Proposal for a Degree of Scientificity in Cosmology

  • Juliano C. S. NevesEmail author


In spite of successful tests, the standard cosmological model, the \(\varLambda\)CDM model, possesses the most problematic concept: the initial singularity, also known as the big bang. In this paper—by adopting the Kantian difference between to think of an object and to cognize an object—it is proposed a degree of scientificity using fuzzy sets. Thus, the notion of initial singularity will not be conceived of as a scientific issue because it does not belong to the fuzzy set of what is known. Indeed, the problematic concept of singularity is some sort of what Kant called the noumenon, but science, on the other hand, is constructed in the phenomenon. By applying the fuzzy degree of scientificity in cosmological models, one concludes that cosmologies with a contraction phase before the current expansion phase are potentially more scientific than the standard model. At the end of this article, it is shown that Kant’s first antinomy of pure reason indicates a limit to our cosmological models.


Big bang Singularity Kant Nietzsche Popper Fuzzy sets Degree of scientificity Standard model Emergent cosmologies Bouncing cosmologies 



This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.

Compliance with Ethical Standards

Conflict of interest

The author states that there is no conflict of interest.


  1. Abbott, B. P., LIGO Scientific Collaboration and Virgo Collaboration et al. (2016). Observation of gravitational waves from a binary black hole merger. Physical Review Letters, 116, 061102.CrossRefGoogle Scholar
  2. Ade, P. A. R., Planck Collaboration et al. (2016). Planck 2015 results XIII. Cosmological parameters. Astronomy and Astrophysics, 594, A13.CrossRefGoogle Scholar
  3. Al-Azm, S. J. (1968). Kant’s conception of the noumenon. Dialogue, 6(4), 516–520.CrossRefGoogle Scholar
  4. Anderson, R. L. (1998). Truth and objectivity in perspectivism. Synthese, 115, 1–32.CrossRefGoogle Scholar
  5. Ansoldi, S. (2007). Spherical black holes with regular center: A review of existing models including a recent realization with Gaussian sources. In Proceedings of BH2, dynamics and thermodynamics of black holes and naked singularities. Milano, Italy.Google Scholar
  6. Ashtekar, A., Pawlowski, T., & Singh, P. (2006). Quantum nature of the big bang: An analytical and numerical investigation. Physical Review D, 73, 124038.CrossRefGoogle Scholar
  7. Babich, B. (Ed.). (1999). Nietzsche, epistemology, and philosophy of science. London: Kluwer Academic Publishers.Google Scholar
  8. Bag, S., Sahni, V., Shtanov, Y., & Unnikrishnan, S. (2014). Emergent cosmology revisited. Journal of Cosmology and Astroparticle Physics, 07, 034.CrossRefGoogle Scholar
  9. Barrau, A., Martineau, K., & Moulin, F. (2017). Seeing through the cosmological bounce: Footprints of the contracting phase and luminosity distance in bouncing models. Physical Review D, 96, 123520.CrossRefGoogle Scholar
  10. Borde, A., Guth, A. H., & Vilenkin, A. (2003). Inflationary spacetimes are incomplete in past directions. Physical Review Letters, 90, 151301.CrossRefGoogle Scholar
  11. Brandenberger, R., & Peter, P. (2017). Bouncing cosmologies: Progress and problems. Foundations of Physics, 47(6), 797–850.CrossRefGoogle Scholar
  12. Carroll, S. M. (2001). The cosmological constant. Living Reviews in Relativity, 4, 1.CrossRefGoogle Scholar
  13. Carroll, S. (2004). Spacetime and geometry: An introduction to general relativity. San Francisco: Addison Wesley.Google Scholar
  14. Coc, A., & Vangioni, E. (2017). Primordial nucleosynthesis. International Journal of Modern Physics E, 26(7), 1741002.CrossRefGoogle Scholar
