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DESCARTES

(1596 — 1650)

 

RATIONALISM (DUALISTIC)

Born in La Haye, France René Descartes, the son of a judge, was educated by the Jesuits at the famous college of La Flèche and at the University of Poitiers, where he studied law. From 1617-23 he was a mercenary in various armies. He lived in Paris from 1625 until 1628 and then in the Netherlands. He liked warmth and working at night. In the winter of 1649 he was invited by Queen Christina of Sweden to act as her tutor, but it would seem he was unable to cope with having to get up every morning at five and succumbed to a fatal fever.

 

METHODOLOGY

[1] Faced with a revival of interest in Greek Scepticism in the sixteenth century after the re-publication of the works of Sextus Empiricus, which tended to undermine metaphysics and religion, and with what he regarded as the inadequacies of scholastic Aristotelianism, Descartes resolved to search for a new and firm foundation for truth through the exercise of pure reason rather than relying on faith or authority. He distinguished two basic capacities or operations of the mind: intuition and deduction. By intuition he means roughly an intellectual, that is, non-sensuous vision of the object of our understanding, which is clear and distinct [a] so that we can be in no doubt about it. (That we are aware of having a pain is clear: that it can be located, say, in our leg, makes the idea distinct). Deduction consists in the logical derivation of conclusions from the first principles given to us in intuition [a]. Descartes claims further that with practice we can grasp the whole process of premiss to conclusion by intuition alone. If these operations are to be employed correctly, a 'method' is needed; and in his Discourse on Method he sets out four Rules (they are broken up into five and a summary in the Rules for the Direction of the Mind):

(1) To accept nothing as true which is not clear and distinct and is open to doubt. He is thus trying to 'out doubt' the sceptics in looking for something which is certain. (This is called Descartes' methodological or hyperbolic doubt [b]. )

(2) To break up complex difficulties into their simplest parts. He calls this 'the method of resolution' or analysis (and 'the order of knowing' or discovery).

(3) To start with intuitions of the simplest and most understandable objects, and to deduce, trace back step by step to knowledge of all the others. This is the 'method of composition' or synthesis ('the order of demonstration' [c] ).

(4) To ensure that his survey is so comprehensive that nothing has been overlooked.

Clearly Descartes' model is mathematics, though in mathematics no justification is given for its first principles. Indeed, underlying these rules is his view that despite the apparent differences between the various sciences (physics as opposed to ethics, for example) there is but one scientific method applicable to them all, and that there is one universal science — grounded in fundamental rational metaphysical principles and not sensory experience. He expressly rejects 'animistic' and 'naturalistic' approaches [d].

 

KNOWLEDGE

[2] Descartes' method of analysis can be seen at work particularly in the Meditations [1 and 2]. Much of what he had believed to be true when young, he says, has been proved to be false. Sense-experience is often unreliable. He therefore supposes that nothing in our experience is immune from error. His present seemingly real experiences of the world, such as his sitting by the fire, may be but a dream. Even the apparently certain propositions of mathematics, for example, 2 + 2 = 4, may be false. He has a firm belief in an all-powerful God: but perhaps this too is an illusion. Maybe there is an 'evil demon' who causes him to be deceived in everything he believes. Can nothing then be known? What is his answer to the sceptics? There is one certain and indubitable truth, Descartes says, namely, that in the very act of doubting he is affirming his existence as at least one who doubts; for to doubt is to think, and he must exist to think: "I think, therefore I am" (cogito, ergo sum) [Discourse 4]; or, as he expresses it later in the Meditations [2], "I am, 1 exist, is necessarily true, every time I express it or conceive of it in my mind". He thus claims that he knows he exists whenever he thinks and, moreover, that he knows himself to be a thing that thinks, a thinking substance, (and for Descartes this includes imagining, perceiving, feeling, willing — even though he has 'thought away' his body). This knowledge is characterized by clarity and distinctness [a].

