**1. Introduction**

Natural Philosophy or Philosophy of Nature has a long intellectual tradition with diverse ways of its identification as a style of inquiry and with the diverse interpretations of its role in the life of human collectives and in the individual reflection on reality. The presence of the qualification of Philosophy by the terms "Natural" or "Nature" does not make the concept easier to comprehend considering the long tradition of disputes about their meaning going back at least to Aristotle. Moreover, Natural Philosophy is the subject of this paper not so much because of its past, but because of its potential for the future of inquiry. This is the reason for the temporal qualification in the name "Contemporary Natural Philosophy" used in this paper and in the series of papers for which the present paper is intended. There is an increased interest in the revival and reconceptualization of Natural Philosophy as the means to adapt intellectual inquiries of reality to the challenges of complexity and of its consequences faced by science and philosophy [1,2]. Natural Philosophy emerged from the attempts to acquire universal knowledge of reality devoid of earlier divisions into separate realms of the Heaven and Earth consisting of separate essences long before the separation of the forms of this style of inquiry into the emancipated disciplines of knowledge. In this sense it can be considered a parent of the disciplines called Natural Sciences. Contemporary Natural Philosophy can be viewed as an attempt to reintegrate the vision of reality fragmented by the overload of complexity into a domain overarching Natural Sciences, but going far beyond these disciplines, and challenging conventional disciplinary divisions.

This paper does not have any ambitions to analyze the entire variety of past and present conceptualizations of the Natural Philosophy, its revival in the form of the Contemporary Natural Philosophy or to advocate for any specific choice for its identifying principles. Instead, its objectives are to look for that which is common in the diverse studies, directly or indirectly associating themselves with the naturalized inquiry of reality and to identify the fallacies which have to be eliminated or avoided, if we want to make this type of inquiry e ffective. In fact, the latter objective is primary and the former just sets the stage for the study.

The present paper is motivated by the view that the Contemporary Natural Philosophy can and should play the leading role in the process of developing an integrated vision of objective reality built with the use of a self-regulated by the feedback control methodology. This process does not have to be limited to the integration of the existing forms of scientific inquiry or to the organization of their accumulated results.

Although the choice of the name "Contemporary Natural Philosophy" for this gradually emerging domain of inquiry is far from being of primary importance, it can be justified by the a ffinity with the loose but identifiable tradition associated with the name "Natural Philosophy" in the intellectual history of humanity and, on the other hand, by the need to avoid the confusion with the existing fragmented, lacking cohesion, and dominated by external values and norms field of human activities conventionally called science. Although, in this paper, this conventional term will be used frequently along with the expression "scientific method", this is not an expression of the view that they refer to some clearly defined and uniform concepts, but rather a matter of convenience.

At present, Contemporary Natural Philosophy has the status of a project discussed in the series of papers presenting a wide variety of views and positions [1]. For this reason, its vision presented here is idiosyncratic and possibly temporary. However, no matter what its future shape will be, there is no doubt that its formation and development will require some adaptations and revisions of the methodologies which it inherited from Natural Philosophy and sciences. The present paper is intended as a preparation for these methodological transformations.

This is the actual focus of the paper and the reason for the reference to Baconian *idola mentis*. Francis Bacon wrote in *Novum Organum* about the fallacies obstructing science in its *statu nascendi*. The present paper is an attempt to remove obstacles for the Contemporary Natural Philosophy, categorized here, rather conventionally, as the Idols of the Number, the Idols of the Common Sense, and the Idols of the Elephant.

The reference to Francis Bacon does not mean an intention of the revival of Baconian philosophy of inquiry. It will become clear that the intentions of this paper are, in some cases, just opposite to those of Bacon. Its reason is the function of Baconian idols as a denouncement of the patterns and habits of human thinking which have to be eliminated for the purpose of achieving the authentic knowledge of reality. The function of the idols presented and discussed here is the same, but their specific characteristics are di fferent and sometimes opposite to those in *Novum Organum*.

The triadic categorization of the Contemporary *idola mentis* which should be avoided in the development of the Contemporary Natural Philosophy is not intended to be comprehensive, exhaustive, or exclusive. It is as idiosyncratic as the vision of the new domain. After all, we are talking about the future domain of inquiry which is being discussed and developed. Possibly other idols will be identified in the future and they all may be re-categorized.

The selection of the three categories and of the examples of idols within these categories is dictated by my own experience from my mathematical-scientific research, from my teaching, and from my work on philosophical reflection. The main criterion for the inclusion of instances and types of fallacious reasoning into consideration in this paper was their hidden omnipresence in the present scientific, philosophical and educational practice, and their detrimental impact on this practice. Their elimination is of grea<sup>t</sup> importance for the development of the methodology for the Contemporary Natural Philosophy.

The last statement can generate disbelief and criticism of my inflated expectations. How can I know that some topics will be of grea<sup>t</sup> importance for the Contemporary Natural Philosophy before it is born and matured? The answer will be given later, but at this moment, I can only give examples of the topics which are addressed in the description of the idols. The Idols of the Number address misconceptions regarding the distinction between quantitative and qualitative methods in scientific methodology. The Idols of the Common Sense address misconceptions regarding the relationship between the formal conceptualization of elements of reality and the way we perceive reality. The Idols of the Elephant address misconceptions regarding the relationship between structural divisions of reality.

The use of the term "misconception" puts some normative load in these descriptions. Does it mean that the subject of the paper is tracing errors in scientific methodology? My preference is to talk not about errors, but rather about fallacies. Errors are deviations from some standards of precision or correctness which are not always available or known, especially in the context of the domain of study which is still in the process of development. Fallacies are more general, as they may be of the type of formal fallacies where the deviation from some standards (i.e., they may be errors), but also of the type of informal fallacies, where the issue is not the deviation from some standards, but in not meeting declared expectations [3]. Certainly, the latter form of fallacies is relative to the expectations and therefore, it requires some context. All idols studied in this paper have the context of the Contemporary Natural Philosophy, although some are formal and can be classified as idols independently from any context. They have the common feature of being based on typically hidden divisions assumed to be obvious and absolute in their status or in their mutual relations. The expectation which serves as the evaluative (negative) criterion is the goal of an integrated view of reality. The idols studied here are obstacles in building this view.
