Because Parmenides, in his well-known didactical poem, identified thought and being and since being in this poem is described in spatial terms, the problem of rationality from early Greek philosophy onwards was related to reflections on the nature of space. As an alternative to ‘continuous extension’ Ponti proposed the idea of ‘position’ (‘place’). The immediate effect of this conversation was that it prompted me to return to the sources of Western philosophy, namely to the early Greek philosophers.

The general habit of saying that rationalism is an absolutisation of (human) reason is not very illuminating, because the term ‘reason’ is not explained. What is reason? And what is rationality? Bernays introduced a meaningful consideration when he claimed that the crucial feature of rationality is found in the conceptual element (Bernays 1974:601). This remark opens up the possibility to account for the nature of concept formation, which, in turn will lead us on the path to a number of related concerns.

It will turn out that concepts are dependent upon distinguishing and identifying universal features. Universality, however, is nowhere encountered ‘on its own’, for it is always accompanied by what is individual. Yet, if concepts are constituted by universality, then it is evident that the individual side of entities – normally captured in the article ‘this’ – exceeds the grasp of concepts. The awareness of this chair (its individual side) unbreakably belongs to the being a chair (universal side) of this chair. Since Aristotle, the dominant legacy in Western thought holds that knowledge coincides with conceptual knowledge, which implies that what is individual cannot be known.

The mistaken restriction of knowledge to conceptual knowledge may be seen as a key characteristic of rationalism. Once this content is given to the term rationalism, the natural question of how knowledge is restricted to what is individual should be designated. It will be argued that this is just the other side of the rationalistic coin, because one can define irrationalism as an over-estimation of knowing what is individual and unique. The contrast between universality and what is individual implicitly explores key features of the aspects of number and space, for what is unique and individual highlights the quantitative intuition of being distinct. Within every multiplicity discrete individuals are discernible. Likewise, the awareness of universality rests on our intuition of space (‘place’ in the above-mentioned conversation between Ponti and myself), in the specified form of all places, everywhere. These distinctions will also appear to be significant for comprehending the elevation of human (conceptual) understanding to be the (formal) law-giver of nature (Immanuel Kant). The law conformity of entities is simply the correlate of the universality of laws for the existence of (natural and social) entities. It will therefore also be argued that order and orderliness (both universal traits) are not themselves rational, although they are intelligible. Historicism relativised universality with its focus on the unique and unrepeatable, thus simply advancing what we shall identify as an irrationalistic alternative to the dominant rationalism of the Enlightenment.

Against this background a few systematic considerations will be introduced, centred in the distinction between two kinds of knowledge: conceptual knowledge and concept-transcending knowledge. Proceeding from a non-reductionist ontology this alternative will attempt to rescue the soundness of these two kinds of knowledge and thus contribute to a more articulated understanding of both rationalism and irrationalism. The aim is thus to arrive at a non-distortive and non-reductionistic ontology.

We proceed now by first looking at some of the Greek roots of the problem of (ir)rationalism. This will provide us with background knowledge for the argument that space does play a key role in concept formation as well as in the definition of rationalism. Without an awareness of space, universality (at all places, wherever, everywhere) will not be understandable.

This explains why Greek (nature) philosophy did not acknowledge an empty space – if the body, which is supposed to be identical to its place, is not present, then it is plain that there simply is no place (equal to no body). What developed here was a metaphysics of spatial place, identified by Parmenides with thinking: ‘for thinking and being is the same’ (Diels & Kranz 1959–1960, B Fragment 3). In the second Fragment it is asserted that what is is and that non-being is not. The space metaphysics in the thought of Parmenides acquired a fuller content when being is described as unborn and immutable, for in the now it is together present as a whole, as one, and as something coherent (continuous) (Diels & Kranz 1959–1960, B Fragm. 8:3–8). The remarkable fact is that although being is characterised as a coherent whole, its unity, which is fully homogenous, cannot be divided (Diels & Kranz 1959–1960, B Fragm. 8:23). Parmenides explored this space metaphysics in his attack both on multiplicity and on movement.

