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1 Idealism Copyright Interdisciplinary Encyclopedia of Religion and Science ISSN: and the author. No part of this article may be reproduced, stored in a retrieval system or transmitted without the prior permission of the Editors. To refer to the content of this article, quote: INTERS Interdisciplinary Encyclopedia of Religion and Science, edited by G. Tanzella-Nitti and A. Strumia, Date: 2002 DOI: / AS-3 Alessandro Salucci [1] I. Idealism in the History of Philosophy. 1. The Roots of Idealism in Ancient Philosophy. 2. Descartes and the Modern Age. - II. German Idealism and its Influences on Contemporary Thought. 1. The German Idealism of Fichte, Schelling and Hegel. 2. Post-Hegelian Idealism. 3. The Principle of Immanence at the Root of the Idealist Position. - III. Idealism and Scientific Knowledge: Classical Physics and Mathematics. 1. Idealism and Classical Physics. 2. Platonic Idealism in Mathematics. - IV. IdeaIist Paradigms in some Modern day scientific theories. 1. Idealism and Relativity. 2. Idealism and Quantum Mechanics. 3. Idealist Paradigms of Theoretical Cosmology. 4. Summarizing Vision. Idealism and Realism in the Method of Sciences : the Search for Objectivity. - V. Theology and the Idealist Principle of Immanence. 1. The Appraisal of the Principle of Immanence according to Theology. 2. The Critique of Religion: God as Projection of the Conscious and the Unconscious. 3. The Method of Immanence and how it acts in Theology. 4. The Existential Exegesis. - VI. How the Idealist Perspective works in Theology: Possibilities and Critical Appraisals. 1. Does an Idea of Christianity exist? 2. The Transcendental Theology of K. Rahner. 3. Truth and History. One generally understands the term "idealism" to mean every philosophy that, in questioning the source of knowledge, identifies it with thought, that is, with ideas. From the idealist perspective, human knowledge would not acknowledge the reality of things placed outside of the conscious subject, because the only phenomena considered to be real are those inner to the subject, also called "representations or states of conscience." "Being" is thus determined by "thought" and is often indicated by the term spirit [2]. In this sense, idealism is primarily opposed to materialism [3], which instead claims that Being exists in itself as materiality, and secondly to realism [4] that instead claims the reality of the existence of objects also outside the conscious mind. Taking the "principle of immanence" as its own method, according to which we do not directly know real objects, but only our representations of them, idealist philosophy bases its gnoseology on the claim that an immediate access to the data of experience on the part of our conscious would be impossible, or at least doubtful. The idealist position, beyond determining a gnoseology, also constructs its own metaphysics: in contrast to realism, that bases reality and truth in being, the principle of immanence maintains that truth is founded on thought. This idealist metaphysical conception has remarkable consequences in anthropology, theology, and also science, when the subject is predominant over the external world, that is, over the knowledge of a reality created independently from the subject itself. Page 1 of 20

2 I. Idealism in the History of Philosophy 1. The Roots of Idealism in Ancient Philosophy. The first philosophical use of the term "idealism" was made by Leibniz ( ), who used it in reference to the philosophy of Plato. Although in the history of philosophy the term "idealism " usually indicates a period from the end of the 1700's to the first decades of the following century, the idealist philosophy has in reality a much broader historical scope. Though recognizing that the German idealism of Hegel, Fichte and Schelling perhaps represents its greatist theoretic consistency, such a philosophical current cannot be confined to this period alone, as it concerns a gnoseological vision that, even with its different shades of meaning, crosses the entire history of Western philosophical thought. Idealism effectively began with the philosophy of Plato ( B.C.), who supported the existence of two worlds, the visible world, that of becoming, and the intelligible world, "the world of ideas" (Gr. hyperouránios), perfect and immutable. In fact the main characteristic of the platonic philosophy is just the vision of this super-sensibile truth, defined as "theory of ideas." The inquiry of nature (Gr. physis), carried out by the pre-socratic philosophers, had tried to explain the reality of things starting from the only mechanical and material causes. These were expressed in the mechanistic combination of what were then believed to be the four fundamental elements of matter: water, air, earth and fire. Plato did not, however, believe that these combinations were the true causes; he thought, in fact, that the cause of the sensible was to be found in something "supersensible" (cf. Phaedo, 97b-98c). For Plato the physical "data" cannot be explained remaining in the dimension of the physical, but rather ascending to the "supersensible", that is, in the ideas. With the term "idea" Plato meant, in a certain sense, something that is opposed to thought, that is "that to which" thought turns to when it thinks, something without which thought itself would not be: thus, the Platonic idea is not a thought, but rather a "being," indeed that being "that is absolutely," the "true being" (cf. Reale, 1975, vol. II, pp ). For Plato, therefore, the idea is the ontological essence and not so much the logical concept. Plato's idealist conception can be found, among other texts, in Book VII of The Republic, where the famous "myth of the cave" is found, and where there is a description, through a metaphorical-mythical process, of the various levels of human knowledge, that proceed increasingly from the sense knowledge to the intelligible knowledge. It is in these pages, and in similar ones of Platonic writings, that the first form of idealism is put, understood as a progressive rebuttal of sensible experience as the basis for knowledge, giving predominance to ideas. Only in this way, Plato claimed, could one hope to move from simple "opinion" (Gr. dóxa) to "science" (Gr. epistéme). If what we have recalled by now is common knowledge accepted by everyone, Plato's position in favor of the reality of mathematical entities is, on the contrary, under a great debate. In the pages of Metaphysics dedicated to the Platonic doctrine of causes, Aristotle ( B.C.) after recalling that it is at the same time similar and dissimilar from the Pythagorean theory says that for Plato, "besides sensible things and forms, there are the objects of mathematics, which occupy an intermediate position, differing from sensible things in being eternal and unchangeable, and from forms in that there are many mathematical objects alike, while the form itself is in each case unique" (Metaphysics, I, 6, 987b). For Aristotle, therefore, Plato admits the existence of "archetypal ideas" of numbers from which, similarly to other ideas, mathematical numbers are derived. In effect, in several works of Plato, such as Philebus, Republic, the VIIth Letter, we find a reference to the existence of ideal numbers that are archetypes of the numbers used by mathematicians. In Plato one can therefore suppose the existence of numbers, but with the shrewdness to remember that he speaks about them only as archetypal ideas, a concept of the number very different to the mathematical reality that he derives. 