On Reading Being and Time:

An Explication and Commentary by Roderick Munday



The Interpretation of Dasein in Terms of Temporality
and the Explication of Time as the Transcendental
Horizon of the Question of Being



The Worldhood of the World



In this document: "Explication and Commentary 8"


III. The Worldhood of the World

  19. The Definition of the 'World' as res extensa

  20. Foundations of the Ontological Definition of the World

  21. Hermeneutical Discussion of the Cartesian Ontology of the World


This is an ongoing project, more content will appear here over the next few months.


For the contents of other sections see the main index

There is also an online glossary of terms referred to in this document.

Your comments are welcome. Please make them at my blog site Synthetic Knowledge




March 2007


(page 123)


THE WORLDHOOD OF THE WORLD (Sections 19, 20 & 21)



¶ 19. The Definition of the 'World' as res extensa

Descartes distinguishes the 'ego cogito' from the 'res corporea' (the thinking 'I' from the unthinking, corporeal 'thing'). This distinction is the origin of his famous mind/brain dualism (see Descartes' Meditations VI). Heidegger claims also that this dualism is also ontologically determinate for the distinction between 'Nature' and 'spirit'. But the problem with this dualism is that the poles of opposition are never properly defined.


Descartes defines the essence of such disparate entities as 'mind', 'brain', 'nature' and 'spirit' in terms of one thing - substance. Descartes says of substance that it alone constitutes the essentially being of all things. However Heidegger points out that Descartes actually seems to use the concept in two quite distinct ways. Sometimes it designates the Being of an entity, while on other occasions it designates the entity itself. That substance is used in two distinct ways is not accidental, Heidegger claims that Descartes borrows this understanding from the ancient Greek conception of Being . But he does not elaborate upon this yet.

What Heidegger is most interested in finding out at this point is what exactly Descartes mean by substance.


The Being of corporeal things

First of all let us omit consideration of mind and spirit for the time being and try to determine first the nature of the res corporea (the corporal thing) ontologically. In order to do this, we much explain what the substance of this 'thing' actually is, we must, as it were, examine the substantiality of substance. This prompts two important questions:

Two Questions

1/ What is it exactly that makes up this substance that Descartes considers to be the authentic Being of the corporeal thing?

2/ How is it possible to grasp the substantiality of a substance in any way except as an idea?

Answering the first question

To answer the first question we might say that substances are known by their qualities. For example, if I am asked "how a know something is a rock?" I might answer: "Because it is hard, cold, heavy and made of stone." Descartes, on the other hand, argues that these qualities are not the way we can genuinely discover what the essential being of a thing is, because qualities themselves can deceive us. There is a famous passage in the Meditationswhere Descartes talks about the mutable qualities of a piece of wax:

It is quite fresh, having been but recently taken from the beehive; it has not yet lost the sweetness of the honey it contained; it still retains somewhat of the odour of the flowers from which it was gathered; its colour, figure, size, are apparent (to the sight); it is hard, cold, easily handled; and sounds when struck upon with the finger. In finality, all that contributes to make a body as distinctly known as possible, is found in the one before us. But, while I am speaking, let it be placed near the fire--what remained of the taste exhales, the smell evaporates, the colour changes, its figure is destroyed, its size increases, it becomes liquid, it grows hot, it can hardly be handled, and, although struck upon, it emits no sound. Does the same wax still remain after this change? It must be admitted that it does remain; no one doubts it, or judges otherwise. What, then, was it I knew with so much distinctness in the piece of wax? Assuredly, it could be nothing of all that I observed by means of the senses, since all the things that fell under taste, smell, sight, touch, and hearing are changed, and yet the same wax remains (Descartes, 1996 part II, §11)

Thus Descartes argues that the essential Being of wax must be found in something other than in its qualities


In fact it is found in something Descartes calls extension.

To extended substance we refer magnitude, or extension in length, breadth, and depth, figure, motion, situation, divisibility of parts themselves (Descartes 2003, Part I, §XLVIII)

According to Descartes, extension is the only attribute that makes up the real Being of any corporeal substance. "For everything else that can be ascribed to a corporeal thing presupposes extension"(Descartes 2003, LIII). For example in the case of wax, we must presume that wax has extension, in other words we must presuppose that it has specific dimensions in space and it must possess these dimensions for it to be considered a thing. For if it has no extension then it could not occupy and specific dimensions in space and would therefore be a ‘no thing’- inaccessible to perception. This is not to say that the extension of wax might not appear to be mutable, because from Descartes description it is clear that this is the case - when it melts " its size increases" Descartes 2003, Part I, §XLVIII). However, no matter how mutable wax may appear, it must nevertheless possess some extension for it to exist at all. Therefore Descartes reasons that extension is the core attribute of Being.

Motion as extension

As we have seen, extension is conceived of in terms of space. But surely reality is actual because it exerts a force on us. Therefore it can be objected that things are real because of the force they exert of other things and not because of extension. Descartes answers no, it is a mistake to conceive of motion as being the result of one mass striking another, for motion is grasped only "if we think of nothing except the position of objects in space at any one time. Therefore we do not ask about the force by which objects are set in motion" (Descartes 2003, Part I, §LXV). In order for motion to be experienceable in its Being, it must be conceived in terms of the Being of a thing in itself, that is to say that motion must be conceived as mere change of location.

Motion... in the ordinary sense of the term, is nothing more than the action by which a body passes from one place to another (Descartes 2003, part II, § XXIV).

So nothing like 'force' counts for anything in Cartesian philosophy. Matter may have such definite characteristics as hardness ' weight, and colour; but these are merely sensory qualities and the can all be taken away from the thing and yet it still remains what it is because of extension.

An additional proof that motion has nothing to do with force can be inferred if we consider Descartes reasons for rejecting the quality of 'hardness' as constitutive of the authentic being of things. This discussion is found in part II of his Principles of Philosophy (1644), which Heidegger quotes from:

For with respect to hardness, we know nothing of it by sense farther than that the parts of hard bodies resist the motion of our hands on coming into contact with them; but if every time our hands moved towards any part, all the bodies in that place receded as quickly as our hands approached, we should never feel hardness; and yet we have no reason to believe that bodies which might thus recede would on this account lose that which makes them bodies. The nature of body does not, therefore, consist in hardness. In the same way, it may be shown that weight, colour, and all the other qualities of this sort, which are perceived in corporeal matter, may be taken from it, itself meanwhile remaining entire: it thus follows that the nature of body depends on none of these (Descartes 2003, Part II, §IV).