  15. Dorato, M. (2002). Kant, Gödel and relativity. In P. Gardenfors, K. Kijania-Placek & J. Wolenski (Eds.), Proceedings of the invited papers for the 11th international congress of the logic methodology and philosophy of science (pp. 329–346). Dordrecht: Synthese Library, Kluwer.Google Scholar
  16. Einstein, A. (1916). Die Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik, 354(7), 769–822.CrossRefGoogle Scholar
  17. Einstein, A. (1917). Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften (pp. 142–152).Google Scholar
  18. Ellis, G. F. R., & Maartens, R. (2004). The emergent universe: Inflationary cosmology with no singularity. Classical and Quantum Gravity, 21, 223–232.CrossRefGoogle Scholar
  19. Freese, K. (2017). Status of dark matter in the universe. International Journal of Modern Physics D, 26, 1730012.CrossRefGoogle Scholar
  20. Friedmann, A. (1922). Über die Krümmung des Raumes. Zeitschrift für Physik A, 10(1), 377.CrossRefGoogle Scholar
  21. Gava, G. (2014). Kant’s definition of science in the Architectonic of pure reason and the essential ends of reason. Kant-Studien, 105(3), 372–393.CrossRefGoogle Scholar
  22. Grier, M. (2018). Kant’s critique of metaphysics. In E. N. Zalta (Ed.), The stanford encyclopedia of philosophy (Summer 2018 Edition). Accessed 10 Aug 2019.
  23. Guth, A. H. (1981). The inflationary universe: A possible solution to the horizon and flatness problems. Physical Review D, 23, 347–356.CrossRefGoogle Scholar
  24. Hawking, S. W., & Ellis, G. F. R. (1973). The large scale structure of space–time. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  25. Hawking, S. W., & Penrose, R. (1970). The singularities of gravitational collapse and cosmology. Proceedings of the Royal Society of London A, 314, 529–548.CrossRefGoogle Scholar
  26. Ijjas, A., Steinhardt, P. J., & Loeb, A. (2013). Inflationary paradigm in trouble after Planck 2013. Physics Letters B, 723, 261.CrossRefGoogle Scholar
  27. Ijjas, A., Steinhardt, P. J., & Loeb, A. (2014). Inflationary schism. Physics Letters B, 736, 142–146.CrossRefGoogle Scholar
  28. Janiak, A. (2004). Kant as philosopher of science. Perspectives on Science, 12(3), 339–363.CrossRefGoogle Scholar
  29. Kant, I. (1998). Critique of pure reason, translated by Paul Guyer and Allen W. Wood. Cambridge: Cambridge University Press.Google Scholar
  30. Kant, I. (2004). Prolegomena to any future metaphysics, translated by Gary Hatfield. Cambridge: Cambridge University Press.Google Scholar
  31. Leech, J. (2017). Kant’s material condition of real possibility. In M. Sinclair (Ed.), The actual and the possible: Modality and metaphysics in modern philosophy. Oxford: Oxford University Press.Google Scholar
  32. Lehners, J. L. (2008). Ekpyrotic and cyclic cosmology. Physics Reports, 465, 223.CrossRefGoogle Scholar
  33. Lemaître, G. (1931). A homogeneous universe of constant mass and increasing radius accounting for the radial velocity of extra-galactic nebulæ. Monthly Notices of the Royal Astronomical Society, 91, 483.CrossRefGoogle Scholar
  34. Linde, A. (2015). Inflationary cosmology after Planck 2013. In C. Deffayet, P. Peter, B. Wandelt, M. Zaldarriaga, & L. F. Cugliandolo (Eds.), Post-Planck cosmology: Lecture notes of the Les Houches Summer School: Volume 100, July 2013. Oxford: Oxford University Press.Google Scholar
  35. Merritt, D. (2017). Cosmology and convention. Studies in History and Philosophy of Modern Physics, 57, 41–52.CrossRefGoogle Scholar
  36. Naraniecki, A. (2010). Neo-Positivist or Neo-Kantian? Karl Popper and the Vienna Circle. Philosophy, 85(4), 511–530.CrossRefGoogle Scholar
  37. Neves, J. C. S. (2016). Are black holes in an ekpyrotic phase possible? Astrophysics and Space Science, 361, 281.CrossRefGoogle Scholar