2. Descartes and the Modern Age. In the context of modern philosophy the term "idea" is altered. If for Page 2 of 20

3 Plato it is something real, for modern philosophers it is rather a "mental representation," that is, the idea is closer to the "psychological" than to the "ontological" dimension. According to many historians of philosophical thought, it is only with the Modern Age that the specifics of idealism are explicitly set out. In this period we find, on the one hand, a world of experience that is considerably valued, thanks to physical-mathematical science, which after Galileo and Newton had grounded its epistemological autonomy on experience [5]; on the other hand, thought is interpreted as "intuition", a thought that looks within itself for the certainty of its truth, a vision that will have its foremost defender in Descartes. But if Platonic idealism can be identified as an "objective" idealism, that of the Modern Age should be defined as a "subjective" idealism, meaning that the ultimate foundation of reality is based in the subject. The role assumed by Descartes ( ) in effecting this change of route is remarkable: with his cogito ergo sum he turns the previous gnoseological outline on its head, giving to "knowing" (the subject) the precedence over "being" (the object). By introducing methodical doubt, refuting the certainties that are not grasped in a clear and distinct manner, that is, in an immediate and intuitive way (the human spirit having "innate ideas" that exist in it as objects of knowledge), Descartes places himself as the remote father of modern idealism, even if, in fact, it is difficult to categorize him as a pure idealist. In fact, in Descartes' gnoseological doctrine "sense" has a certain degree of obscurity and is contrasted with intellect, the faculty of "clear and distinguished ideas," that acts through intuition and deduction to reach true knowledge. In his philosophy there is still, however, the difficulty of establishing whether an effective object existing in reality corresponds to these objects of the mind. In order to answer this problem he recovers, in part, the doctrine of Plato's ideas, thus showing how his way of thinking truly reflects his habit of mathematician. A different gnoseological formulation was that of John Locke ( ). Remembering the admirable synthesis performed by Newton ( ), who was also a friend of his, he does not start from mere sensation, but rather from the "sensible perception," which is itself an act of knowledge. Locke defines the "idea" as: "whatsoever the mind perceives in itself, or is the immediate object of perpection, thought, or understanding" (An Essay Concerning Human Understanding, II, 8). A true admirer of the physics of Newton, Locke never thought of denying the existence of the truth outside of us (cf. ibidem, IV, 11), but indeed he placed the foundation of knowledge in sensible experience. It is from the critique to the concept of substance begun by Locke that subsequently, thanks to George Berkeley ( ), the best-known form of modern idealism would be born. In his critique to Locke, Berkeley was lead to deny the existence of bodies as substances and to say that they are only ideas. All substance would be constituted by "ideas," whose truth consists in the fact that they are perceived by the subject. The esse est percipi would become, from that moment onwards, the typical formula of modern idealism. Only spirits and ideas exist, the spirit is the active substance, the idea is the inert and passive object of knowledge, for which the ideas depend in a certain sense from the spirit (cf. The Principles of Human Knowledge, 25). But, as Berkeley still emphasizes, not all ideas depend on "our" spirit, in fact some of them depend on God. He takes ideas as objects of sense experience: his theory of ideas is a theory that refers not to all being, but only to the sensible world. The jump performed here, with respect to Platonic idealism, is evident. From his gnoseological theory, Berkeley draws as a consequence the rehabilitation of final causes and the critique of Newton's absolute time and space, considered by the Irish bishop as pure abstractions. With Immanuel Kant ( ) idealism is defined in an even more specific way. He calls his philosophy "transcendental idealism," in order to distinguish it from the problematic idealism of Descartes and the dogmatic one of Berkeley. In the Critique of Pure Reason the problem of the possibility of metaphysics is raised, starting from the question of what are the conditions of possibility that allow science to arrive at a certainty (cf. Prolegomena to any Future Metaphysics, 4). Fascinated by Newtonian physics, he claimed that mathematics and physics are the only sciences through which human Page 3 of 20