As Descartes has demonstrated, all the qualities an object has can be taken away from it and yet some essential aspect remains which is extension. And this reasoning can also be flipped around to state that extension in turn does not depends upon any qualities for its existence.

According to Descartes, the answer to question 1/ "What is it that makes up the authentic being of the corporeal thing?" is substance whose only real attribute is extension.

Is substance and idea?

Now let us consider question 2/. For if all sensory stimuli are rejected by Descartes as ways for us to gain access to the essential authentic Being of substance how then is substance to be characterised as anything other than an idea?



¶ 20. Foundations of the Ontological Definition of the 'World'

How is it possible to grasp the substantiality of a substance in any way except as an idea? For Descartes the answer to this question is simple. No. Of course substance is an idea, but in order to understand why something as insubstantial as an idea does not undermine the reality of substance we have to understand just what kind of an idea substance is.

What has to be born in mind here is that Descartes' primary aim in writing his Meditations On The First Philosophy was to furnish a rational proof of the existence of God, not to furnish one of the existence of substance.

I have always been of the opinion that the two questions respecting God and the Soul were the chief of those that ought to be determined by help of philosophy... I have, therefore, thought that it would not be unbecoming in me to inquire how and by what way, without going out of ourselves, God may be more easily and certainly known than the things of the world (Descartes 1996, Dedication, I).

Descartes reasons if it can be proved that corporeal things, whose existence no one claims to doubt, are determined by intellectual rather than sensory properties, then it follows that the existence of God, which is not accessible to immediate perception and therefore also potentially subject to doubt, can be placed on a firmer rational footing. If the existence of everything can be predicated on the same idea—substance as extension—then the existence of God is also assured as the guarantor of this idea.

Now, as modern readers of perhaps a more secular persuasion, we may consider Descartes’ solution to be somewhat unsatisfactory. But let us put theological questions to one side for the moment, because it is important to examine Descartes’ claim, philosophically, within the frame of its own terms of reference. This will reveal if Descartes reasoning is entirely consistent in terms of its own axioms. For if we can prove that Descartes’ reasoning is not consistent, then his argument fails without the need to consider other arguments viz a viz the existence or non-existence of a Supreme Being.

This is the approach that Heidegger takes. He asks, if God exists, can His existence guarantee the reality of the idea of substance? Heidegger argues that the guarantee becomes problematic, precisely because of the symmetry Descartes' is setting up between Being of God and the Being of things in the real word. If everything in the universe consists essentially of substance and extension, this prompts awkward questions like, is the Creator made of the same substance as creation?

Here we begin to untangle quite a thorny theological argument. How is Descartes idea of extension, meant to apply to both the Creator and created?

Descartes in his pronouncements seems to be arguing that substantiality is also the idea of Being to which the ontological characterisation of the res extensa ultimately harks back - i.e. that is to say, the idea of God. On this point Descartes says:

Indeed we perceive that no other things exist without the help of God's concurrence... By substance we can understand nothing else than an entity which is in such a way that it needs no other entity in order to be (Descartes 2003, Part I, §LI).

In other words a substance is something that cannot exists without the help of God. But God is a different kind of substance who needs nothing else in order to create and sustain His Being. This nothing of God is more accurately describes as the "ens perfectissimum." . . . or perfect Being. For only God can satisfy this idea of substance in the authentic sense. Thus Descartes postulates his proof of the existence of God.

If Descartes claim is accepted as true, it seems to presume a radical conception of God, made of the same kind of substance as things in the real world. However, Descartes is quick to refute this interpretation of his theory, he points out that his notion 'God', should be understood in the purely ontological sense as the ens Perfectissimum (perfect being). Again Heidegger does not raise any objections to this, for he intends to examine Descartes ideas on their own terms. He asks instead what does Descartes mean ontologically speaking when he claim that the ens Perfectissimum needs nothing else to constitute its substantiality?

Descartes considers God to be the perfect substance because He is the creator and therefore creates Himself as well as everything else in the universe. All other entities apart from God need to be "produced" and moreover rely on God for their sustained existence. The whole of creation is dependent upon the Creator, while the Creator is dependent on nothing but Himself. Therefore, in the Cartesian sense, Being needs to be understood within a horizon which ranges from God is the ens Perfectissimum everything that is not God - the ens creatum.

The Being of the Creator and created cannot be the same thing

This is where Heidegger argues Descartes’ reasoning becomes problematic, for while he states that the idea of God guarantees the ides of substance he also states that the kind of Being which belongs to the ens creatum is 'infinitely' different from that which belongs to ens Perfectissimum:

the term substance does not apply to God and the creatures univocally... that is, no signification of this word can be distinctly understood which is common to God and them (Descartes 2003, Part I, §LI).

Descartes disclaimer is essentially a theological one not a philosophical one, but philosophically speaking, when he talks about the Being of God and the being of created things being different, Descartes is using "Being" in so wide a sense that its meaning embraces an 'infinite' difference, i.e. a difference so wide and undefined that it is in effect meaningless.

The human being

Now we add to this the special category of being which applies to the human being, what Descartes calls the res cogitans or thinking thing. All entities need to be produced and sustained (by the grace of God the Creator of course); but within the realm of created entities there is a special class of things


These are human beings:

When I think that a stone is a substance, or a thing capable of existing of itself, and that I am likewise a substance, although I conceive that I am a thinking and non-extended thing, and that the stone, on the contrary, is extended and unconscious, there being thus the greatest diversity between the two concepts, yet these two ideas seem to have this in common that they both represent substances [Descartes 1996, part III, §21

Human beings are special because there are in fact two classes of substance found in them: res extensa (extended substance - common to everything else), and res cogitans (thinking substance - which is unique to humans and also the portal through which they perceive the idea of the existence of God the creator)

Descartes argues that any type of Being becomes ontologically definable in principle if we can clarify the meaning of Being which is 'common' to the three kinds of substances, that is to say:

    1. (ens Perfectissimum infinite substance or God),
    2. (ens creatum ) finite substance of corporeal things res extensa
    3. (ens creatum ) finite substance of human minds res cogitans.