What is now to be said about his sense-experience which points to the existence of an external world? [Meditations 2 and 3.]. The ideas (or impressions) of external material things as causes, he says, are 'adventitious'. These ideas, which are produced by means of our our sense organs, are unclear and confused but supposedly correspond to real objects. He also has 'factitious' ideas (such as that of a unicorn), which do not correspond to anything real and which he has himself invented; and innate ideas. By 'innate' Descartes means those ideas we have which are not derived from experience; they come from within the intellect or understanding. (In a wider sense all ideas are innate for Descartes, in that we possess the capacity to experience, say, colour or smell.) Indeed it is possible that all his ideas belong to but one of these categories. How can he tell? What is their origin? Adventitious ideas cannot be said to give him genuine knowledge unless he can find some guarantee that they are veridical. Descartes argues that such a guarantee can be provided by a Perfect Being, a benevolent and non-deceiving God; and that he has knowledge that such a Being exists in that he claims to possess an innate idea of Him, which he could not himself have made. Given the existence of God, Descartes is in a position to reinstate the external world [b] he had rejected in the course of his methodic doubt, and to accept that the buildings, trees, and other people he perceives actually exist.

Let us suppose then that there is a veracious God. How, according to Descartes, do we get our knowledge of the external world? Indeed, what do we know about it? Suppose we observe a piece of wax. [Meditation 2.] It is hard, sweet-smelling, and so on. But when heated it loses these qualities: its smell disappears, it melts, its shape changes. Nevertheless, Descartes says that by an intuition of the mind we judge that it is the same extended wax which has undergone these various changes. We have an innate, clear and distinct idea of matter as extension (a primary quality). Thus we do not acquire knowledge of material bodies through either our imagination or the senses. Rather, our sense experience serves only to draw our attention to and make explicit this innate concept. It is through the intellect that we acquire genuine knowledge of the essences of things. Moreover, secondary qualities such as colour, smell, and the like, do not really exist in corporeal things. They are, as it were, 'powers' possessed by objects, and our ideas are not therefore 'likenesses' or representations [c].

Descartes also offers an account of how we perceive and estimate distance [Dioptrics]. He argues that the distance of an object from us can be determined by a consideration of the angles of the triangle with its base as the line between our two eyes and its apex as the point of covergence with the perceived object. The smaller the angle between side and base the more distant is the object. For Descartes this is a matter of mathematical necessity; for he appeals to a geometry which he considers to be innate [d].

What he has to say about the actual nature of the mind and body is best considered as part of his metaphysics.

 

METAPHYSICS

[3] Substance for Descartes is that in which attributes inhere, as properties exist in a subject; and which can exist in or by itself alone [Arguments demonstrating the existence of God, Defn V]. Strictly, therefore, there is only one substance — the Perfect Being or God, who is infinite, self-sufficient, omnipotent, and independent, the first cause. However, he also distinguishes two finite dependent substances, mind/ soul and body, that is, matter, each of which has its own defining attribute [a]. His first proof for God's existence is set out in Meditations 3. Obviously he cannot begin with sense-experience of the external world. Instead he appeals to the clear and distinct idea of God he has in his mind. Unfortunately he uses somewhat obscure scholastic terminology. Substances, he says, have more 'formal' reality than accidents. A red thing has to exist for there to be redness. God, if He exists, must have more formal reality than finite substances. But Descartes also talks of 'objective' reality. An idea of a complex machine 'represents' objectively a real machine which, if it exists, must contain as much objective reality as the idea of it. Now, the idea of an infinite Being (God) could not have been produced by a finite being (Descartes). Indeed, to recognise himself as finite requires a prior concept of infinite being. The idea of an infinite being contains more objective reality than any idea of a finite being (because as infinite it must contain more perfections or 'complexity': indeed it has the objective property of absolute perfection). So it must have been put into his mind by a being who not only is as objectively real (or more so) as the idea but also contains as much as or more formal reality than he, Descartes, possesses. Put more simply, what Descartes means is that the idea of an infinite being must be caused by a being which has more reality (a) as an existent being, (b) in respect of its properties [b]. A being who is absolute perfection therefore must exist. Descartes further argues that his own existence can be accounted for ultimately only by reference to God. If he had caused himself, he would also have caused the idea he has of perfection; he would have to be the perfect being. The cause of his being must contain more reality than he himself does as effect. To avoid an infinite regress he must therefore suppose that the being who sustains him in existence must be perfect and infinite, namely, God.

Descartes offers a second, 'ontological' proof [Meditations 5]. The essence of a triangle is to have three angles which add up to two right angles. But although we have the idea of a triangle, there may not be any triangles in existence. The idea of God is of a being who possesses all perfections. But according to Descartes existence is a perfection; so God must exist, otherwise He would lack an attribute and could not be God. Thus Descartes is saying that we have to accept that God exists as soon as we grasp what constitutes His essence or nature [c].