4 reason reaches unequivocal results. Their characteristic is that of being based on necessary and universal principles, a priori, and thus principles not derived from experience. Experience, from which science nevertheless is nourished, can only say: "things have always worked this way," but not: "they should work this way." If Locke admits that the laws of physics are simple generalizations of experience and thus he denies that physics has the character of a rigorous science- Kant does not accept this position and asserts, on the contrary, that the laws of physics and mathematics are propositions in which the predicate "adds" something to the subject, calling them "synthetic a priori judgments." Such judgments are possible because the object on which they are delivered is a "phenomenon," that is, something that derives from sensible data and from certain a priori forms that order such data into an objective unity. This entails that all our knowledge is limited to phenomena and that, in fact, we cannot know a thing in itself, the "noumenon." The different phenomena of sensible experience are organized by the subject, who constructs an objective world uniting the phenomena according to the laws of the human intellect, that Kant calls "categories." It is the intellect, Kant says, that prescribes its laws to nature [6] and not vice versa. In Kantian idealism, space and time are not real properties, but a priori structures of our knowledge, forms of our sensitivity, conditions of the object's appearance to our intellect. Therefore, the main feature of the Kantian system is the definition of "transcendental," a term by which the active presence of the human spirit is indicated in every knowledge that concerns experience. Thus, the difference between the scientist and the philosopher consists in the fact that, while the former puts his or her trust in an "experience" approach, in perceptions of the material world derived from the senses, the philosopher examines the same job of the scientist, to make him or her understand that this is only a construction of human spirit, an interpretation of the sensory experience. Kant therefore does not deny the existence of an external reality, indeed he criticizes the idealism of Berkeley: Kant's idealism rather operates a stronger accentuation of the role of the knowing subject. II. German Idealism and its Influence on Contemporary Thought 1. The German Idealism of Fichte, Schelling and Hegel. The form of idealism that came after the philosophy of Kant represents a "continuation" and at the same time a "reaction" to the thought of the philosopher of Königsberg. It is a continuation, because it continues to affirm the knowability of being, and a reaction because it gives free space and ample creativity to the spirit [2]. After Kant, the position of idealism can be summarized by the statement: "there is only the Self and every other reality is a work of the Self." The German idealists will take into consideration only the Critique of Pure Reason, and claim that Kant's work would contain an intrinsic contradiction, that is, if everything that is knowable is set out by the subject, then the thing itself, the "noumenon" will also have to be, so that we can know its existence. The intervention of the subject, of human spirit, is thus moved further: from the phenomenon to the noumenon. The spirit not only creates the form of the knowable, but also the content of the consciousness; it entirely creates the known object and identifies with it. Taking a different position to Kant, J.G. Fichte ( ) attempts the union between phenomenon and noumenon, theoretical and practical, subject and object. If for Kant the "Self," the subject, creates the knowing, for the subsequent German idealism the subject creates being. All reality is thus reduced to thought. If Plato, alongside the "world of ideas" puts the "world of things," caused by as many objects as there are ideas, in German idealism nothing exists outside of the unique Idea (with capital I). The individual beings of things are only modifications of the unique substance, temporary and phenomenal manifestations of the Absolute. However, for German idealists, the identification between object and subject, being and thought, Self and non-self, is not immediate. This takes place though an intrinsic "dialectic opposition" of the spirit. The spirit moves in a triadic process of "thesis", in which the subject Page 4 of 20

5 poses itself, "antithesis", in which the object is placed, and finally the "synthesis", in which the subject, in its self-awareness, acknowledges having placed the object in being. In this framework, the idealism of Fichte is called "subjective idealism", because the Self is the fundamental principle of all knowledge, and "ethical idealism", because the first activity of the Self imposes on every individual the fulfilment of an obligation, that is, conquering one's own freedom (cf. in particular the Foundation of the Entire Science of Knowledge, 1794). In the homonymous "objective idealism" of F.W. Schelling ( ), the object (Nature) is not -as it was for Fichte- an obstacle to be removed, but an autonomous reality, certainly inferior to the spirit, but only by "degree". The idealism of Schelling is also called "aesthetic," because in his opinion, the identity-unity of the Absolute can only be understood by aesthetic intuition. It is interesting to note how, unlike Galileo and Newton, for whom nature is materially conceived and dominated by the inflexible laws of mechanics, Schelling understands nature [7] as a spiritual entity endowed with an inexhaustible free activity. In the philosophical thought of G.W.F. Hegel ( ) we instead speak of "absolute idealism," an overcoming of the idealism of Fichte and Schelling by virtue of the complete realization of the finite in the infinite. According to Hegel the beginning of every reality is Reason, or Absolute, or Idea, from which derive both the world of nature and the world of the spirit. Hegelian idealism is also called "logical", because its fundamental principle is the identity of Reason and Being: "what is rational is real; and what is real is rational" (Preface to the Elements of the Philosophy of Right, 1821). The opposition to Aristotelian logic, where thought and reality are very distinct, is obvious here. Logic is only the "logic of the abstract," because identity between metaphysics and logic is never posed. Hegel accepts the concept of the Absolute as the identity of Nature and Spirit. Reason is understood as a unity that contains reality. The Absolute is not a "substance," nor something static, as it was suggested by Spinoza ( ), but it is Thought, that is, a dialectic development. Therefore, for Hegel the only true reality is the reality of Reason. It is the same to state that the only true being is the being of Thought and that the only true thought is the thought of Being. All that exists is a manifestation of the Absolute. Understood in this way, idealism could not but identify a return to a philosophy that was more humanistic than scientific; it was not by chance that Popper would write that, starting from Hegelism, a dangerous abyss has arisen between science and philosophy (cf. The Nature of Philosophical Problems and their Roots in Science, 1952, in Conjectures and Refutations). German idealism was, in fact, an attempt to put in crisis the relationship that Descartes' philosophy had established between mathematics and philosophy, like that which Francis Bacon and Kant had established between philosophy and natural science. 