Being is not univocal

However how can this commonality be worked out when Descartes states at the same time that - "there can be no signification of this word which can be distinctly understood as being common to God and [to mortal things]… "the term substance does not apply to God and the creatures univocally, to adopt a term familiar in the schools" (Descartes 2003, Part I, §LI).

The term "schools" here refers to the schoolmen. The schoolmen were a group of medieval theological philosophers, including Thomas Aquinas (1224 - 1274) and Duns Scotus (1266 - 1308). Actually they were never an actual group of philosophers, more a convenient category to name individuals working in monasteries which were geographically and temporally isolated from one another. Despite modern prejudices against medievalism as being synonymous with ‘the Dark Ages’, and thus not a time for great achievement in scholarship, C.S. Peirce claims the schoolmen were able scholars, whose pursuit and grasp of logic is perhaps unmatched in the whole of human history [ref. Peirce: CP 8.11).

Heidegger says of Descartes that when he says the relationship between God and creation is not univocal he touches upon a problem with which medieval ontology often busied itself — that is the signification of "Being" and how it can or cannot signify both God and created things. For instance in the simple assertions "God is" and "the world is", we assert Being. But is this the same Being? Surely not. And for the reason that Descartes has also outlined - The word "is", cannot apply to both Creator and created univocally, because there is an infinite difference of Being between them.

Heidegger claims that if the signification of "is" were univocal, then that which is "created" could be just as easily viewed as if it were 'uncreated', or vice versa that which was "uncreated" would be reduced to the status of something "created". In other words the reality of God and substance would be just and idea. But in the view of the schoolmen 'Being' did not function as just an idea for it was not a mere name, but rather it was understood in the positive sense as a signification 'by analogy' i.e. God and creation were compared by isolating and highlighting similar patterns at work in essentially different systems. Thus, the schoolmen always acknowledged that the Being of the creator was beyond human comprehension, however humankind could nevertheless conceive of it, by analogy as an idea of a human being perfected beyond any mortal measure.

Now Heidegger points out that there was no unity in the approach of the schoolmen themselves. In the middle ages many and various kinds of analogy were established, by different Schools and each of them had a different way of taking the signification-function of "Being". However one thread that did unifite them was the philosophy of Aristotle, whose philosophy they had all to a greater of lesser extent been influenced by. In Aristotelian philosophy the problem of immortal versus mortal substance was the Creator/creation dilemma in a protean form. This incidentally is why Heidegger says that Descartes dual use of substance not accidental, because it is derived from a tradition the which began with the ancient Greeks [ref. ¶19, page 123]

In working out the problem of Being, Heidegger claims that Descartes is always far behind the Schoolmen; indeed he actually evades the question of the impossibility of universal Being altogether when he says that. "No signification of this name[substance] which would be common to God and his creation can be distinctly understood" (Descartes 2003, Part I, §LI).

This evasion is tantamount to his failing to discuss the meaning of Being, upon which the very notions of substance and extension are grounded. For Descartes it is enough that God guarantees of the reality substance. But this is Descartes the theologian talking, not Descartes the philosopher. Compare the two following quotations: one from the dedication of his Meditations has Descartes wearing his theologians cloak, in the other, from Part I of the same work, he is wearing the cloak of a philosopher:

Although it is quite true that the existence of God is to be believed since it is taught in the sacred Scriptures, and that the sacred Scriptures are to be believed because they come from God, nevertheless, this cannot be submitted to infidels, because they would consider it a circular argument (Descartes 1996, Dedication).

The knowledge we have of God renders it certain that he can effect all that of which we have a distinct idea: wherefore, since we have now, for example, the idea of an extended and corporeal substance, though we as yet do not know with certainty whether any such thing is really existent, nevertheless, merely because we have the idea of it, we may be assured that such may exist; and, if it really exists, that every part which we can determine by thought must be really distinct from the other parts of the same substance (Descartes 2003, part I §LX).

These quotations demonstrate that Descartes the philosopher never quite freed himself of the circular arguments Descartes the theologian vowed to eschew.

A summary of Heidegger’s critique of Descartes

The problem with Descartes’ claim that the idea of God guarantees the idea of substance is that there are actually two distinctly different ideas being expressed here. As Descartes states, for the idea of substance to be real, God must also be real. But if there is an "infinite difference" between the idea of God and the idea of creation, then it is hard to see how one can guarantee the other. Therefore, philosophically speaking, If "no signification that can be distinctly understood," which is common to both Creator and created, how can the idea of God guarantee the idea of substance in any way other than as a leap of faith?

Being as a thing

Descartes not only evades the question of how his substance can be anything more than an idea, but he also emphasises explicitly that the existence of substance is self evident. That is to say in effect that a substance is substantiality in and for itself, and is therefore inaccessible from the outset. Yet substance cannot first be discovered merely by the fact that that it is a thing that exists, (128) for the existence of the thing itself does not affect us If the qualification of existence itself becomes thingness it is not surprising that 'Being' itself is not considered to be existent.


This is why Kant said "Being is not a Real predicate" (Kant 1993, p410). He was merely repeating Descartes' principle. Thus the possibility of a pure problematic of Being gets renounced in principle time and time again both by Descartes and by those philosophers who have followed him.

But as Heidegger has shown, Descartes invented a duplicitous way for arriving at those definite characteristics of substance he claims are so constitutive of the being of entities. Because 'Being' is not in fact accessible as an entity through extension. And even Descartes concedes this point, by admitting that Being in the first instance expressed through its attributes:

Substance cannot be first discovered merely from its being a thing which exists independently, for existence by itself is not observed by us. We easily, however, discover substance itself from any attribute of it, by this common notion, that of nothing there are no attributes, properties, or qualities: for, from perceiving that some attribute is present, we infer that some existing thing or substance to which it may be attributed is also of necessity present (Descartes 2003, I, LII).

If qualities grant us initial access to the idea of substance as extension. What Descartes is saying is that we discover the idea of essential reality of substance through those very things he has been strenuously denying any reality to.

The Cartesian Paradox

Therein lies the paradox! Being is not expressed through its qualities but rather through those satisfying in the purest manner that meaning of "Being" and "substantiality", and yet these are things which have to be tacitly presupposed through an object’s qualities.

