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.
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\(\varLambda\) is the cosmological constant, and CDM means cold dark matter.
Weinberg (2014, p. 1) defines typical freely falling observers as “those that move with the average velocity of typical galaxies in their respective neighborhoods.”
For some authors, dark energy and dark matter are extra ingredients as well. According to Merritt (2017, p. 41), dark matter and dark energy “are auxiliary hypotheses that were invoked in response to observations that falsified the standard model.” The author considers dark energy and dark matter as conventionalist stratagems and non-falsifiable alternatives in cosmology.
Problems like flatness, isotropy, and homogeneity in the observable universe, i.e., inflation may generate a flat, isotropic, and homogeneous universe. Moreover, the inflationary mechanism is a powerful way to provide quantum fluctuations in the early universe, which are considered as seeds for the structure formation.
Popper’s philosophy within a Kantian or neo-Kantian tradition is found, for example, in Naraniecki (2010).
I adopt a common convention among Kant scholars. In passages of the Critique of pure reason, it is indicated the letter B, second edition, and the correspondent page number.
An interesting discussion on the concepts of space and time in Kant, comparing them to the relativity’s point of view, is found in Dorato (2002). According to the author, it is possible to support a Kantian interpretation of space and time (or space–time) in the Einsteinian context.
I suggest that the notion of field in modern physics plays the role of the notion of substance or substratum in Kant’s philosophy. According to the philosopher of Königsberg, “the substratum of everything real, i.e., everything that belongs to the existence of things, is substance, of which everything that belongs to existence can be thought only as a determination” (Kant 1998, B 225). A classical or quantum field cannot be “observed,” only its determinations or states (particles).
In Timaeus, Plato describes the creation of the universe using a metaphor. The maker of the universe, Demiurge, acts through thought or ideal objects as patterns in order to construct the organized world, our cosmos, from chaos (see Plato 1931, 29a).
See Pula (1992) for Nietzsche’s relation to Sapir–Whorf hypothesis in linguistics. The Sapir–Whorf hypothesis states that the structure of a language influences the speaker’s world view. In Twilight of the Idols, Nietzsche (2005, p. 170, “Reason” in philosophy, 5) emphasizes this point in a famous passage: “I am afraid that we have not got rid of God because we still have faith in grammar...”.
Nietzsche (2002, p. 15, §14).
One of the clearest passages in which Nietzsche states this point of view is in Beyond good and evil, aphorism 230: “(...) ‘spirit’ resembles a stomach more than anything.” This point is studied in Neves (2019a).
Nietzsche (2003, p. 206), fragment 10  of 1887.
Nietzsche (2002, p. 22, §22).
Nietzsche is among those who do not distinguish between thing in itself and noumenon. According to Nietzsche Source, the word noumenon does not appear in Nietzsche’ works. Thing in itself, on the contrary, is common in his books (see http://www.nietzschesource.org).
In this sense, Kant indicates a hypothetical intellectual intuition (Kant 1998, B 308).
A similar conclusion is shown in Romero (2013), in which space–times singularities are interpreted as nonphysical realities and defective products of Einstein’s theory, since energy conditions are obeyed.
Following Nietzsche, as the thing in itself is an absurd, then every object is given by the understanding’s properties and relations in statements.
According to Leech (2017, p. 98), logical and real possibilities, in Kantian philosophy, mean that “something is logically possible just when the concept of it is non-contradictory, and something is really possible just when the concept of it is non-contradictory and consistent with the a priori constraints on experience arising from the forms of intuition and the categories.” In our science, the word logic does not present the same meaning compared to Kant’s science. Non-classical logics, like the fuzzy logic, challenges the traditional view.
According to Popper, following Weyl, simpler theories or statements provide less parameters (see Popper 2005a, pp. 127–128). The falsifiability of an statement decreases with the number of parameters.
Popper defended a content measure of a theory and justified that Einstein’s theory has a greater content than Newton’s theory: “This makes Einstein’s theory potentially or virtually the better theory; for even before any testing we can say: if true, it has the greater explanatory power. Furthermore, it challenges us to undertake a greater variety of tests” (Popper 1994, p. 53).
Linde (2015) tries to answer this criticism.
Metaphysical in Aristotelian sense, or at least in the sense of commentators on Aristotle, i.e., beyond nature (physis in Greek). Nature is empirical and as such it is thought of and intuited from space and time.
See Ashtekar et al. (2006) for some proposals in a supposed quantum big bang.
See Grier (2018) for an introduction to Kant’s antinomies.
The second antinomy talks about the world and its parts, the third is about freedom, and the fourth antinomy of pure reason concerns God.
Olbers’ paradox says an infinite and eternal universe would provide bright nights for us due to an infinite number of stars.
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Neves, J.C.S. Proposal for a Degree of Scientificity in Cosmology. Found Sci 25, 857–878 (2020). https://doi.org/10.1007/s10699-019-09620-9
- Big bang
- Fuzzy sets
- Degree of scientificity
- Standard model
- Emergent cosmologies
- Bouncing cosmologies