2, Post-Hegelian Idealism. In the period that goes from Kant to Hegel the development of idealism can be subdivided into four different stages, summarized in the following theses: a) there is no knowledge without categories (Kant); b) There are no categories without the self-awareness that produces them, and the productive self-awareness must be absolute (Fichte); c) Self-awareness is absolute only if it is the identity of nature and spirit (Schelling); d) This identity cannot be aware if it is not self-conscious reason, that is, Spirit, which represents the unanimous principle of the world (Hegel). Though reaching its peak with Hegel, idealism would also find its continuation in posterior philosophical thought that we can divide into two main streams. The first of these is represented by "neo-idealism," developed in Italy thanks to authors as Spaventa, Croce and Gentile; in Holland through the work of Bolland, and in England at the universities of Oxford and Cambridge. Apart from the study of the relationship between phenomenology and logic, one of the main aims of Italian Neo-Idealism was that of opposing positivism [8] and its claim to scientifically explain all reality. Neo-idealism only acknowledges the Spirit as the sole absolute reality in history. The immanentism of the Spirit, and the identity between history and philosophy, is then derived, providing an origin to historicism in its diverse and complex forms, which, however, are still the offspring of Hegelian Page 5 of 20

6 phenomenology. For Benedetto Croce ( ) all that is real is life or history of the Spirit, nothing is outside of the Spirit (immanentism), nothing is outside history (historicism). For Giovanni Gentile ( ), however, the beginning of all reality is the universal "Self", or absolute Subject, that is realized as Absolute Thought. Thought does not precede thinking and therefore does not derive from a pre-existing subject, but rather from a subject that exists precisely because it thinks, and in the act of thinking creates itself. The universal "Self" is therefore the thinking present (actualism) and immanent in all things (immanentism). In France, with the exception of Octave Hamelin and Leon Brunschvig, idealism did not have a major development. The situation was quite different in England, where an idealist school blossomed at Balliol College (Oxford) by the end of the 19th and the beginning of the 20th century. But this was nothing more than a group of individual scholars who used idealism as an inspiring philosophy. Among others we remember E.J. Mc Taggart, R.G. Collingwood and F.H. Bradley. Their role, however, was of a certain importance, because it was these three thinkers who marked the cultural climate of England at the beginning of 20th century, when G.E. Moore and B. Russell, founders of analytical philosophy, began their university studies at Cambridge. The second stream that originated from post-hegelian idealism, rather than assuming idealistic philosophy, is indirectly influenced by it and, especially in the works of Husserl and Heidegger, it confronts with idealistic philosophy as well. All of Edmund Husserl's ( ) philosophy is dominated by the idea of science. He came from the world of mathematics and his work begins with the attempt to define the mathematical entity. Intending to fight psychologism, Husserl was very interested in consciousness that he always meant as "consciousness of something." In this idea of consciousness there is a distinction between subject and object: the subject is the body of facts of consciousness, such as perceiving, judging, representing itself, and the object is that which manifests itself in these facts, such as sounds, colored objects, memories and images. Our psychic actions always refer to an object (we never see "the green," but only a "green object"). But this does not mean that Husserl endorses a realistic vision. Beginning with the publication of Ideas Pertaining to a Pure Phenomenology and a Phenomenological Philosophy (1913), Husserl begins to question the problem of what reality is, and claims that, in order to resolve the question, one must adopt an attitude of "suspension of judgment" (Gr. epoché) regarding all that that, until now, has been said by the various sciences or by several philosophical schools. That is, from the persuasion of the existence of world one must not deduce any philosophical proposition, because at the root of every reflection that wishes to be philosophical, only that which is intuitive, that which is self-evident, is placed. The only thing we can be certain of, is not so much the existence of the external world, but that of consciousness. Husserl continued to question this topic and in his later writings there are traces of a certain type of idealism in his vision of the relationship between scientific knowledge and philosophical knowledge. These idealist nuances are obvious, in particular, when he opposes the developments caused by positivist (and neo-positivist) vision of science, understood as the refusal of every philosophy (cf. The Crisis of European Sciences and Transcendental Phenomenology, 1954). But Husserl did not define exactly what this "consciousness" consisted of, making his position in the idealistic panorama difficult to evaluate. Even if defined by some as an idealist because of his recovery of Descartes', and in part, of Kant's philosophy, Husserl goes beyond realism and idealism. Even if we acknowledge his relationship with idealistic philosophy, we shal conclude that this was neither conflictive nor resolutive. It was, instead, Bertrand Russell ( ), in the first phase of philosophical thought, who turned to idealism to find a solution to his key problem, that is, the search for the foundations of mathematics and the question of the reality of the number. But his idealist position did not last very long, because at the beginning of the 20th century, he would abandon it to embrace as a reaction first an extreme realism inspired by Alexius Meinong ( ), and then a more moderate realism. The change in Russell's position regarding idealism happened as a result of the critique that G.E. Moore ( ) addressed to Page 6 of 20