Descartes says that to all finite substance we must assign the primary aspect of extension. "Indeed we understand the Being of ourselves as partly res extensa, (extended substances - bodies) and partly res cogitans (thinking substances - minds)". However substance may be separable from things intellectually, but it certainly is not separable in reality. For if this were possible, we would first have to disregard the Being who thinks or is extended — in other words the Being of Dasein. For Descartes’ ontology is totally ‘object orientated,’ in that he ignores the role human beings play in actualising the world


The ontological grounds for Descartes defining the 'world' as res extensa have been made plain in this and the previous section. Therein lies the idea of substantiality, and the problem of Being, because in Cartesian philosophy, not only does the meaning of Being remain unclarified, but gets passed off as something incapable of clarification

Descartes way of defining substance is through some substantial entity. This is in fact why the term "substance" is used in two ways. Substance signifies substantiality; and gets understood in terms of a characteristic of being some thing which is itself an entity. There is an infinite kind of regress here. Any ontology which defines itself in the self-evident terms as a characteristic of that which it already is, cannot be said to stand on a stable footing. This is possibly why the infinite regress calls for the existence of an immutable substance in order to protect it from its own absurdity.

Heidegger argues the reason for this unstableness is because something ontical has been made to underlie the ontological. This means that the expression "substance" functions sometimes with a signification which is ontological, sometimes with one which is ontical, but' mostly with one which is hazily ontico-ontological.

Behind this seemingly slight difference of signification there lies a massive but hidden failure to master the problem of Being. Heidegger suggests that in order to treat this adequately, we must now track down and identify all of Descartes equivocations in the correct ontological way. Heidegger says we do not do this merely by busying ourselves with verbal significations'; but by "venturing forward into the most primordial problematic of the 'things themselves."

It puzzles Heidegger that this mere idea of substance has persisted for so long in Western philosophical thought. He reasons that since Descartes methods at arriving at the Being of substance have been refuted before there must be some other reason for its persistence. And of course there are other reasons, which will also be discussed in the next section.



¶21. Hermeneutical Discussion of the Cartesian Ontology of the 'World'

Before we discuss other reasons why Descartes’ theory of Being has persisted for so long we must consider two critical questions:

1/ Does the Cartesian ontology of the 'world' seek the phenomenon of the world at all,

2/ And, if the answer to question 1/ is "No", does the ontology of the 'world' at least define some entity within-the-world fully enough so that the worldly character of this entity can be made visible in it?

Heidegger forestalls any examination of these issues by stating that the answer to both questions is an emphatic "No". The reason why it is such a forceful "no", is because these are essentially Cartesian questions, that is to say predicated on an understanding of Being that is at bottom ontical not ontological. Descartes’ conception of Being is so foreign to Heidegger’s that it can not simply be laid out over his ontological understanding of the world, because the two philosophies have no point of contact. Now Heidegger sets about outlining the reasons why this is.

Heidegger ontological critique of Descartes

According to Heidegger, the entity which Descartes is trying to grasp ontologically and in principle, with his "extensio", is discoverable first of all by going through an entity within-the-world in terms of what we might call ‘proximally ready-to-hand-Nature.’ That is to say, by talking about Being of the world in terms of objects and nature, Descartes is trying to define that which has already been tacitly presupposed — namely that the world’s Being is therefore something to do with the nature and objects.

Heidegger in his own analysis of these issues has already pointed out, the reasons why it is not possible to gain access to the phenomenon of the world through the concepts of nature and objects. Nature is already within the world and is therefore determined by the world not determinative of it [ref. ¶14, page92]. And objects or things present-at-hand are only realised through Dasein’s involvement with the world. Heidegger concludes by saying any ontological characterisation of an entity within-the-world using Descartes methods may lead us further into obscurity

However even if we forestall our objections to his methods, the problem still remains of the radical separation of God, the "I", and the 'world' in Descartes’ ontology which prevents the understanding of the Being of the world from getting formulated and further advanced.

Nevertheless, Heidegger reasons it might be possible that Descartes has somehow hit upon a correct characterisation of the phenomenon of the world, though his methods are flawed. Otherwise how is one to explain the fundamental role his ideas have played in the traditional of Western ontology as well as the extraordinary tenacity of his ideas?

Heidegger does not think the above statement is true but, in order to discount Descartes completely, he says we must do two things:

1/ The first we have done already. This is to demonstrate explicitly how Descartes' conception of the world is ontologically defective from within his own terms of reference.

2/ The second is to examine the reason Descartes interpretation of the world and the foundations on which it is based have led him to pass over both the phenomenon of the world and also the Being of those entities within-the-world which are proximally ready-to-hand.

This second point Heidegger will demonstrate by applying Descartes method to his own problematic of Being-in-the-world. Here he will focus particularly in how Descartes has attempted to grasp and interpret worldhood.

What kind of Being gives us access to the Cartesian Being-in-the-world?

In our exposition of the problem of worldhood [ref. ¶14], we suggested the importance of obtaining proper access to the phenomenon of the world. So in criticising Descartes’ point of departure, we must ask ourselves which kind of Being he advocates as giving us genuine access to the world? The answer is Descartes considers the authentic being of things to be found the idea of substance as extension, this it is an intellectual being that grants us access to these ideas. An intellectual being is also the one we derive knowledge of mathematics and physics from. And in this sense it is opposed to the sensory kind of Being who grants us knowledge of entities within the world in terms of their qualities.

The traditional hierarchy of ideas over the senses

Mathematical knowledge is regarded by Descartes as an assured way of knowing that the Being of entities has been securely grasped. This is because Mathematic knowledge itself is regarded as being a more precise and immutable kind of knowledge than sensory knowledge. Therefore, according to the logic that Descartes adheres to, it follows that if anything about Being can be expressed mathematically it is going to be a more authentic kind Being. The continues the traditional hierarchy of thought that ranked eternal immutable ideas above perishable contingent sensory information.

This tradition was established in ancient Greece, notably with Pythagoras, Plato and Aristotle.

For instance, in the twelfth book of his Metaphysics, Aristotle identifies three types of substances:

1. sensible and perishable

2. sensible and eternal

3. non-sensible and eternal (immovable).

The first kind of substances designate plants, animals and everything in the world. The second kind designates the heavenly bodies, which move, but do so eternally. The third kind of substance is not perceivable at all by the senses but Aristotle reasons that it must exist because: "substances are primarily existing things, and if they are all destructible, all things are destructible" (Aristotle §12 part 6).