What then of the two finite created and dependent substances? Descartes is a committed dualist. Mind and body are intrinsically and fundamentally different in their nature, and different kinds of explanation are required to account for their behaviour [See Meditations 2 and 6]. Mind or soul is a spiritual substance. It is without shape and does not occupy space; it has no extension. Its essence is thought, that is, it is characterized by 'states' comprising understanding, perceiving, feeling, willing. Individual souls are created by God, and their activity is explicable by reference to ends and thus in terms of final causes — though we can have no knowledge of God's purposes [d]. Body, by contrast, does not think, is material and extended, and is in motion or at rest. The behaviour of bodies may be explained mechanically in terms of efficient causes and the laws of nature — which are ultimately reducible to mathematics. The total quantity of motion in matter never changes, and originates from God as the first cause [e]. Descartes asserts also that extension cannot be distinguished from the space or 'internal place' a body occupies. There is therefore no empty space or vacuum, because a distance between one piece of matter and another would itself constitute extension. It seems then that all individual corporeal things are continuous with each other but manifest greater or lesser amounts of motion in their parts. There can therefore be no atoms except in our thinking about an extended object. And the world's extension must be indefinite. As for time, this is explained by Descartes as a 'mode of thinking' by which the duration of things can be measured [f]. Time is discontinuous because the parts of duration do not depend on each other and do not coexist. God also conserves the universe in being through what is in effect a perpetual re-creation, giving material things and souls continuity of existence, which they would otherwise lack because of the discontinuity of time and motion.

Now, given Descartes' dualist thesis, how can he account for the interaction of mind and body? Indeed, how can two different substances, whose essences are respectively non-extended spirituality and extended corporeality, and whose behaviour is to be explained in terms of respectively final and efficient causation, interact at all? The soul, he says, is lodged in the body — but not just as a pilot in a ship is, but "very closely united to, and so intermingled with it that I seem to form a complete whole with it" [Meditations. 6]. In a letter to Princess Elizabeth of Bohemia [28 June 1643] he even refers to this union of body and soul as "a kind of third substance, not known clearly but rather lived through, put into practice". But in general his solution, such as it is, is to retain the real distinction between mind and body but to allow for the effecting of an interaction in the brain, where the soul influences the 'animal spirits' (material particles) of the pineal gland to modify the direction of bodily movements. Conversely bodily movements ('actions') might excite 'passions' in the soul, that is, perceptions and emotions caused by the body (as contrasted with actions of the soul itself, which are clear and distinct perceptions of its own feelings) [Passions of the Soul I, passim]. Animal spirits are also involved in memory recall in that they seek physical traces in the brain. It follows that while Descartes believes the soul's immortality to be certain (though not demonstrable) he has to accept that memories are lost after death [g].

The real distinction between mind and body also allows Descartes to preserve human freedom. While physics deals with extension and motion, the behaviour of which is explained in terms of efficient causality and is predictable, freedom is an aspect of the will. Our very capacity to doubt as thinking substances presupposes freedom to choose [Meditations 6] [h]. However, he does not seem to have appreciated the difficulties for the concept of freedom implicit in his dualism. Rather he is concerned more to reconcile human free will with God's preordination, and in the event he provides inconsistent solutions — oscillating between some version of predestination and the view that although God foresees how a man will choose he does not himself determine that choice. Similarly God, who is not a deceiver, cannot be held responsible for human error — which Descartes attributes to misuse of the will [i]. The will, he says, is "much more wide-ranging and extensive than the understanding" and he does not confine it to the same limits, extending to things he does not understand [Meditations 4]. So if we are to use the will properly and strengthen it, if we are to avoid assenting to a doubtful proposition, or resist undesirable passions, we must have recourse to natural knowledge assisted by Divine grace.

 

CRITICAL SUMMARY

In so far as they made a clean break with mediaeval scholasticism either Bacon or Hobbes might seem to have a better claim than Descartes to be regarded as the 'Father of Modern Philosophy'. However, the description is probably justified by Descartes' methodological scepticism and his quest for an indisputable foundation on which to reconstruct the edifice of knowledge — and in the light of which his own limited use of scholastic terminology and arguments can be appreciated. Nevertheless, for all its greatness and originality there are many difficulties with his philosophy.