7 the esse est percepi proposition of Berkeley by the pages of his work The Refutation of Idealism (1903). Moore would criticize the idealist proposition not so much on the logical or metaphysical level, but rather at the level of linguistic significance. He wanted to show how the statement esse est percepi, in fact means nothing, thus giving rise to that important philosophical stream that would dominate the 20th century: "analytical philosophy." This was also a product, albeit indirectly, of the critique of idealism. Someone who would instead confront himself with German idealism, in a systematic and profound way, was Martin Heidegger ( ). He was committed in his philosophical journey to give back to philosophy the uncontaminated purity of its origins. Heidegger attempted to clean up philosophical thought from the waste that contaminated it, caused by the methods and aims of science. Re-examining the concept of science, as formulated by Fichte, Schelling and Hegel, who had assigned only to philosophy the property of rationality, Heidegger reaffirms that philosophy is not interested and cannot be interested in positive science, because philosophy itself is true science, the true way to reach absolute knowledge. At the same level as the German idealists, Heidegger lets philosophy go back to being the indisputable queen of thought. 3. The Principle of Immanence at the Root of the Idealist Position. Throughout its articulated philosophical journey, the specific argument of idealism thus remains the "principle of immanence." It consists of stating the assumption according to which the act of the subject (the Self) produces nothing outside of itself, but is put inside the subject that placed it. According to the idealists one cannot think of a being outside of thought; as soon as something is thought, because of the fact that is thought, it is present in my Self and no longer externally. This position was thought by Berkeley to be an obvious and self-evident statement: "Some truths there are so near and obvious to the mind, that a man needs only open his eyes to see them. Such I take this important one to be, viz. that all the choir of heaven and furniture of the earth, in a word all those bodies which compose the mighty frame of the world, have not any subsistence without a mind, that their being ( esse ) is to be perceived or known" (The Principles of Human Knowledge, n. 6). The concept of immanence is directly opposed to that of transcendence. In the strictly gnoseological sense, the latter coincides with the realistic perspective, that is, the possibility of knowing something external to the same subject. Idealism coincides with the denial of this gnoseological transcendence, since it denies that conscience can go beyond its own limits and recognize as existing, a reality that is external to it. The idealist conclusion is therefore immediate: that which is known must be in thought, and an object that was not in thought would not be known. Therefore, we cannot know realities external to thought. The American philosopher C.S. Peirce ( ) puts this concept in the following way: "But if it be asked us, whether some realities do not exist, which are independent of thought; I would in turn ask, what is meant by such an expression and what can be meant by it. What idea can be attached to that of which there is no idea? For if there be an idea of such a reality, it is the object of that idea of which we are speaking, and which is not independent of thought. It is clear that it is quite beyond the power of the mind to have an idea of something entirely independent of thought -it would have to extract itself from itself for that purpose; and since there is no such idea there is no meaning in the expression" (C.S. Peirce, Toward a Logic Book. On reality, in "Writings of Charles S. Peirce", ed. by C.J. Kloesel et al. [Bloomington: Indiana University Press, 1986], v. 3, pp ). Its strong gnoseological resonances, especially as regards the relationship between idea and truth, would allow idealism to accompany a good part of the elaboration of scientific thought. That was not be confined to the debate betweeen realism and idealism, but would involve science as such: one is reminded of, for example, the relationship between reality and models, the foundations of mathematics, or finally the relationship between theory and experiment, the relevance of the latter being obvious in the debate Page 7 of 20

8 between the various philosophical interpretations given to quantum mechanics. An analysis of the idealist perspective of sciences thus becomes necessary. III. Idealism and Scientific Knowledge: Classical Physics and Mathematics The direct or indirect repercussion of idealism on science is to be found in at least three meaningful ways: a) in the definition of what we mean by science; b) in the formation of the basic knowledge used by science and, specifically, by mathematics c) in the interpretation of scientific theories. In particular, as far as aspects a) and b) are concerned, the idealistic perspective has shown itself mainly as "Platonic" or Platonicizing idealism (see above, I.1), while as c) is concerned, we mainly deal with modern Kantian, or post-kantian, idealism (see above I.2 and II 1-2). In this and in the next section we will try to provide an essential picture of the main epistemological viewpoints of mathematized scientific theories, in relation to the different degrees of their development along the history. 1. Idealism and Classical Physics. In classical physics, that is Galilean and Newtonian science, which was also for a long time the epistemological reference model for all other natural sciences, the definition of science has directly involved an "observative" or "experimental" component as well as a mathematical one. Beginning with Galileo, science was considered as a mathematical description-explanation of nature, capable of being controlled by experiment. The success, historically proven, of this way to understanding the natural sciences marked the overcoming of "Platonic" idealism on Aristotelism, as Koyré correctly observes: "If you claim for mathematics a superior status, if more than that you attribute to it a real value and a commanding position in Physics, you are a Platonist. If on the contrary you see in mathematics an abstract science, which is therefore of a lesser value than those - physics and metaphysics which deal with real being; if in particular you pretend that physics needs no other basis than experience and must be built directly on perception, that mathematics has to content itself with the secondary and subsidiary role of a mere auxiliary, you are an Aristotelian. What is in question in this discussion is not certainty no Aristotelian has ever doubted the certainty of geometrical propositions or demonstrations but Being; not even the use of mathematics in physical science -no Aristotelian has ever denied our right to measure what is measurable and to count what is numerable- but the structure of science, and therefore the structure of Being. [...] It is obvious that for the disciples of Galileo just as for his contemporaries and elders, mathematicism means Platonism [...]