  38. Neves, J. C. S. (2017). Bouncing cosmology inspired by regular black holes. General Relativity and Gravitation, 49, 124.CrossRefGoogle Scholar
  39. Neves, J. C. S. (2019a). Nietzsche for physicists. Philosophia Scientiæ, 23(1), 185–201.CrossRefGoogle Scholar
  40. Neves, J. C. S. (2019b). Infinities as natural places. Foundations of Science, 24(1), 39–49.CrossRefGoogle Scholar
  41. Neves, J. C. S., & Saa, A. (2014). Regular rotating black holes and the weak energy condition. Physics Letters B, 734, 44–48.CrossRefGoogle Scholar
  42. Nietzsche, F. (2002). Beyond good and evil, translated by Judith Norman. Cambridge: Cambridge University Press.Google Scholar
  43. Nietzsche, F. (2003). Writings from the late notebooks, translated by Kate Sturge. Cambridge: Cambridge University Press.Google Scholar
  44. Nietzsche, F. (2005). The Anti-Christ, Ecce Homo and Twilight of the Idols, translated by Judith Norman. Cambridge: Cambridge University Press.Google Scholar
  45. Novello, M., & Perez Bergliaffa, S. E. (2008). Bouncing cosmologies. Physics Reports, 463, 127–213.CrossRefGoogle Scholar
  46. Palmquist, S. R. (1986). Six perspectives on the object in Kant’s theory of knowledge. Dialectica, 40(2), 121–151.CrossRefGoogle Scholar
  47. Planck, M. (1900). Zur Theorie des Gesetzes der Energieverteilung im Normalspektrum. Verhandlungen der Deutschen Physikalischen Gesellschaft, 2, 237.Google Scholar
  48. Plato. (1931). Timaeus, translated by B. Jowett. London: Oxford University Press.Google Scholar
  49. Popper, K. (1994). Objective knowledge: An evolutionary approach. Oxford: Clarendon Press.Google Scholar
  50. Popper, K. (2005a). The logic of scientific discovery. London: Routledge Classics.CrossRefGoogle Scholar
  51. Popper, K. (2005b). Unended quest: An intellectual autobiography. London: Routledge Classics.CrossRefGoogle Scholar
  52. Pula, R. P. (1992). The Nietzsche–Korzybski–Sapir–Whorf hypothesis? ETC: A Review of General Semantics, 49(1), 50–57.Google Scholar
  53. Quintin, J., & Brandenberger, R. H. (2016). Black hole formation in a contracting universe. Journal of Cosmology and Astroparticle Physics, 11, 029.CrossRefGoogle Scholar
  54. Robertson, H. P. (1935). Kinematics and world structure. Astrophysical Journal, 82, 284.CrossRefGoogle Scholar
  55. Romero, G. E. (2013). Adversus singularitates: The ontology of space-time singularities. Foundations of Science, 18(2), 297–306.CrossRefGoogle Scholar
  56. Starobinsky, A. A. (1980). A new type of isotropic cosmological models without singularity. Physics Letters B, 91, 99–102.CrossRefGoogle Scholar
  57. Wald, R. M. (1984). General relativity. Chicago: The University of Chicago Press.CrossRefGoogle Scholar
  58. Walker, A. G. (1937). On Milne’s theory of world-structure. Proceedings of the London Mathematical Society, 2–42(1), 90.CrossRefGoogle Scholar
  59. Watkins, E., & Stan, M. (2014). Kant’s Philosophy of Science. In E. N. Zalta (Ed.), The stanford encyclopedia of philosophy (Fall 2014 Edition). Accessed 10 Aug 2019.
  60. Weinberg, S. (2014). Cosmology. Oxford: Oxford University Press.Google Scholar
  61. Werkmeister, W. H. (1977). The critique of pure reason and physics. Kant-Studien, 68, 33–45.CrossRefGoogle Scholar
  62. van den Berg, H. (2011). Kant’s conception of proper science. Synthese, 183, 7–26.CrossRefGoogle Scholar
  63. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353.CrossRefGoogle Scholar
  64. Zimmermann, H.-J. (1996). Fuzzy set theory and its applications. Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar
  65. Zimmermann, H.-J. (2010). Fuzzy set theory. WIREs Computational Statistics, 2, 317–332.CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Centro de Ciências Naturais e HumanasUniversidade Federal do ABCSanto AndréBrazil

Personalised recommendations