Yet it was Zeno, a member of the school of Parmenides, who first realised that wholeness (being a totality) can be divided and in fact entails the feature of an infinite divisibility (see Diels & Kranz 1959–1960, B Fragm. 3). The two parts of this Fragment both proceed from the assumption that there is a multiplicity, but they reach opposite conclusions.

Aristotle explains discreteness in terms of things in succession such that ‘there is nothing of their own kind intermediate between them’. That ‘which is intermediate between points is always a line’ (Phys. 231 b 7–10 in Aristotle 2001:316). A line is therefore constituted by the pattern of point-line-point-line-point-line …. From this Aristotle concludes that a continuous whole is infinitely divisible: ‘Moreover, it is plain that everything continuous is divisible into divisibles that are infinitely divisible’ (Phys. 231 b 15–18 in Aristotle 2001:316).

In the first case there must be as many things as there are, in which case their number is limited, and in the second case there are always others in between such that the number of existing things is unlimited. Fränkel is justified in using the whole-parts relation to explain what is here at stake (Fränkel 1968:425ff): if one starts from the (multiple but limited number of) parts and then proceeds to the whole that is constituted by this limited number of parts, then they add up to the whole. But if the different parts are further divided, this process of division can proceed indefinitely, and then the multiplicity is unlimited.¹

Whilst the substance concept largely dominated ancient Greek and Medieval philosophy, the rise and development of the modern natural sciences shifted focus towards functional relationships between things. Naturally this was enhanced by the mathematical formulation of natural laws and law-conforming relations, which even prompted scholars to think that the universe itself has a rational structure.

Van Huyssteen refers to Davies who believes that the ‘true miracle of nature’ is found ‘in the ingenious and unswerving lawfulness of the cosmos’ (Van Huyssteen 1998:66). Van Huyssteen accepts this view by declaring: ‘What is astounding, however, is to what a great extent our world is truly rational, that is, in conformity with human reason (p. 68). Three pages further he elaborates on this view:

It is indeed fascinating to see, precisely through the fact that the rational nature of our universe is reflected in its basic mathematical structure, that Davies ultimately comes to the point where he has to acknowledge the limits of this reasonableness. (Van Huyssteen 1998:71)

The crucial point in this stance is given in the idea that our world is truly rational in the sense that it is in conformity with human reason. To be in conformity with human reason presupposes that human reason acquired the status of being a law for the world which is conforming to this law. This view asserts that human understanding actually operates as a law (-giver) for the world. Although Van Huyssteen formulated this conviction within the context of his postmodern orientation, it is actually derived from the rationalistic tradition since the Renaissance – the line of Descartes, Hobbes up to Kant. The nominalistic denial of universality outside the human mind caused Descartes to hold that number and all universals are modes of thought (Principles of Philosophy, Part I, LVII inDescartes 1965:187). Kant defended the radical view that human understanding is the law-giver of nature, whilst it was already within the thought of Hobbes that the new (modern) motive of logical creation surfaced. Let us explain this in more detail.

The thought experiment conducted by Galileo eventually contributed to Kant’s idea that human understanding is the formal law-giver of nature. In 1638 he imagined a body in motion on a path extended into infinity. According to him – and this argument constitutes his law of inertia – such a body will continue its movement if nothing hampers it. This prompted Immanuel Kant to contemplate the question: how is it possible that one can produce a thought experiment merely proceeding from the spontaneous subjectivity of human thought and then deduce from it a natural law and apply it to moving bodies? Does this experiment entail that human knowledge serves as the law-giver of nature and that our understanding contains structural features preceding our experience?

This is what traditionally was designated as what is a priori to experience, that is, what precedes experience. Kant did not hesitate to affirm the claim that there are a priori elements of human understanding making possible our knowledge of reality.

In post-Kantian freedom idealism Fichte, Schelling and Hegel elaborated the rationalistic element by ascribing to human thought the capacity to conceptually bring forth the content of the world independent of experience. According to Hegel the idea is the unity of concept and reality (Hegel 1949:239).⁴ This position once more evinces the perennial philosophical problem of thought and being. Cassirer remarks that it appears as if the circle of philosophical contemplation found its closure and reached its aim in identifying reality and reason: ‘Hegel believed that this is the point where his “Wissenschaft der Logik” is positioned’ (Cassirer 1957:10).