The mathematics of Being

But in addition to the existence of this tradition there is another more important reason why Descartes ontology has been so successful. This is because it allows us to grasp the world in terms of a definite mathematical equations. Substance is extended as a point on a graph can be extended, consequently it becomes possible to map the world mathematically through geometry. Which is something Descartes himself excelled at.

Analytical geometry is essentially a mathematical tool for practically every physical scientist, Descartes invented it. The essence of his discovery is the one-to-one correspondence between a plane curve and an equation involving coordinates in the plane. The equation holds at every point of the curve and expresses its every property. A well defined curve implies the existence of a well defined equation, and, equally, as well defined equation implies the existence of a well defined curve (Massa 1996, 274).


The Cartesian coordinate system evolved from Descartes’ geometry of curves:

Fig 1 — Cartesian coordinate system

We start by drawing x and y coordinates vertical and horizontal lines that intersect at right angles. Their point of intersection is 0. The lines are marked off at regular intervals using a scale of ascending numbers. Numbers on the vertical axis lying above the horizontal are positive, those below are negative. Points on the horizontal to the right of the vertical are positive, those to the left are negative. Points in any of the four sectors established by the lines can now be located exactly by specifying their values on the x and y axes. Trajectories can be represented by equations: points in any four quadrants can be smoothly connected to form a line (Massa 1996, 277 - 278).

This coordinate system can also represent three dimensions by adding a z axis (Fig 2).

(fig 2)

Substance as extension is diagrammed in fig 2 as the extension of along x, y, and z axes of point P to form a square. As Benjamin Waters points out, Science on this basis can turn a 3-dimensional world into a bunch of numbers and abstract relations (Walters 2005).


Why has Cartesian ontology persisted?

The answer to the answer to the question posed at the end of section 20. Why has Cartesian ontology persisted is because.

A/ It is rooted in a powerful tradition that promotes ideas above sensory perception and,

B/ It permits a mathematically description of the world according to a precise coordinate system invented by Descartes himself.


The mathematisation of Being

With all this talk about mathematics it is worth remembering that Descartes prescribes for the world a 'real' Being. This was not a Being based on just an idea of Being. Descartes was very clear on that point. He claimed to have discovered the source of the real Being and to have demonstrated its existence. But it is important to understand that Descartes Being is in fact just an idea. It is an idea which is merely equated with an actual presence-at-hand, rather than one which describes a philosophically proven connection. It is also important to understand that, while Descartes’ ontology of the world is not primarily determined by mathematics, mathematical knowledge, it is nevertheless exceptionally well suited to descibing Being conceived of in terms of extention, substance and the constantlt present-at-hand presupposed by them. Descartes reality is a simplified, abstracted reality that is idally suited to being expressed in mathematical equations. Descartes argument consequently becomes even more slippery, because he explicitly switches over from an ontology allegedly proving the reality of substance, to an ontology based on numbers and their transcendental foundations.

Sensation and intellect

One of the consequences of this switching is that the problem of how to get appropriate access to entities within-the-world is never raised. For one could argue that if one adopts the mathematical view of being, the solutions to the equations are their own kind of proof. And if the territory can be mapped so successfully using equations, what need is there to seek confirmation from the actual territory?

According to Cartesian ontology, you do not need to grasp the essential Being-in-the-world in and for itself, because it can be described mathematically. Although in this case the ontological basis for your equations has already been decided in advance. This is the whole problem that Heidegger is trying to highlight in Being and Time. For it is not that the problem of Being has been solved, nor that it is insolvable, but that the problem of Being has never been properly raised.


The blame for this must lie first and foremost at the door of the ancient Greeks, specifically with their notion of 'beholding.' Beholding can be defined as all the ways that humans Beings grasp the world. Thus beholding takes everything in a very large spectrum between the first fleeting apprehension of sensory precepts to their intellectual synthesis in the form of ideas. However the Greeks judged the intellectual end of the spectrum to be more important that the sensory end because they considered ideas to be a fully developed form of beholding than the perceiving of sensations. Thus sense and sensation were relegated to a lower order of knowledge whilst the intellect and ideas were promoted to a higher one.

In this way, the kind of beholding that Descartes advocates can be regarded as well within tradition instigated by the ancient Greeks and therefore as a genuine kind of beholding. However Descartes knows very well that entities do not proximally show themselves in their real Being as ideas. For instance his meditation on wax, quoted earlier, makes it clear that what is 'proximally' given is the qualities of the wax, not the idea of wax as extension. But in adhering closely to the Greek tradition of beholding Descartes says that:

It will be sufficient to remark that the perceptions of the senses are merely to be referred to this intimate union of the human body and mind, and that they usually make us aware of what, in external objects, may be useful or adverse to this union, but do not present to us these objects as they are in themselves (Descartes 2003, Part II, §III).

Thus the senses are not considered to be of any importance ontologically, because they " merely serve to announce the ways in which 'external' Things within-the-world are useful or harmful for human creatures encumbered with bodies"... And for that reason they cannot "teach us what kinds of things exist in themselves" (Descartes 2003, Part II, §III). This means, according to Descartes, that if we relied on the senses alone, we would be able to perceive the things as hard or heavy or coloured, but we would not be able to perceive, in general, the nature of the substance that possessed these qualities


However, when Descartes applies his principles in practice, it becomes clear that he does not adhere to his own rules. For example, if we subject the interpretation of hardness and resistance to a critical analysis, it is plain that Descartes is unable to separate qualities and substance completely, except by a sort of philosophical slight of hand.

A further analysis of hardness

Unlike his analysis of movement, where force is exorcised completely, Descartes does equates hardness with resistance of a sort. But this resistance is not understood in the phenomenal sense, as something which is experienced in itself. For all Descartes definition of resistance amounts to is that an object does not undergo any change of location. Descartes explains resistance in the following way: imagine there are two objects, let’s call them ‘object 1’ and ‘object 2’. Descartes says that if object 1 resists, it means that it remains in a definite location relative to object 2. Object 2 is moving, but with a velocity that permits it to 'catch up' with object 1. Heidegger notes that in such an analysis, the nature of hardness cannot actually be determined. But rather, in order for it to make sense of it, one must have decided what hardness is in advance. Thus the nature hardness is actually presupposed before it is analysed. For only then can it be defined in a way that denies the kind of Being which is normally thought to belongs to hardness. Thus, sensory perception is obliterated even before the analysis commences. Which means that any possibility of grasping the genuine Being of entities is also obliterated.

