Consistency and Some Other Requirements of a Formal Theory in the Context of Multiverse Models
References
- Balaguer, M. (1998). Platonism and anti-Platonism in mathematics. Oxford University Press.
- Bangu, S. (2020). Mathematical explanations of physical phenomena. Australasian Journal of Philosophy, 99(4), 669–682. https://www.tandfonline.com/doi/abs/10.1080/00048402.2020.1822895?journalCode=rajp20
- Birkhoff, G., & Neumann von, J. (1936). The logic of quantum mechanics. Annals of Mathematics, 37, 823–843.
- Chudnoff, E. (2020). In search of intuition. Australasian Journal of Philosophy, 98(3), 1–16.
- Côté, G. (2013). Mathematical Platonism and the nature of infinity. Open Journal of Philosophy, 3(3), 372–375.
- Descartes, R. (1989). Sochineniya [Essays]. Mysl.
- Everett, D. (2007). Recursion and human thought: Why the Pirahã don’t have numbers. The Edge. https://www.edge.org/conversation/daniel_l_everett-recursion-and-human-thought
- Everett, H. (2015). The many-worlds interpretation of quantum mechanics. Princeton University Press.
- Feferman, S. (Ed.). (2001). Kurt Gödel Collected Works. Vol 1. Oxford University Press.
- Filler, A. (2009). The history, development and impact of computed imaging in neurological diagnosis and neurosurgery: CT, MRI, and DTI. Nature Proceedings, 7(1), 1–76.
- Hilbert, D. (1902). Mathematical problems. Bulletin of the American Mathematical Society, 8(10), 437–479.
- Jaśkowski, S. (1969). Propositional calculus for contradictory deductive systems. Studia Logica, 24, 143–157.
- Karpenko, I. (2017). Fizicheskie teorii v usloviyakh mnozhestva vozmozhnykh mirov [Physical theories in the conditions of many possible worlds]. Filosofskii zhurnal, 10(2), 62–78.
- Karpenko, A. S. (2001). Paraneprotivorechivaya logika [Paraconsistent logic]. Novaya filosofskaya entsiklopediya [New encyclopaedia of philosophy]. https://iphlib.ru/library/collection/newphilenc/document/HASH6e472c9660a3b326ebfc6e
- Kleene, S. C. (2012). Introduction to metamathematics. Literary Licensing, LLC.
- Lektorskii, V. A. (Ed.). (2017). Perspektivy realizma v sovremennoi filosofii [Perspectives of realism in contemporary philosophy]. Kanon+.
- Lewis, D. (2001). On the plurality of worlds. Blackwell.
- Linde, A. (1982). A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems. Physics Letters B, 108(6), 389–393.
- Linde, A. (1983). Chaotic inflation. Physics Letters B, 129(3–4), 177–181.
- Linnebo, Ø. (2020). Philosophy of mathematics. Princeton University Press.
- Panza, M., & Sereni, A. (2013). Plato’s problem: An introduction to mathematical Platonism. Palgrave-Macmillan.
- Porus, V. (2021). Istoricheskaya epistemologiya —Trigger reformy filosofii poznaniya [Historical epistemology—The trigger of the reform of the philosophy of knowledge]. Voprosy filosofii, 5, 47–57.
- Pronskikh, V. (2021). Vsegda li vosproizvodimost’ vazhna i vozmozhna dlya nauchnogo eksperimenta? [Is reproducibility always important and possible for a scientific experiment?] Voprosy filosofii, 8, 103–115.
- Pruss, A. R. (2011). Actuality, possibility, and worlds. Continuum.
- Snapper, E. (1979). The three crises in mathematics: Logicism, intuitionism and formalism. Mathematics Magazine, 52(4), 207–216.
- Susskind, L. (2003). The anthropic landscape of string theory. https://arxiv.org/pdf/hepth/0302219.pdf
- Szmuc, D., Pailos, F., & Barrio, E. (2018). What is a paraconsistent logic? In J. Malinowski & W. Carnielli (Eds.), Contradictions, from consistency to inconsistency (pp. 89–108). Springer.
- Tegmark, M. (1988). Is ‘the theory of everything’ merely the ultimate ensemble theory? Annals of Physics, 270(1), 1–51.
- Terekhovich, V. (2019). Tri podkhoda k probleme kvantovoi real’nosti i vtoraya kvantovaya revolyutsiya [Three approaches to the problem of quantum reality and the second quantum revolution]. Epistemologiya i filosofiya nauki, 56(1), 169–184.
- Tieszen, R. (2011). After Godel: Platonism and rationalism in mathematics and logic. Oxford University Press.
- Tieszen, R. (2015). Arithmetic, mathematical intuition, and evidence. Inquiry: An Interdisciplinary Journal of Philosophy, 58(1), 28–56.
- van Heijenoort, J. (2002). From Frege to Gödel. A source book in mathematical logic, 1879–1931. Harvard University Press.
- Van-Quynh, A. (2019). The three formal phenomenological structures: A means to assess the essence of mathematical intuition. Journal of Consciousness Studies, 26(5–6), 219–241.
- Vasyukov, V. (2005). Kvantovaya logika [Quantum logic]. PER SE.
- Vizgin, V. (2007). Ideja mnozhestvennosti mirov [The idea of multiple worlds]. Izdatel’stvo LKI.
- Weinberg, J. M., Nichols, S., & Stich, S. (2001). Normativity and epistemic intuitions. Philosophical Topics, 29(1), 429–460.
- Yau, S., & Nadis, S. (2010). The shape of inner space: String theory and the geometry of the universe’s hidden dimensions. Basic Books.
- Zeh, H. D. (1970). On the interpretation of measurement in quantum theory. Foundations of Physics, 1, 69–76.
DOI: https://doi.org/10.2478/sh-2024-0022 | Journal eISSN: 2299-0518
Language: English
Page range: 23 - 34
Published on: Jul 29, 2024
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