Although Greek philosophy already gave prominence to reason (nous) the term rationalism was not employed yet. Anaxagoras characterised the eternal and immaterial form origin of the world as the Nous, which has all knowledge and the greatest power. It is not determined by any limits and it is not mixed with germs of matter because it is self-sufficient (Diels & Kranz 1959–1960, B Fragment 6, 11, 12, 14). Later on, when Plato compared the good with the sun, it becomes clear that the ontic forms (eidè) owe their existence, being and knowability to the idea of the good. Viewed in coherence with the nature of the divine workman of Timaeus the idea of the good (agathon) has its seat in the divine demiurg (work master/craftsman). The active operation of the nous with its focus on ordering is portrayed by Jäger as focused on the relation of the nous to the agathon. This illustrates the influence of Anaxagoras (and Socrates, nous and dynamics): through the primordial design of the idea tou agathou the workman, as the divine nous, is the origin of the eidè, and therefore the form-giver of the world of the senses (see Jäger 1967:106ff).⁵

Thomas Aquinas held that the unity of ideas cannot be obtained by assuming just one idea in God. Rather, he holds, the multiplicity of ideas is constituted in such a way that the Divine Mind, as first form, observes the multiple possible ways according to which it can be copied (Questiones Disputate de Veritate, III, 2 in MacKenna 1956).

The first time the word ‘rationalist’ (rationaliste) was explicitly used was apparently in 1539 when it was already employed in opposition to experience (the empirical: empirique). A rationalist was seen as a person who assigned a greater value to pure thought than to experience. For some time, since the beginning of the 17th century, the term rationalism acquired a more specific theological meaning. An English source from the year 1646 mentions the rationalists as a new sect within the sphere of the Presbyterians and Independents whose adherents accepted their own reason as their point of departure (Böhling 1992:45).

At the time when the term rationalism was liberated from its theological use, it opened the way to describe the great philosophical systems of the 17th and 18th centuries. Simultaneously, atheists and those liberated in their thought introduced the term rationalism during the 19th century as a slogan against the superstition of traditional religions, whilst believing that they had reason and science on their side. Historians now also extrapolate the meaning of this term by generalising it mainly into the epoch of the Enlightenment. Rationalism combines the key elements of the Enlightenment, such as its criticism of understanding, its optimism and its faith in progress (Böhling 1992:46; see also Lecky 1910).

Perhaps this insight may help us also to understand why Habermas, in his desire to make an ongoing plea for the dignity of rationality as it is embedded in communicative action, does not really want to transcend this essential trait of modernity, although he is willing to let go of the optimistic utilitarian spirit that marked its emergence in the period of Enlightenment:

The concept of modernity no longer comes with a promise of happiness. But despite all the talk of postmodernity, there are no visible rational alternatives of this form of life. What else is left for us, then, but at least to search out practical improvements within this form of life? (Habermas 1994:107).

Earlier in the 20th century we find a remarkable trust in human rationality. After Heidegger moved beyond the rationalism of Husserl, the latter experienced it with a sense of hopelessness positioned by him within the broader context of a crisis of Europe and of the academic disciplines. According to him this crisis is rooted in a misguided rationalism (‘einem sich verirrenden Rationalismus’):

In order to comprehend what is wrong in the present crisis the concept Europe once again has to be viewed by means of the historical directedness towards the infinite aims of reason; it must be demonstrated how the European world was borne from reason-ideas, that is, out of the spirit of philosophy. The crisis will then clearly emerge as the apparent failure of rationalism. The basis of this failure of a rational culture, however, … is not inherent to rationalism, since it is only found in its externalization, in its decay into naturalism and objectivism. The crisis of European existence provides only two options: the decline of Europe in the alienation from its own rational existential meaning, the decay into an animosity towards the spiritual and a lapse into barbarism, or the rebirth of European existence through the spirit of philosophy, particularly through a heroism of reason that will consistently triumph over naturalism. (Husserl 1954:347–348)

Cysarz points out that under the influence of Xenocrates an early goal of Aristotle was to accept an individual substrate, a ‘próte usía’ which could be neither defined nor mathematically proven. It is precisely that which every child but no computer achieves: distinguish a rabbit from a dog. For this reason, so he concludes, a pure science of what is individual is impossible (Cysarz 1983:12–13).