The continually present-at-hand

Descartes takes the kind of Being which belongs to the perception of a given ‘something’, and translates it into the only kind Being he knows, the res extensa, or what Heidegger now calls, ‘the continually present-at-hand’. The continually present at hand is what is being exemplified when Descartes talks about hardness. His perception of resistance as ‘Object 1’ reacting upon ‘Object 2’, becomes a definite way of conceiving of what Heidegger calls the Being-present-at-hand-side-by-side of entities rather than just their Being in an authentic sense. Object 1 and object 2 have already been characterised as a mode of extension, thus they have to be related to one another.

Now of course there is some truth to the contention that hardness and resistance are related to the being alongside of entities. This is a phenomenon that Heidegger has already spoken about [ref. ¶12, page 81]. While it is true that relative positionality must play some kind of role in the apprehension of the present-at-hand, because our knowledge of touch is itself grounded on a knowledge of the closeness of things. This does not mean that the ontological understanding of touching and the hardness therefore consists entirely in apprehending the different velocities of two corporeal things in respect to one another. Heidegger says that Descartes misses a crucial point here, which is that qualities such as hardness and resistance do not show themselves at all unless there is a Being like Dasein--or at least some other living entity present who can perceive them.

Object-orientated Being

This brings up another problem with Descartes' ontology. The fact that it is dominated by an idea of Being which has been gathered from the realm of entities themselves, rather than from the from realm of Dasein (who is after all the Being who actually does the perceiving and the thinking). Heidegger argues omitting Dasein from his analysis is how Descartes arrives at his characterisation of Being as the continuous present-at-hand. This has two major implications. It not only provides him with a motive for identifying all things within-the-world with the phenomena of worldhood in general. But it also allows him to omit consideration of Dasein and its ways of behaving.


Why Being in the world cannot be reached by Cartesian ontology

However, by omitting Dasein, the way is blocked to seeing the founded character of all the sensory and intellectual awareness Descartes speaks of. This also prevents him from reaching any genuine understanding of the phenomenon of the world. Therefore we arrive at the reason why Being-in-the-world' lies quite outside of Descartes’ ontology, because he treats the Being of 'Dasein' in exactly the same way as he treats the Being of a ‘thing’ as res extensa, or substance.

Salvaging Descartes

Heidegger wants to make it clear, despite giving the impression that he rejects Descarte’s ontology completely. He does not. The Cartesian ontology must hae something to do with the phenomenon of the world, for if it were otherwise, and Descartes did not know the phenomenon of the world, he would not even be able to identify the world with certain entities within-the-world in terms of the Being which they possess.

Deconstructing the orthodoxy of common sense

Heidegger notes that if there is ever any controversy over principles, one must do two things.

1/ be conscious of those precepts which can be grasped doxographically, that is to say according to the particular philosophical tradition one happen to be situated in.

2/ And once these precepts have been securely grasped, one should attempt to go beyond them.

Doxography [literally the study of common belief] can be defined as an uncovering of the arguments of past philosophers which now constitute our common sense understanding of the world, and therefore also our taken-for-granted beliefs. Even if we consider ourselves to be phenomenologists, according to the conditions laid down in Heidegger's doctrine [ref. ¶ 7, page 59], and we hold that the world is better described by Heidegger’s theory of Being than Descartes’ theory of Being, because it answers many of the questions left open by the latter. We must nevertheless concede that the place from, where we derive our ontological orientation, is also the position that Descartes was responsible for establishing. Therefore we owe him a debt, because it is from the objective tendency of his problematic that we take our departure. In the light of this, our opposition to Descartes is ironically part of the legacy of his success. As Descartes’ himself owes a dept of gratitude to the Schoolmen and the ancient Greeks, for he likewise carved his philosophical niche into the edifice of the tradition they had built.

However, Heidegger’s emphasises that this does not mean that we should be afraid of questioning those terms and going beyond them. But we should be under no illusions that there is anything radical about this questioning. For in order to take an unorthodox approach, one must at first become, as it were, very orthodox, because one must know where the boundaries of the territory lie in order to transgress them.


Descartes is not radical enough

In his doctrine of the res cogitans and the res extensa (See Meditations I and VI), Descartes claims to have solved the problem of the "I" and the "world" in a radical manner. But Heidegger argues, if anything, he has been not nearly radical enough. This is because he has not subjecting the ontological traditional of his own time to the positive criticism it deserved. By which Heidegger is talking about the philosophical prejudices of the ancient Greeks of which Descartes never really freed himself. For example Heidegger argues his failure to lay bare the primordial problematics of Dasein has as a consequence prevented him from appreciateing the phenomenon of the world. In addition to this, it is also the reason Descartes could compress this whole ontology of the 'world' into certain entities within-the-world.

However, although this is a horribly distorted view of worldhood, it is not true to say that it is no view at all. For Cartesian ontology does allow us to glimpse this phenomenon, albeit in a very partial and restricted way. In this sense perhaps we should congratulate Descartes for laying bare the basic ontological characterisation of the world. So Heidegger sets about trying to correct the distortions in Descartes’ ontology.


He takes his departure from the Cartesian conception of Nature as a way of accessing the phenomenon of the world. This is problematic for two reasons

1/ Nature itself contained within the phenomenon of the world

2/ And as such it stands in the way of both the problem of the world and the problem of Being, both of which remaining concealed in the Being of the things that one encounters within Nature.

Despite these objections, Heidegger thinks that worldhood can still be conceived in terms of the entity called Nature, by allocating to this entity the function of a container within which the Being of every other entity can be founded. In other words, Nature can be made to perform the same ‘container’ function as the world performed in Heidegger initial analysis of worldhood [ref. ¶12, page 80].