(1) Perhaps the most obvious criticism that can be made is that both the method and his postulation of the 'cogito' as his basic principle fail to 'deliver the goods', as it were. Many commentators have argued that he makes a number of assumptions which are inconsistent with his scepticism, for example, that no clear distinction can be made between the waking and dreaming states, and that because some of our perceptions may be illusory we must doubt all perceptions. But even if these kinds of difficulties can be dealt with, and universal doubt accepted as a working hypothesis, the 'cogito' itself, and the use Descartes makes of it, is open to serious objections. (a) The establishment of the 'cogito' as the sole indubitable assertion presupposes articulation in terms of a language and therefore, it is argued, a 'public' frame of reference in which such a language can meaningfully operate; and this would seem to be inconsistent with the privacy of the contents of the thinking from which Descartes starts. (b) 'I think, therefore I am' is not a necessary proposition; I might not have existed. And while it is in some sense absurd to doubt it, the 'cogito' does not justify Descartes' claim that the self is a thinking substance. (If the self is equated with the sequence of ideas, he must cease to exist when unconscious. If it is that in which the ideas inhere, we can have no knowledge of it.) It follows of course that a 'foundationalist' theory which seeks to ground our knowledge claims in the 'private' contents of the mind is unlikely to be successful (as against accounts which look for criteria for the justification of statements).

(2) Descartes' criterion of truth, 'clarity and distinctness', seems to offer only a subjective certainty; and Descartes himself requires a veracious God to underpin any inferences he draws from it. He has been accused of circularity in allegedly using this criterion to prove God's existence. This objection is probably not sustainable: but he does seem to need God to support the reliability of memory and therefore a chain of reasoning until the chain can be intuited as a whole and its necessity revealed.

(3) From a wider standpoint it can be argued (and Aquinas, the empiricists, and Kant all concurred in this view) that 'pure' rationalism as such cannot provide indubitable truths about the world. Descartes' proofs for the existence of God in particular can be rejected on this ground. There are also internal difficulties with the arguments themselves; and they are not helped by the somewhat obscure scholastic terminology he employs ('formal' and 'objective reality', 'adequacy', for example). As to the first (causal) argument, unless 'existence' is taken to be a perfect attribute of God, it can establish (at the very most if at all) that the idea of God is caused only by some finite being which possesses more formal and objective reality than the idea; it does not prove the existence of an infinite God. The supposition that existence is a perfection, which is also central to the second (ontological) argument, is open to standard objections. This is a serious matter for Descartes; for if God's existence cannot be proved, then his whole philosophy collapses back into the privacy of the thinking self.

(4) Perhaps the most common criticism of Descartes relates to his dualism and to his attempt to deal with the problem of interaction between the two different kinds of substance: non-extended spiritual mind and extended matter. It is difficult to accept (in the light of modern neurobiology and cognitive psychology) his solution which is couched in terms of 'animal spirits' and the pineal gland. However, it should be noted that a recent commentator, D. M. Clarke, has argued cogently that Descartes should not be regarded as a substance dualist at all — a position that defines mind and body as having no common properties (thereby ruling out any possibility of an explanation of interaction). The concept of 'as such' substance is in fact empty; we know only its properties. Descartes should therefore be described more accurately as a property dualist.

(5) Given that God does exist and that the 'essential nature' of external bodies can be known through the reason, Descartes' account of error — that it occurs when the will goes beyond what is given in the understanding — may have some justification: but many philosophers would argue that error occurs as a result of misdirection of judgement; judgement should be grounded in the senses, a view that cuts at the heart of Descartes' rationalist premisses.

 

READING

Descartes: Discours de la Méthode (1637) (Discourse on Method); Meditationes de Prima Philosophia (1641) (Meditations on the First Philosophy); Principia Philosophiae (1644) (Principles of Philosophy). There are Penguin editions of the Discourse and Meditations; and there is a most useful collection of these and other writings in the abridged edition of J. Cottingham: Descartes: Selected Writings. Other standard comprehensive editions are those edited by Haldane and Ross, and by Anscombe and Geach.

