RNDr. Peter Zamarovský, CSc.

A collection of contributions based on lectures organized by the sceptic association Sisyfos in Czech Academy of Science, which promote critical thinking in science and everyday life. In my part I analyse from historical and philosophical perspective the concept of infinity.

The concept of infinity is the product of human imagination, nevertheles infinity remained linked to phenomena and practice, even though more critical thinkers (Aristotle first and foremost) doubt its reality. The fact is that infinity does not manifest itself directly and clearly, and Aristotle claimed that mathematics can make do with finiteness, which can be constantly extended when necessary. So potential infinity suffices. It was St. Augustine who wrought a fundamental change in the understanding of infinity, by bringing God into the game. Omniscient must know all numbers, and we know for certain that they are endless. This theological proof of the existence of infinity was taken seriously right up to the beginning of the 20th century. But mathematicians failed to realise that it could be questioned even on the grounds of theology itself. For, as Thomas Aquinas pointed out, if the concept were a meaningless creation of fantasy, it could not be given legitimacy by claiming that the Omniscient must know it. But most mathematicians did not regard infinity as nonsense. Divinely guaranteed infinity also formed part of Bolzano’s set theory and subsequently was intrinsic to Cantor’s theory too. That theory multiplied it, i.e. created a tool for constructing an infinite number of infinities of various sizes (cardinalities) and thus became the mathematicians’ paradise. Infinities formed a kind of Tower of Babel rising up to the divine Absolute. In the second half of 20th century Czech mathematician Petr Vopěnka created his Alternative Set Theory, inspired by phenomenological philosophy. Vopěnka’s infinity is more modest; his tower of infinities has only two storeys. So mathematics, which originated in calculation and measurement – i.e. praxis – returns to the world of phenomena via a grandiose Platonic and theological metaphysical detour.

Mathematics, as a scientific discipline, developed from the rather humble beginnings of practical counting and measurements. The Pythagoreans shifted this discipline to the ideal, intelligible world—the “Pythagorean paradise”—where it remains to this day. However, there have been doubts as to whether some of the more peculiar mathematical concepts (irrational numbers, zero, negative numbers, infinity…) also belong to this “Paradise”. Within Theo-Platonism of the fourth century, the Christian God legitimised the concept of infinity. God then acted as guarantor for the existence of infinity even in the nineteenth and twentieth centuries. Later, however, God was played down with explicit references to Him having been eliminated. He remained hidden, as it were, in the “supernatural axioms” of set theory. Attempts to “excommunicate” Him consistently from the foundation of mathematics had only a negligible impact on the mathematics itself. Was it due to the fact that those formal foundations of mathematics (the set theory) are not the true foundations, with the actual basis being in mathematical practice?

The story of discovery and solution of so called dark night sky paradox. Overview of history and philosophical background of conceptions of spatial and temporal structure of the universe.

The concept of the beginning of Cosmos appears to be problematic. Not only ancient philosophical and theological (Plato. Aristotle, st. Augustine, st. Thomas), but also present-day physical approaches evoke many questions. They originate in the definition of time, its dimensionality and its scale. If we accept the Standard cosmological model, all physical processes including processes utilised in clock, lose their theoretical basis in the vicinity of the singularity. Does it mean that the singularity did not exist?

Among the many scenes decorating the walls of Rekhmire's tomb in the Thebian necropolis of Sheikh Abd el-Qurna, there is a figure of a girl playing the lute with a bow. If our interpretation of the painting is correct, this is the first (and till now the only known) depiction of a bowed musical instrument not only in Egypt, but in whole Mediterranean area. Although the lute came perhaps from Mesopotamia or Cappadocia, the oldest bowed musical instrument - the ravanastron - has its cradle in Ceylon. In Europe the first bows did not appear until the 7th - 10th century A.D.

Paper summarises the most important events in the history of invention and improovements of astronomical telescope.

Paper deals wit thermodynamical and philosophycal aspects of relation between evolution of life on Earth and evolution of Cosmos.

New view on ontological status of integers and real numbers is presented. Mathematical view on numbers, on their "reality" and "nature", does not correspond with reality of physical word. In this point we agree with alternative set theory. On the contrary with this set theory, we do not doubt justification of building process of real numbers, i.e. mathematical induction, but the building material itself, i.e. small integers. We try to show that their reality is not so confirmed, that it is not founded on anything existing in nature, that the do not "come from God". Their reality is constituted only by our approximations and conceptions. Real numbers as well as integers are only products of our limited "categorizing mind", they are concepts and as such they exist in our consciousness only.

Oweview and analysis of various conception of time in physics and philosophy.

Analysis of the role of reductionism in scientific and also general wayes of thinking

Nonbeing and other "negative" concepts represent dangerous source of misunderstanding in science, philosophy and also in everyday life.

The role of reductionism in the framework of scienticic thinking is criticaly analysed

Concept of "metaphysics" is analyzed from historical viewpoint and from view of presend-day philosophy. The role of metaphysics in natural science and especially in physics is presented.

Paper deals the problem of the relations between objective and subjective definitions of the concepts of chaos, order and entropy.It deals wit various definition of the entropy in physics and informatics.

The discussion of the concepts of time, time flow, time direction etc. based on the critical view on the book "The Arrow of time" writen by P. Coveney and R. Highfield.

Mach`s approach to inertia served as inspiration for Einstein general relativity. According to Mach free space is totally empty and therefore cannot principally act on mass bodies. As the source of inertial forces are therefore identified "far stars", i.e., mass of universe. The main problem with incorporation of Machian principle into physics was the assumption of instant action of all bodies, even most distant. This hypothesis contradicted the finite speed of signal, which is demanded by special relativity. Therefore Einstein did not accepted Mach approach and supposed that the space-time itself is the source of inertial effects. Contrariness of Einstein and Mach`s approaches reflects more general philosophical problem, which was formulated already by Eleatic school. It is the problem of existence of free space. With a little exaggeration we can say that it was already Parmenides who warn against Mach`s approach. And if not Parmenides, surely his disciple Melissus fro