Medieval Scholasticism continued this view by assigning universality to the human mind or intellect and what is individual to what could be sensed. What is individual is considered to be inexpressible (omne individuum est ineffabile). A well-known South African philosopher captures this legacy in a work on logic and epistemology and highlights the ‘individual delimitation’ (De Vleeschauwer 1952:213). Regarding what is individual, he holds that our intellectual capacities must fail because ‘knowledge of what is individual is simply impossible’ (according to De Vleeschauwer, philosophy had clarity about this issue since its inception, De Vleeschauwer 1952:213).

Within the development of modern philosophy one may see the 18th century, the era of Enlightenment, as a period in which conceptual rationalism dominated the scene. It echoes the new spirit of rational criticism, exemplified in what Kant said in the Foreword to the first edition (1781) of his Critique of Pure Reason:

Our age is, in every sense of the word, the age of criticism and everything must submit to it. Religion, on the strength of its sanctity, and law on the strength of its majesty, try to withdraw themselves from it; but by doing so they arouse just suspicions, and cannot claim that sincere respect which reason pays to those only who have been able to stand its free and open examination. (Kant 1961:21)

The rise of historicism during the transition from the 18th to the 19th century made possible a new appreciation of what is unique, individual and contingent as an attempt to escape from the grip of conceptual knowledge and its entailed universality. In the Third Part of the Fourth Volume of his work on the problem of knowledge within philosophy and the modern sciences, Ernst Cassirer dedicates the first chapter to the emergence of historicism and the second one to the ideas of B.G. Niebuhr, Leopold von Ranke and Wilhelm von Humboldt (see Cassirer 1957:225ff, 233ff). Cysarz characterises the 19th century as the era of individuality (Cysarz 1983:16). He could have added the issue of continuous change, with reference to Darwin‘s theory of evolution.

During the 19th century, the tension between the general nature of concepts and what is uniquely historical could not be reconciled. Habermas mentions that, analogous to Peirce, Dilthey also struggled with the relationship between universality and what is individual (see Habermas 1970:200–201). He explains that hermeneutical understanding must grasp an inexpressible individual meaning in categories that are unavoidably general (Habermas 1970:201).⁶

Yet, as Cysarz correctly remarks, every (professional) practice must proceed in an individual manner. What is healed in medical praxis is not illness, but the individual sick person, even though this cannot happen outside the matrix of general norms (standards) (Cysarz 1983:13). This remark highlights an important fact, namely that whatever is universal is always accompanied by what is individual and vice versa. An individual sick person shows, in its being sick, that it shares in the universal feature of sickness. A succinct way to capture this situation is to say that this sick person (individual side) has an illness (universal side). Clearly, sickness, even in its abnormality, displays universal abnormal traits. Disorderliness depends like a parasite on what is normal.

The position assumed by Leibniz anticipated the views of Kant: just consider the following statement of Leibniz (1965):

Now reflection is nothing but an attention to what is in us, and the senses do not give us what we already bring with us. This being so, can we deny that there is a great deal that is innate in our mind, since we are innate, so to speak, to ourselves, and since there is in ourselves being, unity, substance, duration, change, activity, perception, pleasure, and a thousand other objects of our intellectual ideas? And since these objects are immediate to our understanding and are always present, ... why be surprised that we say that these ideas, and everything which depends on them, are innate in us?’ (p. 146, cf. p. 173)

On the verge of anticipating Kant’s criticism of Hume’s empiricism, Leibniz, more than 30 years before the first appearance of Hume’s A treatise of human nature (1739), wrote as follows in his New Essays:

Now all the examples which confirm a general truth, whatever their number, do not suffice to establish the universal necessity of that same truth, for it does not follow that what has happened will always happen in the same way. (quoted from Stich 1975:45, cf. Kant 1787:5)

Paul Bernays, the co-worker of the famous German mathematician David Hilbert, points out that rationality cannot be understood apart from concepts: the ‘proper characteristic of rationality’ is ‘to be found in the conceptual element’ (Bernays 1974:601). This view supports what we saw above, namely that in general rationality is crucially connected to conceptual knowledge and to universality. Universality, in turn, cannot be understood apart from its connection to what is individual.