Studies:

Introductory

T. Sorrell, Descartes.

More advanced

D. M. Clarke, Descartes's Theory of Mind.

A. Kenny, Descartes: A Study of his Philosophy.

B. Williams, Descartes: The Project of Pure Enquiry.

M. Wilson, Descartes.

Collections of essays

J. Cottingham (ed.), The Cambridge Companion to Descartes

W. Doney (ed.), Descartes: A Collection of Critical Essays

M. Hooker (ed.), Descartes: Critical and Interpretive Essays

 

 

CONNECTIONS

Descartes

 

Note: In the context of his 'hyperbolic' doubt Descartes claimed to have rejected all he had been taught on 'authority' and claimed to start a new through the exercise of pure reason. However, the influence of scholastic Aristotelianism — particularly its terminology — was not entirely eliminated. (Much of his knowledge of earlier philosophy may have been acquired from the text-books of Suarez; and he certainly studied Aquinas's Summa Theologiae.) The influence of Galileo's mathematical physics should also be noted (though he had apparently not read the Italian's text-books). But for the most part Descartes is here regarded as an original and independent thinker.

 

[1a] Use of pure reason not faith/ authority; two operations of mind: intuition and deduction

   Augustine

   Ockham

   Bruno

   Bacon (Francis)

Spinoza

Locke

Vico

Diderot

Condillac

Kant

Merleau-Ponty

[1i]

[3c]

[1a]

[2e]

[1a 4c]

[2j]

[1b]

[2a]

[2a]

[2d 4a]

[3a]

 

[1b; cf. 2a] 'Hyperbolic' doubt to undermine scepticism; all sense-experience unreliable (so possible to reject existence of external world)

   Sextus

   Augustine

Hobbes

Spinoza

Locke

Hume

Condillac

Kant

Peirce

Husserl

Schlick

Wittgenstein

Sartre

Merleau-Ponty

Ricoeur

[2a-c]

[1a-c]

[6a]

[4b]

[2i j]

[1b]

[3a]

[2d 4a]

[2b]

[2c 7i]

[1b]

[2i]

[1c 4a]

[1c 2a 3c f]

[5a]

 

[1c] Methods of 'resolution' (analysis) and 'composition' (synthesis)

   Aristotle

   Bacon (Francis)

   Hobbes

   Locke

Malebranche

Diderot

Condillac

[6b 20b]

[2e]

[2b c 6b]

[CSa]

[3c]

[2a]

[2a]

 

[1d; cf. 3e] Universal science grounded in rational metaphysical principles (anti-naturalistic and anti-animistic ); role of mathematics

   Aristotle

   Bacon (Francis)

   Hobbes

Spinoza

Locke

Malebranche

Diderot

Condillac

Kant

Herder

Comte

Ortega y Gasset

[7c]

[2e]

[2b c]

[1a]

[2n CSa]

[3b]

[2a]

[2a]

[2d 4a]

[1a]

[2b]

[2b]

 

[2a 1a; also 3a] One certain truth: the cogito; criteria of clarity and distinctness; introspective knowledge of self as thinking substance (without regard to body)

   Sextus

   Augustine

Hobbes

Spinoza

Locke

Malebranche

Leibniz

Vico

Berkeley

Hume

Kant

Schelling

Brentano

James

Nietzsche

Husserl

Dewey

   Whitehead

Scheler

Schlick

Wittgenstein

Ryle

Sartre

Merleau-Ponty

Ayer

Hampshire

Ricoeur

Strawson

[2a]

[1d-f]

[6a]

[1a 4c]

[2c 2h k 2o]

[3c h]

[2d]

[1a]

[2f]

[2c d]

[2d 4a]

[2b 3b]

[1a 3b]

[2a b]

[2a]

[5a 6b 7d i]

[2a]

[4e]

[4a]

[1b]

[2d]

[3a 4a c]

[1c]

[1b 3a f]

[2b 3d]

[1b]

[1a b 4c 5a]

[2c]

 

[2b] Ideas: adventitious (from sense-experience — and are confused), factual, innate; real knowledge of the essences of things (given God's guarantee)

   Aristotle

   Aquinas

   Duns Scotus

Spinoza

Locke

Malebranche

Leibniz

Vico

Berkeley

Hume

Kant

Herder

Husserl

Santayana

Popper

[16b]

[6f]

[5e]

[4b]

[2a 2m 2o]

[3d]

[6b c]

[1d]

[2b e]

[1c 2a c]

[2d 4a]

