Can science grow into something new and better with something like mathematical theology, as Ark suggested ?
The idea of mathematical theology was born during our discussions with Ark. Theology is an interesting discipline of knowledge because the object of research are metaphysical beings. In addition, few people know that modern mathematics, and thus also other exact sciences, owe a lot to theological considerations.
Theology and mathematics are usually viewed as mutually distant disciplines of knowledge. The first one is classified as a humanistic science, while the second one is classified as an exact science. However, there are some indications that the commonly accepted separateness of the two domains is in fact only apparent.
The object of research in both theology and mathematics are abstract beings, and thus, over the centuries, both sciences have repeatedly interpenetrated and influenced each other.
The common origin of theology and mathematics can already be seen in the philosophy of Ancient Greece. It is well known that for Plato, mathematical objects were examples of entities from another world. Using mathematical tools, the philosopher undertook attempts to describe what is ontologically or epistemologically transcendent.
When analyzing the history of Christianity, it is easy to notice that theology made a significant contribution to the development of mathematics, which is particularly well shown by the historical analysis of the thought of the Middle Ages.
Medieval theologian Nicholas of Cusa pointed out that mathematicians deal with infinitely small and infinitely large numbers in order to at least partially understand God's infinity.
The works of Nicholas of Cusa, which are devoted to mathematics, are primarily a record of looking for a transition from mathematical conclusions to metaphysical ones. The philosopher emphasizes the importance of the analogy between mathematics and metaphysics, inter alia, in "De mathematica perfectione" from 1458 and in "Aurea propositio in mathematicis" from 1459.
For Nicholas of Cusa, mathematics was not an art in itself, nor was it only a method of getting to know the physical world. He saw it primarily as a discipline enabling a deeper understanding of the world in relation to God in accordance with the maxim "fides quaerens intellectum" attributed to Anselm of Canterbury.
Anyway, Anselm also used mathematical tools and developed them to clarify metaphysical questions.
Another example is the nineteenth-century mathematician Georg Cantor. His first work was primarily on number theory. His research on trigonometric series eventually led him to the creation of set theory. One of the greatest discoveries of a mathematician was that infinite sets can be of different cardinality. He also showed that the set of natural numbers is infinite but countable, while the set of real numbers is not only infinite but also uncountable. This meant that these sets, although both are infinite, are not of the same cardinality.
Cantor's ideas were initially not enthusiastically received. In his defense, the scholar referred to theological arguments. He referred, inter alia, to Augustine, who proclaimed centuries ago that "natural numbers exist as ideas in the Divine Mind." Consequently, there is no reason why the cardinal numbers should not also constitute ideas that exist in the Divine Mind, which is intended to be unlimited.
From a historical point of view, considerations of a logical or even mathematical nature can also be seen by analyzing the numerous theological disputes that have taken place in the past. These include, inter alia, differences in views on the generally recognized doctrine noticeable in the Arians, Nestorians or Monophysites. Due to the multitude of interpretations of these views, it was very easy to make an equivocation (ambiguity that stems from a phrase having two or more distinct meanings, not from the grammar or structure of the sentence) at that time.
For example, the claim attributed to Monophysites that Christ had one divine-human nature and did not exist in two natures (divine and human) is extremely difficult to interpret unequivocally. Due to many similar disputes, theology needed strict definitions and disambiguation.
Another issue is possible arguments concerning the non-empirical nature of theology, manifested, for example, by the fact that revelation is regarded as a kind of axiom. It ought to be noted, however, that also in mathematics there are objects called primitive notions. They are, for example, sets or their features (elements).
Primitive notions play the role of universally accepted, undeniable obviousness, but for the person experiencing the revelation it becomes the undeniable obviousness. Primitive notions in mathematics were built on the basis of our intuition.
The idea of mathematical theology is therefore roughly that we should seek in the exact sciences the possibility of describing metaphysical and extrasensory beings. We should look at the world from a theological perspective, make metaphysical beings the objects of our research and apply appropriate mathematical tools that will allow us to at least attempt to describe these beings.
At the moment, such objects are subjects of philosophical (irrational philosophy, metaphysics, etc.) and theological research. The point is, however, to clarify these considerations. Of course, making the considerations more precise has some drawbacks, as it narrows our point of view to some extent, but on the other hand it may be necessary to make it sufficient for any conclusion.
In philosophy at the moment, no unambiguous conclusions are reached. There are so many different philosophical currents, so many systems, so many discourses that virtually any philosophical thesis can be refuted.
It is different in the exact sciences. We have specific systems of axioms and a well-defined methodology. This makes the proofs of the claims clear. We are able to state that a specific theorem has been proven in a given system.
Of course, our mathematical description of nature is not perfect, but that does not prevent us from advancing in technology and the benefits that come from developing science. Nevertheless, I think it is time for a new era of romanticism.
The natural sciences, and physics in particular, must stop concentrating solely on describing the material world. Time, consciousness, information - all these issues are very interesting. It seems to me that we are only observing their manifestations, but we know nothing about their source. Kant would say that we observe phenomena, but we do not know things in themselves, the causes in themselves.
And I personally believe that it is in theology or in irrational and metaphysical philosophy that inspiration ought to be sought, which can then be to some extent mechanized and refined.
The point is also not to become entangled in the current methodology of natural sciences, but to work on extending it.
History, even though it is an idiographic field, shows that such attempts have often been successful in the past. Nowadays, again, mainstream science is highly materialistic. I think that if we do not deviate from this approach, much progress will not be made.