. The Dialogue and the Discourses tell us the history of the discovery, or better still, of the rediscovery of the language spoken by Nature. They explain to us the manner of questioning her, i.e., the theory of that scientific experimentation in which the formulation of postulates and the deduction of their implications precedes and guides the recourse to observation. This too, at least for Galileo, is a proof 'by fact.' The new science is for him an experimental proof of Platonism" (Koyré, 1943, pp. 421, 424, 428). This orientation of natural sciences towards the mathematical ideal does not arise suddenly with Galileo or Descartes. It follows a long course of preparation that has its roots as far as in the 13th century, in the heated debate between the school of Paris, which was mainly Aristotelian, and the school of Oxford, more Platonic in character (cf. Crombie, 1995; Hackett, 1980). Among the representatives of this school, who were absolutely convinced of the necessity to elaborate all knowledge according to a strictly mathematical point of view, was Roger Bacon ( ), who expressed the matter thus: "Now in mathematics it is possible for us to reach a complete, error-free truth and a universal certainty, without a shadow of doubt, because here one progresses with necessary proofs (in ea convenit haberi demonstrationem per causam propriam et necessariam). And the demonstration introduces the truth [...]. Only in mathematics are there proofs in the true sense of the word (per causam necessariam); and therefore only in the sphere and by virtue of this science man can reach the truth [... ]. In mathematics Page 8 of 20

9 alone one attains full certainty. It follows that if in the other sciences we want -and is our duty to reach a level of certainty that excludes every doubt, and a truth, that excludes every error, it is necessary that mathematics become the foundation of our knowledge, in that, prepared by this, we can reach full certainty and truth also in other sciences" (The "Opus maius" of Roger Bacon, edited by J.H. Bridges, Oxford , vol. I, pp ). In this sense, the influence of Platonic idealism in order to conceive and build modern science is expressed by the idea of "mathematization": for science the world of Platonic ideas is nothing but a mathematical empyrean. The success of Galilean sciences, however, would have to pay the price of a gradual move towards nominalism with the loss of analogy [9], of realism [4], and of the cognitive value of science itself. The latter would increasingly be seen as an instrument of calculation and prediction, rather than as a true (or at least verisimilar) knowledge of reality. The influence of Platonic idealism on science would tend to join, over time, with idealism, understood in its "modern" and "subjectivist" sense. Thus, Kant would seek an a priori philosophical interpretation of the absolute space and time of Newton, identifying them with the same structure of the way of knowing of the subject, rather than with external and objective properties. 2. Platonic Idealism in Mathematics. Another, still very important aspect of Platonic idealism in science, directly concerns mathematics. The way it works can be seen in the answers that would be given to the following questions: a) Do mathematical entities have a purely mental existence, moreover an objective existence outside of the human mind, placed in some world of ideas? b) How are mathematical notions formed in our knowledge? For as much as these questions may seem remote, they have become nowadays extremely current, bringing back to the limelight, in the area of reflection on scientific thought, the names of Plato and Aristotle. These names appear to have surpassed in the final decade of the 20th century those of Descartes and Kant, that appear to have reigned for a long time, almost undisputed, as the founding fathers of true critical philosophy. When the above questions are asked, the great names of mathematics, physics and science in general, reflecting as philosophers, tend to offer either a Platonic solution or an answer of empiristic-abstractive kind. One easily notices the almost natural tendency of mathematicians towards Platonic idealism: mathematical objects have a dignity and a beauty that demand an extramental ontological state. Often this reflects an enthusiasm of an aesthetic nature, not founded on fully demonstrated arguments, but extremely significant. The passionate reflection of Roger Penrose, for example, is relevant to all: "How 'real' are the objects of the mathematician's world? From one point of view it seems that there can be nothing real about them at all. Mathematical objects are just concepts; they are the mental idealizations that mathematicians make, often stimulated by the appearance and seeming order of aspects of the world about us, but mental idealizations nevertheless. Can they be other than mere arbitrary constructions of the human mind? At the same time there often does appear to be some profound reality about these mathematical concepts, going quite beyond the mental deliberations of any particular mathematician. It is as thought human thought is, instead, being guided towards some eternal truth a truth which has reality of its own, and which is revealed only partially to any one of us. [...] Is mathematics invention or discovery? When mathematicians come upon their results are they just producing elaborate mental construction which have no actual reality, but whose power and elegance is sufficient simply to fool even their inventors into believing that these mere mental constructions are 'real'? Or are mathematicians really uncovering truths which are, in fact, already 'there' truths whose existence is quite independent of the mathematicians' activities? I think that, by now, it must be quite clear to the reader that I am an adherent of the second, rather than the first, view, at least with regard to such structures as complex numbers and the Mandelbrot set" (Penrose, 1989, pp ). But, supposing that a world of the ideas exists, in a Platonic sense, at least as far as mathematical ideas Page 9 of 20