Note that we rather speak of ‘what is individual’ than of ‘individuality’ because the latter is still a universal feature. In being an individual every individual, in a universal way, evinces its uniqueness. We noted that in our everyday experience we fully understand the difference between a chair (a universal feature) and this chair (its individual side).

Within the tradition of reformational philosophy, the emphasis on making sound distinctions created an equally important sensitivity with regard to reductionism in all its negative variants. Both Dooyeweerd and Vollenhoven articulated their views in terms of well-thought-out systematic distinctions and they both attached specific meanings to terms capturing those philosophical stances in which a distorted account is given of universally accessible states of affairs.

Interestingly, Vollenhoven explicitly mentions that rationalists from the 18th century, such as J.G. Walch in his introduction to philosophy of 1727, maintain ‘that what he and those who thought like him – the rationalists – had to say was built on the state of affairs’ (Vollenhoven 2005:5).

He briefly discusses the slogan of Descartes, cogito ergo sum (I think therefore I am), by pointing out that some are of the ‘opinion that this “therefore” denotes a connection of identity’. But according to him this is incorrect, ‘for Descartes does not identify being and thinking’ since besides thinking he ‘also presupposes extension’; therefore, for Descartes ‘thinking is only a component of being’ (Vollenhoven 2005:10).

Yet Vollenhoven (2005) on the same page points out that:

Descartes meant this in a rationalistic way, that is, in the sense that thinking is the essence of being; an opinion that we, of course, reject, as much as we reject the division of being indicated here. (p. 10)

This does not entail that Vollenhoven think it is ‘rationalistic’ ‘to subsume thinking and knowing under being, for it makes good sense to speak of a non-thinking and a non-knowing being. There are clearly many things – for example, minerals, plants, and animals – that are but that do not know’. Vollenhoven therefore concludes negatively ‘that knowing is not the same as being’ and positively ‘that knowing is a component of being’ (Vollenhoven 2005:10).⁷

In general Dooyeweerd refers to the strict correlation of the law side (cosmonomic side) and factual side of reality in order to explain how he understands both rationalism and irrationalism. In the first Volume of his Magnum Opus, A New Critique of Theoretical Thought (NC), he states that in a rationalistic type of thinking ‘the subject-side of reality within the special modal aspects is reduced to the nomos-side’ (Dooyeweerd 1997:98). In the context of his philosophy of time he rejects both rationalistic and irrationalistic conceptions because the former ‘absolutizes the cosmonomic side and the latter the factual-subjective side of time’ (Dooyeweerd 1997:28; see also Dooyeweerd 1940:196).

However, Dooyeweerd did not properly distinguish between law and law-conformity (lawfulness). He frequently exchanged these expressions. Earlier we remarked that universal conditions ought to be distinguished from the universal way in which individual entities show that they conform to these conditions or laws. By identifying law and law conformity Dooyeweerd strips factual reality of its universal side. For this reason he often explicitly speaks of the individual factual side.

Although concretely existing things and processes function within all aspects of reality, they at the same time transcend the theoretical grasp of anyone of these modal aspects in which such entities and processes function. We have theoretical access to them through the gateway of the modal aspects which therefore also serve as modes of explanation for our investigations.

Concept formation is made possible by the universality of specific (logically identifiable and distinguishable) features. The universality here involved could be either that of a universal order for, holding for the type of entities subject to it, or it can refer to the universal orderliness of things, reflecting the universal way in which entities show that they are subjected to the applicable order for their existence. Since conceptual knowledge is tied up with these two forms of universality (order for and orderliness of), the individual side of entities simply transcends the possibilities of conceptual knowledge. When we acknowledge that what is individual exceeds our conceptual grasp, it does not imply that we do not have knowledge of what is individual. But if this knowledge cannot be conceptual, it must be concept transcending. This kind of knowledge may also be designated as idea knowledge.