An argument for Nature as worldhood

As a container, Nature could be considered to be the grounding notion of worldhood. This argument would run as follows:

1/ The extended Thing Nature is make to serve as the ground for those definite characters which show themselves as qualities. For example the substance lead is found in nature. lead is soft and mutable, therefore a useful substance for moulding into movable type because it can carry the impression of a letter and can be easily melted down and recycled once a print run is finished. (In this case, the soft quality of lead would have to be considered as a quantitative modification of its mode of the extension)

2/ Qualities, reduced in this way, would then provide the ground upon which such specific qualitative judgements as "beautiful", "ugly", "appropriate", or "not appropriate" could be based. By giving substances assignments disguised as what Heidegger is terming "specific qualitative judgements," we have started to consider substances as ready-to-hand.


What this shows is that even if one is primarily oriented by Thinghood, it is still possible to salvage the notion of Being characterised as equipment ready-to-hand. However these qualities would have to be taken as non-quantifiable value-predicates applies in the first instance to the ‘material thing’. In this case the thing would merely get stamped as something "beautiful", "ugly", "appropriate", "not appropriate," etc, rather than being authentically ready-to-hand.

A rounding out of the Things of Nature

But what this demonstrates is, that with a bit of massaging, the Cartesian analysis of Nature can be a way to uncover what is proximally ready-to-hand, and moreover using Descartes system we are able to do this on a fairly secure footing.

Problems with the procedure

But nagging doubts emerge as to whether the Being of what we encounter proximally within-the-world can be reached ontologically by this procedure. The problem is, when we speak of material Thinghood, have we not also tacitly presupposed its Being as a constant presence-at-hand. Thus, rounding out ontologically the Being of things of nature, has the effect of just elevating the ontical characteristics of those things, creating an edifice that further obscures the true ontological characteristics of the Being of the world as a nexus of involvements of entities which are ready-to-hand.

Defence of the procedure — "Goods"

These problems can be addressed if we consider the Cartesian definition of "things" more in terms of how we would regards goods. As Heidegger has pointed out Descartes definition of things is always hazily ontico-ontological [ref. ¶20, page 127], while the definition of things as goods is already more ontologically distinct. Goods are things imbued with a purpose, and consequently a value. Thus, if one considers things as goods, one is also considering the in-order-to of entities. Heidegger says that goods genuinely require assignments, and therefore an involvements structure.

So, while it is true that adding on value-predicates cannot tell us anything new about the Being of goods (For the reason that it merely presuppose that the goods have pure presence-at-hand as their kind of Being). Values could nevertheless be regarded as determinate characteristics a Thing can possess, and, although these too would be present-at-hand, rather than ready-to-hand, they would have their ultimate ontological source in the previously laying down the actuality of Things, that is to say in the nexus of involvements rather than in the continually-present-at-hand.

Our pre-phenomenological experience shows us that there is something which is not fully intelligible when an entity is regarded as a thing. Thus the Being of Things has to be rounded out pre-ontologically before it can become intelligible. This pre-ontological understanding can be summarised as follows - in order to know what things are we have to name them. In order to name them we have to differentiate them from the manifold of existence. If things themselves are unable to tell us what they are, how is this possible to do this? The only way it is possible is that we possess a pre-ontological understanding, based on the entity considers as a things of use (ready-to-hand) that allows us to distinguish entities.

But what, then does the Being of values or their 'validity' (which Lotze took as a mode of 'affirmation') really amount to ontologically? Lotze’s mode of affirmation characterised, as nothing more than linguistic propositions, those so called self evident truths that philosophers are wont to place so much emphasis on, such as Descartes contention that substance is extension. For Lotze, the function of linguistic propositions is to suggest a context in which the content of a given notion can be brought into relation with the content of another given notion. Thus Lotze rejects the Cartesian claim that reality is composed of simple unchangeable substances, because it is totally dependent on the notion of ‘relation,’ which is not an observable phenomenon. Moreover, Lotze like Heidegger pointed out that it is folly to characterise the Being of things as ‘relation,’ because this judgement already presupposes their existence. It therefore stands to reason that things must already Be, before they can exist in relation to one another, which means that Being cannot be predicated on a priori notions like substance or extension as Descartes claimed(Sullivan 2005).

Heidegger asks, what does the phrase "Things to be 'invested' with values" signify ontologically? For, pertaining to his own attempt to round out the Cartesian Thing of Nature, it seems a questionable exercise, as long as the matter of values remains obscure.

Reconstructing the Thing of use

The 'rounding-out' of the traditional ontology of the 'world' results in our reaching the same entities we uncovered when we analysed the readiness-to-hand of equipment and the totality of' involvements. So if we are to reconstruct this Thing of use, which supposedly comes to us in the first instance 'with its skin off', does not this always require that we have regarded previously the phenomenon of the world? For of it were otherwise, would we not be attempting to assemble our reconstruction without a plan?


On could argue that, in the process of trying to round our the Being of entities, one has actually clarified their Being, or has at least has clarified it enough for it to become a problem. But what this underscores is that by taking the Cartesian extension of entities as their essentially Being, Descartes could not have reached the Being of substance. But in saying this, Heidegger wonders if he is also just as far from catching a glimpse of his aim? For is not the true being of the ready-to-hand lost when he takes refuge in 'value'-characteristics? Heidegger concedes that it is hard to see how this reverse engineering of Descartes could ever become an genuine ontological theme for his inquiry.


Descartes dubious legacy was that he narrowed down the question of the world to that of Things of Nature, or in Heidegger’s terminology - entities within-the-world which are proximally accessible. He also confirmed the opinion of the Ancients, particularly the neo Platonists, that to know an entity (in supposedly a rigorous ontical manner) is the only possible way one can gain access to the primary Being of that entity. But in order to do this, Heidegger argues that we must at the same time have a pre-ontological insight about the nature of its Being, perform and operation Heidegger calls the 'roundings-out' of the Thing-ontology, in order to grasp its Being in terms of knowledge and ideas. But Heidegger wonders, in doing this are we not operating on the same dogmatic basis as Descartes himself?