10 are concerned, in that way we can know them? In other words: does every type of knowledge come through our senses (nihil est in intellectu quod prius non fuerit in sensu, says the Scholastic adage) and then reach the mind in the form of universal concepts (Aristotelian thesis); or do ideas - and in particular mathematical ideas - reach the mind though intuition, or direct illumination, not contaminated by matter and the senses (Platonic thesis)? This is how ontological idealism is reflected in a gnoseological idealism, and in every enquiry about the formation of mathematical knowledge. It is interesting to observe how the return to Platonic idealism, on the part of some mathematicians and physicists, begins with the demand for a recovery of objectivity against the subjectivism of modern idealism, and is based on a realistic statement (the "exaggerated" realism of Plato that attributes an extramental existence to ideas) in opposition to the subjectivist idealism that denies the reality of being as such outside of the subject and thought. A totally subjectivist and arbitrary science, purely conventional, lacks cognitive content and it is unacceptable for scientists who dedicate their greatest energies to it. IV. Idealist Paradigms in some Modern Scientific Theories In relation to how much the physics of Newton already had, the physics of the 20th century has attributed to mathematics an increasing and even more significant role, also because it progressively distanced itself from direct, human scale experiences. Very high speeds such as that of light, that come into play in the theory of special relativity, enormous dimensions and times, that come from the cosmology of general relativity, extremely small dimensions in microphysics governed by quantum mechanics, are all things far removed from our daily experiences. This has implied that physics, and the sciences related to it, have ultimately moved towards Platonic idealism. It is now idealism in the modern sense: Cartesian, Kantian and post-kantian, that, rightly or wrongly, has come into play. 1. Idealism and Relativity. As regards the theory of relativity [10], it must be said that it is spontaneously associated by many with subjectivist idealism. Sometimes the relativity of measures of time and space, of simultaneity, etc., has lead some authors to believe that in this theory, objective elements do not exist independently from the measuring observer (subject), and that this legitimatizes idealism, relativism and subjectivism. An idealist interpretation of general relativity was proposed by Gödel, a keen follower of the philosophy of Kant, basing his arguments on a solution he found to Einstein's equations, in which a global synchronization of time [11] is not possible and in which, indeed, it is conceivable to travel back in time, in contrast to what happens with cosmological solutions of a physical kind. But Gödel's solution is ultimately only a mathematical curiosity, not, in fact, a physically realizable one (cf. Gödel, 1949). On the contrary, the theories of relativity can be considered theories of "invariants" or absolutes. They are aimed at, and succeed in, giving a formulation of the physical laws completely independent from the choice of the observer. While the mechanics of Newton was applicable only by the so-called "inertial observers," (general) relativity, in its definitive form, achieves applicable laws which are operative by any observer. The subjective interpretation of space and time as a priori categories of the knowing subject, proposed by Kant, is no longer conceivable here. General relativity tends, moreover, to move closer to the Aristotelian concept of motion, space, time and matter, rather than to the Platonic ones. It may instead mirror a certain Platonic, if not quite Pythagoran, idealism. In fact, it places all physics into one single geometric outline, of Spinozan inspiration. Einstein himself declared that he felt, in a certain sense, close to the pantheist philosophical vision. 2. Idealism and Quantum Mechanics. The issue of "subjectivist" idealism has instead assumed an important role in the interpretation of quantum mechanics [12]. Unlike what occurred in other fields of science, here the same scientists have defined their interpretation as "idealist" or "realist," opting for a Page 10 of 20

11 decisive "philosophical" formation. People such as Einstein, De Broglie, Schrödinger, Bohm, shared a realist interpretation, while among those who supported an idealist interpretation we find Bohr, Heisenberg and Born. The latters' interpretation would prevail as the official one, under the name of "interpretation of the Copenhagen school." We refer to other entries of this Encyclopedia for the detailed discussion of these interpretations. Here we observe that, in approaching the problem, one must keep two elements in mind: a) on the one hand, the philosophical convictions stated by the authors that define themselves as "idealist" or "realist," according to the meaning they give to the respective terms, which are not necessarily identical to the corresponding philosophical terms; b) on the other hand, what do the terms "idealism" and "realism" effectively mean when one refers to an interpretation of a scientific theory. If the first aspect is interesting for the biographer, the second aspect interests more in-depth epistemological enquiry. Following the official vision of the Copenhagen school, it is worth emphasizing that the interpretation of quantum mechanics is considered idealist for two reasons. From the "experimental" viewpoint, in that the observable data appears inseparable from the measuring device, and the resultant measure is the combined action of the subject's action on the object: According to Heisenberg, this looks as if an element of subjectivism had been introduced into the theory, as if we meant to say: what happens depends on our way of observing it or on the fact that we observe it (cf. Heisenberg, 1958). When looked at closely, all of this reminds us of Kantian idealism, according to which the thing in itself ("noumenon") is not knowable, but that which we know ("phenomenon") is the result of the combination of the a priori of the subject with the investigated object. And this also holds from a "theoretical" viewpoint, as it is not possible to find a single model, accurate enough and in line with reality, that entirely describes a quantistic object. Instead, we must refer to complementary and mutually exclusive mathematical outlines, such as that of the "wave" and that of "particle," that are applied alternately. A similar situation makes us think of an unknowability of reality, of a "weak" science from the gnoseological point of view, and of an "instrumentalist" epistemology (cf. Kuhn, ). 