...) sobre o ritmo da passagem do tempo e das respostas “segundo a segundo”. Neste texto também se procura mostrar, que esta teoria metafísica, aqui proposta, possui outras virtudes que testemunham a seu favor. Palavras-chave : existência dinâmica, fluxo do tempo, presentismo, velocidade de passagem do tempoThe paper analyzes some recent versions of the objection to the existence of the flow of time based on the question: “How fast does time flow?”. It shows that the replies given to the problem are implausible and instead proposes a solution for the issue in the form of a conception of the flow of time which can avoid such a difficulty. The proposed metaphysical theory develops the ideas of Broad and Prior in a radical way and invalidates the objection resulting from the question about the rate of passage and answers “second per second”. The paper also tries to show that this metaphysical theory has other virtues which testify in favor of it. Keywords : flow of time; rate of time’s passage; presentism; dynamic existence. (shrink)

Journal Name: Philologus Issue: Ahead of print.

Author: Sawicki Jerzy Title: THELEOGICAL PRINCIPLE IN KANT’S METHODOLOGY (Zasada teleologiczna w metodologii Kanta) Source: Filo-Sofija year: 2005, vol:.5, number: 2005/1, pages: 281-292 Keywords: KANT, THELEOGICAL PRINCIPLE, FINALISM, MECHANICISM Discipline: PHILOSOPHY Language: POLISH Document type: ARTICLE Publication order reference (Primary author’s office address): E-mail: www:The work contains a concise of I. Kant’s views on the problem of the laws of nature and the theleological principle presented in this context, which Kant proposes in the character of a regulative methodological postulate. (...) The analysis of fundamental philosophical notions (the law of nature, necessity, causality, purpose) carried out from the position of an extreme aprioristic rationalism leads Kant to the conclusion about the basic impossibility of educing the conception of purpose (in relation to nature) from aprioristic transcendental laws, ie. such laws which the theoretical reason imposes to the nature by necessity. However, the fact of a total functioning of an organism does not fit, according to Kant, into the frames of a mechanically understood causality. Kant tries to solve this problem choosing the way of conclusion by analogy and finally he suggests to introduce into the living nature a specific causal relation in which the purposes constitute a particular kind of causes and results at the same time. That conception oscillates between mechanicism and theological finalism, and the fitting of a science system into the frames of aprioristic categories does not permit a finally decide about the supremacy of one or the other way of seeing the world. However, nevertheless, the perceiving and stressing of the peculiarity of organic symptoms, the formulation of the postulate about their unreductability to the law of a mechanical type constitute unquestionable and great merit of the author of the Criticism of the Judgment Authority. The idea of the totality of organism, though involved in subjective idealistic non consequences of Kant’s conceptions has in the given historical period all features of a deep and progressive thought, outpacing and inspiring several later research ideas, both in philosophy and in natural science. (shrink)

The old-fashioned concept of state is shown to be inadequate and misleading. Replacing it by a concept of information and taking advantage of the invariance of the mechanical description under time reversal puts the problems of the interpretation of quantum mechanics in a new light. A more realistic interpretation appears to be possible. Moreover, a new explanation of the Einstein-Podolsky-Rosen paradox is presented, too.

In this article I subject to criticism Field's argument, according to which field theory takes space-time to be substance since it ascribes field properties to space-time points. There is petitio principii error made in this reasoning because Field does not give any justification for his controversial assumption that fields are properties of space-time points. What is more, I suggest, Field's interpretation of field theory is incompatible with the way this theory is understood and utilized by its users, namely scientists. My (...) criticism is based on the assumption that one cannot propose an ontology of a given scientific theory, at the same time imposing on it an interpretation which clashes with the interpretation current among its users. I also suggest that in order to establish the ontology of a scientific theory one should also take into account the way it has been constructed. According to this criterion, field theory does indeed take space-time to be a substance. (shrink)

Charles Darwin’s theory of evolution by means of natural selection finds application far outside biology, for which it was originally invented. Its consequences for science proved far-going, influencing practically every field from thermodynamics to the humanities. While acting on biological systems, the Darwinian mechanism is a source of progress and the local-scale abandonment of the universe’s general tendency towards chaos. However, observations of changes taking place in selection-exposed organisms show that evolutionary success requires some essential limitations. The application of this (...) reasoning to social evolution may appear thought-provoking: stable evolution requires not only intense selection but also a conservative approach to ideas. (shrink)