The problem is, that Descartes failure to consider the world and those entities which we proximally encounter within in is not accidental. It is not an oversight which is simple to correct, but something which is grounded in a kind of Being which belongs essentially to Dasein itself. If we compare this ontology to the analytic of Dasein that Heidegger has been outlining in Being and Time, we can see that Heidegger main aim has been to uncover those main structures of Dasein, which are of the most importance in the framework of this problematic. Heidegger aims to assign to the concept of Being in general the horizon within which its intelligibility becomes possible, so that readiness-to-hand and presence-at-hand also become primordially intelligible ontologically. When he has done this he hopes, for the first time, we can critique the Cartesian ontology of the world. An ontology which Heidegger reminds us is, in principle, still the one that dominates our thinking today. He are not able to express this critique fully yet, although he is able to indicate what form it is likely to take. In part 1 division 3 of Being and Time, Heidegger will:

  1. Show why was the phenomenon of the world was passed over at the beginning of the ontological tradition.
  2. Show why this passing-over has kept constantly recurring.
  3. Show why entities within-the-world have intervened time and time again as the ontological theme blocking access to the phenomenon of the world itself
  4. Explain why are these entities always tend to be found in the first instance in 'Nature'
  5. Finally explain why it seems necessary to round out such an ontology of the world


On the first point Heidegger refers to Parmenides explicitly. Parmenides was a Greek philosopher and poet, born circa BCE. 510. He argued that the phenomenal world is a delusion and that perception is actually the result of thoughts directed to the pure essence of being (anonymous 2006).



In sections 19 to 21 of this part we have subjected Descartes’ ontology to positive criticism we are now able to do three things:

  1. For the first time reach a positive understanding of the problematic of the world.
  2. Recognise the sources of our failure to do this before.
  3. Demonstrate why we should therefore reject traditional ontology if we wish to understand the world

There are three ontologically constitutive states which are closest to us:

  • The world
  • Dasein
  • Entities within-the-world

We have no guarantee that we will be able to uncover the Being of these as phenomena if we take our departure from common sense and start by considering the Things of the world, still less by taking our orientation from what is supposedly the most rigorous knowledge of entities. Our critique of Descartes should have clarified this.

Extension and spatiality

But Heidegger will rescue the Cartesian analysis of the 'world' using the notion of Spatiality. Spatiality is manifestly one of the constituents of entities within-the-world. Heidegger has criticised Descartes for not being radical enough in his ontology, but in one respect he was extremely radical, in suggesting that extension is the essential characteristic of the Being of corporeal things. In doing this Descartes prepared the way for Kant’s a priori understanding of space. As we have already intimated, there is some phenomenal justification for regarding extension as a basic characteristic of the 'world', even if by doing this we cannot conceived of anything in a manner than is ontologically adequate. But within certain limits the problems with the notion of extension can be separated from Descartes neglecting to provide an explicit interpretation for the Being of extended entities.


C. The Aroundness of the Environment' and Dasein's Spatiality


In our first preliminary sketch of the ‘Being-in’ [ref. ¶12, page], we contrasted Dasein’s Being with a way of Being in space which we called "insideness". This expression means that an entity which is itself extended is enclosed by the extended boundaries of another entity that is also likewise extended.

Spatiality can therefore be defined as both the enclosed entity inside and the entity outsider which encloses both Being present-at-hand in space. However, if the first entity is Dasein, how can the concept of spatiality be applied? For Heidegger has told us often enough that Dasein is not a thing and therefore should not be considered to be present-at-hand? Even if we deny that Dasein has any such insideness in a spatial receptacle, this does not in principle exclude it from having any spatiality at all. For perhaps there is something like a special kind of spatiality that is constitutive for Dasein. This is the notion Heidegger says must now be set forth.

But inasmuch as any entity within- the-world is likewise in space, its spatiality will have an ontological connection with the world. We must therefore determine in what sense space is a constituent for that world which has in turn has been characterised as an item in the structure of Being-in-the-world.


In particular we must show how the aroundness of the environment and the specific spatiality of entities encountered in the environment, is founded upon the worldhood of the world, while contrariwise the world, for its part, is not something present-at-hand in space at all.

Our study of Dasein's spatiality and the way in which the world is spatially determined will therefore take its departure from an analysis of this ready-to-hand in space within-the-world. We shall consider three topics:

1. the spatiality of the ready-to-hand within-the-world (Section 22);

2. the spatiality of Being-in-the-world (Section 23);

3. space and the spatiality of Dasein (Section 24)-



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This is an ongoing project, the next section will appear shortly



Heidegger, Martin (2000), Being and Time, John Macquarrie & Edward Robinson (trans), London: Blackwell Publishing Ltd.


Additional References

Anonymous, Internet Encyclopaedia of Philosophy (2006) "Parmenides," html document, URL http://www.iep.utm.edu/p/parmenid.htm [accessed March 2007]

Baltussen, Han (2005) "The Presocratics in the doxographical tradition" pdf document, url: http://www.ut.ee/klassik/sht/2005/baltussen1.pdf [accessed March 2007]

Descartes, Rene (1996), 'Meditations on First Philosophy', Translated by John Veitch, HTML document, url: http://www.wright.edu/cola/descartes/ [accessed March 2007]

Descartes, Rene (2003), 'The Principles of Philosophy,' Translated by John Veitch, html document, url: http://www.gutenberg.org/dirs/etext03/ pnpph10.txt [accessed March 2007]

Kant, Immanuel, Critique of Pure Reason, Translated by J. M. D. Meiklejohn, London: Everyman, 1993

Massa, Lou (1996) "Physics and Mathematics" in David Weissman (Ed) Discourse and Method and Meditations on First Philosophy: Descartes, Rethinking the Western Tradition, London, Yale University Press

Peirce, Charles Sanders (1931-1935), The Collected Papers of Charles Sanders Peirce, Vols. I-VI, Charles Hartshorne and Paul Weiss (editors), Cambridge, MA: Harvard University Press

Sullivan, David (2005) ‘Entry on Hermann Lotze in the Stanford Encyclopaedia of Philosophy,’ html document, url: http://plato.stanford.edu/entries/hermann-lotze/ [accessed March 2007]

Waters, Benjamin (2005) "Lectures to Heidegger’s Sein und Zeit," html document, url: http://www.benjaminwaters.org/wat002.0.9.htm#38 [accessed March 2007]



Two dimensional Cartesian coordinate system diagram taken from url: http://www.ccd.rpi.edu/Eglash/csdt/na/rugweaver/nrw/symmetry.html [ref. ¶21]

Three dimensional Cartesian coordinate system diagram taken from url: http://www.geom.uiuc.edu/docs/reference/CRC-formulas/node39.html [ref. ¶21]


This is the eigth part of my explication and commentary of Being in Time, for contents of previous sections see the main index

There is also an online glossary of terms referred to in this document.

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