Małgorzata Godlewska from the SWPS University of Social Sciences and Humanities defines intuition, explains how it works and what stimuli help us tap into its potential.

We talk about the crossovers between science and art with the artist and pedagogue Prof. Adam Wsiołkowski.

The article addresses the problem of properties and epistemic functions of Russellian ‘knowledge by acquaintance’ interpreted here as a variant of intuition. The epistemic functions of intuition can be performed in two ways: first, as propositional knowledge of direct and immediate kind (a foundational function), and secondly, as a non-‑propositional form of consciousness that provides a justifying basis for intuitive truths. The distinction between these two functions of intuition presupposes a differentiation – not explicitly articulated by Bertrand Russell – between acquaintance and knowledge by acquaintance. Acquaintance as a form of non‑propositional consciousness is not epistemically autonomous, which is to say that it is not a judgment and cannot be qualified as either true or false, so a separate epistemic problem arises here, one of the shift from acquaintance to knowledge by acquaintance. The author points out that the shift from acquaintance to knowledge by acquaintance is difficult to accomplish, and she offers the opinion that the epistemic function of acquaintance or, more generally, of various similar kinds of consciousness, should not be interpreted in terms of justification. They should be understood not as a justifying element or a justifying reason for propositions that underlie other propositions, but as a factor that is an indispensable genetic and simultaneously structural element of propositional content in the sense assumed in transcendental philosophy.

The paper depicts some negative consequences of the attempts of history comprehension. In the light of the settlements of the contemporary psychology such attempts lead to the biases in historical cognition results.

The aim of this article is to show that philosophy of Blaise Pascal can be interpreted as defeating skepticism not by supernatural intuition but by pragmatic reasoning. For this purpose, I present in the article: (1) the geometrical method as the best available method for justifying statements, (2) circumstances that make human reason fallible, (3) the defense against skepticism pointing out that besides reasoning we still have intuitive knowledge of first principles, (4) remarks indicating that intuition cannot be a source of certainty, (5) the resulting contradictions are not problematic for Pascal because they serve the apologetic purpose of his work, and that the skeptical arguments presented do not prevent rational action.

The problem of the existence of mathematical entities is the subject of lively discussions. Realists defend the independence and autonomy of mathematical objects, while antirealists point to their dependence and conventionality. The problem of the existence of mathematical objects is also strongly linked to the problem of mathematical cognition: do we recognize mathematical truths in special acts of intuition, as some realists claim, or do we create mathematical knowledge only by building appropriate formal systems – as some anti‑realists imagine? In this article we present the K. Gödel’s and W.V. Quine’s realistic stances and comment on them from the perspective of Roman Ingarden’s phenomenology. We point out the role that Gödel attributed to his mathematical intuition, and then we present the process of eidetic intuition in Ingarden’s perspective (indicating Gödel’s and Ingarden’s common points of view). We also argue that Ingarden’s rich ontology could contribute in a significant way to the debates currently taking place in the mainstream philosophy of mathematics.

The article considers Roman Ingarden’s fundamental questions in the context of the position called philosophical fundamentalism. It turns out that the defining feature of this position, i.e. the search for answers to the question about the conditions of validity of statements in the sphere of traditional branches of philosophy: ontology, epistemology, ethics and aesthetics, finds its counterpart in Ingarden’s ontological and epistemological assumptions in phenomenology. They guarantee the legitimacy of any other claims. Ingarden’s philosophical fundamentalism, considered here in relation to the work- ‑scheme, weakened with time, which seems to be evidenced by the author’s doubts as to the legitimacy of the existence of the sphere of ideal objects determining this work. It seems highly possible that this is Ingarden’s bow to culture, and to cultural and historical relativization of the unchanging sphere of ideal objects.

Science means here mathematics and those empirical disciplines which avail themselves of mathematical models. The pragmatic approach is conceived in Karl R. Popper’s The Logic of Scientific Discovery (p. 276) sense: a logical appraisal of the success of a theory amounts to the appraisal of its corroboration. This kind of appraisal is exemplified in section 6 by a case study—on how Isaac Newton justified his theory of gravitation. The computational approach in problem-solving processes consists in considering them in terms of computability: either as being performed according to a model of computation in a narrower sense, e.g., the Turing machine, or in a wider perspective—of machines associated with a non-mechanical device called “oracle” by Alan Turing (1939). Oracle can be interpreted as computer theoretic representation of intuition or invention. Computational approach in another sense means considering problem-solving processes in terms of logical gates, supposed to be a physical basis for solving problems with a reasoning.

Pragmatic rationalism about science, seen at the background of classical rationalism (Descartes, Gottfried Leibniz etc.), claims that any scientific idea, either in empirical theories or in mathematics, should be checked through applications to problem-solving processes. Both the versions claim the existence of abstract objects, available to intellectual intuition. The difference concerns the dynamics of science: (i) the classical rationalism regards science as a stationary system that does not need improvements after having reached an optimal state, while (ii) the pragmatical version conceives science as evolving dynamically due to fertile interactions between creative intuitions, or inventions, with mechanical procedures.

The dynamics of science is featured with various models, like Derek J. de Solla Price’s exponential and Thomas Kuhn’s paradigm model (the most familiar instances). This essay suggests considering Turing’s idea of oracle as a complementary model to explain most adequately, in terms of exceptional inventiveness, the dynamics of mathematics and mathematizable empirical sciences.