It follows from the proved theorems that ifM π=〈Q, ϕ〉 (whereQ={0,q 1,q 2,...,q α}) is a machine of the classM F then there exist α machinesM πi such thatM πi(〈1,c〉)=M π(〈q i,c〉) andQ i={0, 1, 2, ..., α+1} (i=1, 2, ..., α).And thus, if the way in which to an initial function of content of memoryc∈C a machine assigns a final onec′∈C is regarded as the only essential property of the machine then we can deal with the machines of the (...) formM π=〈{0, 1, 2, ..., α}, ϕ〉 and processes π(t) (wheret=〈1,c〉,c∈C) only.Such approach can simplify the problem of defining particular machines of the classM F , composing and simplifying them. (shrink)

Problem republikanizmu należy do zespołu problemów polityki, którymi Kant zajął się już pod koniec życia. Rozwój i doskonalenie się człowieka nie mieści się w działaniu ludzkiej natury, która jest niezmienna, ale w osobowym działaniu wolności. Ostatecznym tego celem jest wieczny pokój. Warunkiem zaś rozwoju i osiągnięcia celu najwyższego jest zbudowanie ustroju republikańskiego. Kant pokazuje to m.in. na przykładzie rewolucji francuskiej. Choć jest zdecydowanym przeciwnikiem każdej rewolucji, ze względu na sposoby jej realizacji, to w tym przypadku jej skutki ocenia pozytywnie, gdyż (...) wyraziło się w niej prawo narodu do swobodnego nadania sobie ustroju obywatelskiego prawego i uznanego za dobry, jakim jest ustrój republikański. Ustrój republikański jest najlepszy ze wszystkich i określa formę państwa oraz ważniejszą od niej formę rządu, charakteryzującą się rozdzieleniem władz ustawodawczych i wykonawczych oraz trzema istotnymi zasadami: 1) zasadą wolności wszystkich obywateli; 2) zasadą zależności wszystkich od wspólnego prawa; 3) zasadą równości obywateli. (shrink)

Civil society was defined in various ways. Among others, J. Locke, G.W.F. Hegel and A. de Tockeville presented the most relevant characteristic of what civil society is or could be. For the purpose of the paper we distinct civil society and the state. To the first one we assign spontaneity and diversity, the second we treat as procedural and homogeneous. In the paper we will stand for the thesis: civil society is the nest of virtues and as such characterized plays (...) one of the most prominent parts in contemporary social and political reality. The problem is not that presently civil society does not exist. The problem is that once it was established within the state, it has been developed in such a way that it became a hybrid combined from the state and what could be called apolitical human activity. The core of the problem is that the hybrid is more political than apolitical. To the essence of civil society belong: existence of free associations of any kind, economy free from political coerce as much as it could be and public sphere of opinion, all organized in such a political way that the political power is limited by division of it to three independent institutions: a legislature, an executive and a judiciary and also by the law. A ground for apolitical human social activities was prepared by J. Locke in his political theory. The state is one of possible emanations of apolitical society in the state of nature. Montesquieu expanded such a vision of society that it exists within the state but the state itself is limited by division of political power and civil rights which allow the members of the society to protect their freedom and dignity. Moral civil society we are developing protect the citizens from overwhelming influence of the state and particular egoisms of individuals. As such it promotes moral activity, it brings trust to the public sphere and it protects human dignity. (shrink)

Callender [2017] claims that contemporary science demonstrates that there is no objective present and no objective flow of time, especially since all sensed events come from the past, our various senses need different amounts of time to react, and there are enough asymmetries in the physical world to explain our experience of time. This paper holds that, although Callender’s arguments for the subjectivity of the flow of time are unconvincing, the scientific discoveries and arguments he indicates can still be applied (...) to improve theories of the objective flow of time. The paper develops precisely such a theory, one which introduces multiple individual proper presents for all of the objects that make up our world. (shrink)

The paper analyses the argument proposed by Milne against truthmaker maximalism and shows that the objections raised to this argument by de Sa and Zardini, and Rodriguez-Pereyra are misguided because the first one misuses the vagueness of some terms; and the second one is based on a fallacy of petitio principii.