[1a]

[7a]

[3b]

[2a]

 

[2c] Innate clear & distinct idea of extension; primary and secondary qualities — latter not real in things; knowledge only through intellect (guaranteed by God)

   Democritus

   Aquinas

   Hobbes

Spinoza

Locke

Malebranche

Berkeley

Hume

Kant

Ortega y Gasset

[2b]

[1c 6c d]

[3a]

[4a 4b]

[2a 2b c 2i]

[3d]

[2c 4a]

[2c]

[2d 3c 4a]

[2b]

 

[2d] Estimation of distance through appeal to innate geometry Berkeley [2a]

 

[3a; also 3d e] Substance — exists by itself and (as a subject) in which attributes inhere; God as the one independent substance and first cause; mind and body dependent substances

   Aristotle

   Aquinas

   Hobbes

Spinoza

Locke

Malebranche

Leibniz

Hume

Holbach

Kant

Spencer

Scheler

Heidegger

[4b 7b]

[1c]

[6c]

[2b]

[2d 2e]

[1a]

[2a 5a]

[1e]

[1d]

[3d]

[4b]

[4a]

[1a]

 

[3b] Proof of God's existence (first cause of mind and matter) from clear and distinct idea — formal and objective reality

   Chrysippus

   Aquinas

   Suarez

   Bruno

   Locke

Malebranche

Vico

Hume

Kant

[3h]

[3e 3g]

[1e 1g]

[1b]

[2l]

[1c d 1f]

[1c]

[5a]

[5d]

 

[3c] Ontological proof — existence as a perfection

   Anselm

   Bonaventura

   Aquinas

Spinoza

Locke

Malebranche

Leibniz

Vico

Hume

Kant

Mill

[1e]

[1c]

[3d]

[2c]

[2l]

[1e]

[5b]

[1c]

[5a]

[5d]

[5d]

 

[3d; cf. 2a 3a; also 3g] Soul/ mind created by God; spiritual thinking substance; explanation by final causes; no knowledge of God's purposes

   Aristotle

   Aquinas

   Bacon (Francis)

Spinoza

Hobbes

Locke

Malebranche

Leibniz

Hume

Holbach

Kant

Brentano

Merleau-Ponty

Ayer

[6a sec. 9 15b]

[5a 5e]

[1a-c]

[1b 2g]

[4a]

[2g]

[1a 1d]

[2e 4a]

[1h]

[1c]

[3b 5a]

[3b]

[4a]

[3d]

 

[3e; also 3g] Body/ matter: extended substance — explanation in terms of material/ efficient causes; total quantity of matter unchanging — caused by God

   Bacon (Francis)

Hobbes

Spinoza

Locke

Malebranche

Leibniz

Hume

Diderot

Holbach

Kant

Merleau-Ponty

[1c 2e]

[2a b 4a 6a b]

[1b 2g]

[2c 2g]

[1a 1d]

[2e 3a 4a]

[1h]

[1b]

[1a]

[3d]

[4a]

 

[3f] Space is real and absolute, equivalent to extension — not empty; time as mode of thinking

Leibniz

Berkeley

Kant

[3b]

[4a]

[2b]

 

[3g; cf. 3d e] Mind-body dualism; mind not form or animating principle; interaction in brain (not quite like 'pilot in ship'); soul immortal but no memories; bodily movement and passions in the soul

   Alexander of Hales

   Aquinas

Hobbes

Spinoza

Locke

Malebranche

Leibniz

   Condillac

Kant

Herder

Schopenhauer

Brentano

James

Whitehead

Scheler

Ryle

Merleau-Ponty

Searle

Kripke

[2a]

[5a d e]

[5a]

[2g]

[2e]

[1b c]

[2e 2f 4b]

[4b]

[5b]

[1a]

[1d 3g]

[3b]

[2b]

[4h]

[4a]

[3a]

[1b 2a]

[2a]

[2a]

 

[3h] Freedom presupposed by capacity for doubt; belongs to will

   Hobbes

   Spinoza

   Husserl

[5c]

[3d]

[5c]

 

[3i; cf. 2a] Error as 'sin' — misuse of will (assent to what is unclear/ confused)

   Augustine

   Aquinas

   Duns Scotus

Spinoza

Malebranche

 

[5b 7b]

[9a]

[5e]

[4d]

[3a]