Proper conceptual knowledge of a triangle or a human being includes those universal features found in all triangles and all human beings. Since this kind of knowledge does not preclude concept-transcending knowledge (idea knowledge), a balanced (and non-reductionist) understanding of reality should acknowledge both.

On the basis of this characterisation and distinction we can now introduce a more advanced definition of rationalism and irrationalism:

1. Rationalism deifies (absolutises) conceptual knowledge.

2. Irrationalism deifies (absolutises) concept-transcending knowledge.

An additional perspective on idea knowledge is obtained when the various ways in which terms derived from the different modal aspects of reality are employed. The most basic option is to consider modal (aspectual) terms in their reference to phenomena appearing within the domain of any specific aspect. For example, no one will doubt that our awareness of the ‘one and the many’ presupposes the meaning of number. Counting a number of things usually follows a sequential pattern that exhibits an order of succession, albeit in a cardinal (how many: one, two three, etc.) or ordinal sense (how many-th: first, second, third, etc.) (see Maddy 1997:17). But when Plato discusses the hypothesis that the One is without multiplicity (subsequently further explored by Plotinus), the numerical term ‘one’ points beyond the arithmetical aspect towards the origin of the universe. In this case the numerical one is stretched beyond the confines of the quantitative aspect of reality, revealing that it is actually employed in a concept-transcending sense. In a similar way one may reflect on the mere conceptual use of spatial terms and ways in which spatial terms are employed in order to refer to realities exceeding the boundaries of the spatial aspect.

We have noted earlier that although Greek philosophy initially wrestled with an idea of wholeness not allowing division, the ripened conception of Aristotle saw that anything continuous could be divided into divisible parts (see Aristotle, Phys. 234 a 8 inAristotle 2001:322). His general and encompassing description reads: ‘Everything continuous is divisible into divisibles that are infinitely divisible’ (Aristotle, Phys. 231 b 15–18 in Aristotle 2001:317).

If all the divided parts are taken together they constitute a genuine whole or totality. A conceptual use of the terms whole or totality will refer to spatial figures, such as lines or two-dimensional figures. Suppose now that we use these spatial terms in order to refer to the existence of something in all it aspects (of which the spatial is but one amongst many others). Then we may speak of that something in its totality. The referent of this term encompasses more than the spatial aspect alone and therefore represents a concept-transcending use of a modal spatial term.

Although the relationship between what is universal and what is individual may suggest that an over-estimation of either could be captured in the opposition between universalism and individualism,⁸ it is preferable to reserve the latter opposition as an indication of alternative basic denominators for the diversity of ontic aspects and entities – alongside ismic orientations such as physicalism, vitalism, psychologism, logicism, economism, aestheticism, and so on.

In other words, it seems as though it is more nuanced to advance our proposal, namely to hold that rationalism leaves no room for true concept-transcending knowledge whilst irrationalism leaves no room for genuine conceptual knowledge. In terms of this perspective an acknowledgement of the horizon of human experience and the dimensions of (ontic) modal aspects and type laws is meaningful. It at once avoids elevating human understanding to the a law-giver of the world, which ultimately is a full-blown rationalistic conviction.

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3. Cassirer explains this view of Kant with reference to the following statement of the latter: ‘das wir “von den Dingen nur das a priori erkennen, was wir selbst in ihr legen”’ [concerning things we can only know a priori that which we ourselves have embedded in them] (Cassirer 1957:239).

4. Hegel phrases it also as follows: ‘Idea is the unity of concept and reality, the realized concept as such’ (Hegel 1931:155).

5. In his negative theological approach Plotinus feared that the word demiurg may introduce multiplicity into the absolute One (first hypostasis). As a result he rather applies the term demiurg as designation of the Nous (second hypostasis). See Theiler (1966:127) and also Plotinus (En. 1I, 3, 18; II, 9, 6; V, 9, 3; MacKenna 1956).

8. Vollenhoven uses the terms universalism and individualism to indicate an over-estimation of individuality and universality, respectively.