3. Idealist Paradigms of Theoretical Cosmology. The epistemological charter of cosmology [13] is rather a special one. Focusing on the study of the universe [14] on a large scale, unlike other fields in physical and chemical sciences, cosmology works on systems that are "non-reproducible" in the laboratory, and tries deduce physical properties on a cosmic scale, starting from verifiable knowledge on a local scale. Moreover, cosmology makes wide use of models, known as "cosmological models." In its theoretical formulations cosmology often relies on multiple assumptions and the proposed solutions for a specific model play the role of particular cases within very wide generalizations. Cosmology is therefore not only introduced as a "science of the universe," but also as "science of the assumptions that must be made so that it is possible to formulate a science of the universe" (cf. Heller, 1986). Having the need to include within its models also space-time regions that are inaccessible to observation, cosmology unconsciously tends to move its own criteria of truth from the sphere of verifiability to that of the simple inner, logico-mathematical coherence. Its epistemological peculiarity favors the use of some paradigms of the idealist type, according to two procedural principles: a) the attempt to conceptualize the universe as a whole, and therefore to confront the philosophical problem of entirety; b) the ideal abstraction of a priori "bringing into being," by means of a specific cosmological model, the object under analysis (that coincides with the whole physical reality), moving therefore in a deductive manner from the mathematical model towards the observables of the model, if these exist. Maintaining the adopted terminology up to now, it must be said that this state of affairs gives place to paradigms both of a Platonizing and of a subjectivist kind. Intending it to be a part of physical sciences, although unique in its character, the scientific charter of cosmology is supposed to depend on its ability to maintain a certain relationship with the observations Page 11 of 20

12 (observational cosmology) and to formulate "models of the universe" subject to falsifiability, that is, to an experimental check. When this is lacking, it inevitably migrates from the field of physical sciences to that of mathematical logic. The realist question on the physical truth of the formulated models is then transformed into an idealist question on their logical coherence, then taking the shape of a if-then science (if some unverifiable assumptions are true, then the conclusions drawn from them are also true; cf. Heller, 1986). But, as regards what happens in the axiomatic theories of mathematics, there is a very important difference here! The object of abstraction is no longer just the numerable element, but is all of physical reality; and on all of physical reality, the various cosmological models demand their implications. In so doing, it is still the subject who places the object, but places it in its highest and greatest possible state. Implicit reference is made to this state of things when cosmology speaks of "parallel universes" or "plurality of worlds," without any causal connection between them, at least starting from a certain time towards the future; or, also, when cosmologists make hypotheses about the quantum conditions of the universe "before the Big Bang" or on its future state "after" the eventual Big Crunch in which its evolution could come to an end, if gravitational energy is sufficient to reverse its expansion. Cosmology attempts to reconstruct a past that lies beyond "horizons of observability" of increasing severity, as the "era of the decoupling of the matter from the radiation" and, even much before, the "Planck era." The popularization of science, most active in this field of research, often exalts the implicit recourse to such paradigms that, inevitably, are already operative in the methodology of cosmologists' daily work. Within cosmology there are also epistemological trends that try to remember the need for maintaining a link with observations (W. McCrea in the 1960s, and, more recently, G. Ellis, W. Stoeger, M. Heller). To neglect this aspect would be to put this discipline in the difficult situation of no longer being regarded, in the strictest sense, as a Galilean science, because it would be concerned with mathematical models, of absolutely equivalent value, that are not verifiable, and therefore non-decidible among themselves. Such a "return" of cosmology to the observational sphere, however, will always present physiological limits, owing to its specific formal purpose, that of trying to get closer to the universe in its globality. That gives rise to a sort of "uncertainty principle" at work also in cosmology. For example, there will always be various cosmological models compatible with the same set of observed data, keeping open the choice on which among these, within great families of parametric solutions, is the most correct one. Moreover, any model can never be exhaustive and in its attempt of giving a complete description of physical reality it will always run into "problems of incompleteness." If the framework adopted is that of the field equations of general relativity, such equations do not contain the definition of their own topology. In order to calculate the probability that a certain metric is the right one, and to thus provide a reason why the geometry of the universe is one and not another, we must ask, in advance, for the definition of the constants of nature and of the physical laws to be applied. On the contrary, if we want to evaluate why the properties of the universe its physical laws and its boundary conditions are precisely those observed and not others, we require the beforehand choice of an appropriate geometry for space-time. We are faced with the necessity of a decision which is, so to speak, "external" to the system being studied. Such a decision could certainly be favored by a link to the observations, thus offering a coupling of the realist kind, but it may not be so, due to the physiological limits of the model or the family of models it uses. In this latter case, the choice falls back on assumptions of the idealist kind, leaving the scientist, according to his or her own "world vision," to trust in criteria of a Platonizing nature, such as simplicity, symmetry or aesthetics, or of a subjectivist kind, such as that of "replacing the mind of God" or wanting to recognize its finalistic action at all costs. 4. Summarizing Vision. Idealism and Realism in the Method of Sciences: the Search for Objectivity. At the conclusion of our considerations regarding the influence of the various forms of idealism on scientific thought (cf. III and IV), in particular mathematics and mathematical sciences, it is worth stressing that the Page 12 of 20