Schopenhauer On The PSR

1 Schopenhauer’s Fourfold Root

Schopenhauer wrote On the Fourfold Root of the Principle of Sufficient Reason (Über die vierfache Wurzel des Satzes vom zureichenden Grunde) in 1813 when he was 25. It served as his doctoral dissertation, which he eventually submitted to the University of Jena for his doctorate in Philosophy. Various parts of are central for arguments in his later (and most famous) work The World as Will and Representation (1819). As Schopenhauer developed his views both in the initial volume of WWR and in subsequent edititions and expansions, he came to revise the FR as well. In 1847 he published a second and revised edition of FR, containing various modifications of his views in light of his more developed position in WWR. This results in various complications in the interpretation of the text that are well described in the introduction of (Schopenhauer 2012). For simplicity’s sake we will largely ignore these textual issues in what follows.

Schopenhauer frames his discussion in terms of the Wolffian version of the PSR – Nihil est sine ratione cur potius sit quam non sit (Nothing is without a reason why it is rather than is not).1 This will turn out to be only an approximate formulation of the claims that are of interest to Schopenhauer.

For our purposes there are two main claims made in FR – one positive and one negative. The positive claim is that the principle of sufficient reason, which Schopenhauer describes as the “basis of all science” (9), has a fourfold structure, and thus that there really are four laws rather than a single one. The negative claim is that these four laws each apply in parallel, and thus cannot be mixed. Indeed, Schopenhauer charges much of the history of philosophy (and particularly German philosophy after Kant) with confusing and conflating the various forms of the PSR. Such confusions result in various invalid arguments, such as the ontological and cosmological arguments for the existence of God.

In what follows I discuss first the relationship between the PSR and science. I then look at the so-called “root” of the PSR in the subject-object distinction before turning to the four principles. Finally, I look at the negative claim that these principles apply in parallel only.

2 The PSR & Science

Schopenhauer is remarkably brief in his discussion of the importance of the PSR, but he seems to hold the view that science, as a systematic body of knowledge of some subject matter, is only possible if some or other version of the PSR is correct. As he puts it,

The very thing that distinguishes any science from a mere aggregate is that each of a science’s findings follows from another as its ground. (§4, p. 10; see also §46 p. 143)

In this he expresses a fairly traditional view of science (i.e. a Wissenschaft), one that Kant also clearly articulated and endorsed in his work on what counts as “proper” science. Kant regards a proper science as a body of systematically ordered cognitions linked by ground-consequent relations that are knowable via some principle or principles with apodictic certainty (MFNS 4:468).2

Schopenhauer does not question whether we can have cognition or knowledge. Nor does he seem to question whether this cognition may be systematically connected in terms of ground and consequent. His aim, rather, seems to be showing why it is that our explanations of phenomena have the structure that they do, and how we can go wrong, or become otherwise confused, when we mistake one type of explanation for another.

3 The Root of the PSR

Schopenhauer contends that the PSR constitutes the form of all inquiry because it is rooted in the nature of all representation as the expression of the relation between subject and object. All cognition displays a subject-object structure, and so there is nothing that could be the basis for inquiry (or a ’why question’) that does not manifest this structure.

All of our representations are objects for the subject, and all objects for the subject are our representations. Now, however, it occurs that all of our representations stand to one another in a connection that is governed by laws and of a form determinable a priori, by means of which connection nothing existing of itself and independently, likewise nothing existing in isolation and apart, can be an object for us. It is this connection that the principle of sufficient reason expresses in its generality. (§16, pp. 30-1)

Hence a condition of the possibility of inquiry in any form is that it have subject-object structure, and thus be constituted by a representation that is the object for some subject. Schopenhauer denies that we can posit the existence of anything outside this structure, and thus in this sense he is both an idealist (all object are understood in terms of their relation to possible cognizing subjects via representation) and a critic of Kant’s idealism, in that he rejects the notion of a “thing in itself”, understood as an object for which there is no possible (finite) cognizing subject.

The fact that all (possible) cognition displays subject-object structure is not, however, sufficient for contending that any version of the PSR is applicable in inquiry. Schopenhauer further contends that the connection of representations relating subject and object is a lawful one, and that it is the PSR that expresses in the most general form the nature of this connection.

Schopenhauer, in this way, is deeply indebted to the method of argument Kant uses in his Analytic of Principles in the first Critique to show that all possible cognition is lawfully connected by principles governing quantity, quality, relation, and modality. In that work Kant argues that we have a priori knowledge of the basic principles governing experience, which he understands in terms of lawfully connected sensible representations. Schopenhauer here effectively accepts a similar position, but argues that we can see the principles as even more general and as explicitly implicating not just our faculty of judgment (or the “understanding” as Kant conceives of it) but reason as well.

Schopenhauer contends that there are four basic ways of relating a subject and object, and thus four determinate ways of articulating the more general PSR.

this connection assumes different forms according to the different kinds of objects, and the principle of reason in turn modifies its expression to indicate these forms, yet the connection always retains something common to all the forms, which our principle, conceived generally and abstractly, expresses … these relations separate into definite species, quite different from one another, whose number can be reduced to four since the number agrees with the four classes into which everything is divided that can become an object for us, thus all of our representations. (§16 p. 31)

The four principles are supposed to exhaust the ways in which subject and object can be (fundamentally) related. These are:

  1. The principle of sufficient reason of being
  2. The principle of sufficient reason of becoming
  3. The principle of sufficient reason of knowing
  4. The principle of sufficient reason of acting

The first two laws concern the conditions of being and of becoming an object in space and time. Both are forms of a subject’s relating to an intuition (or its intuited object). The third concerns the conditions of knowing some object in space and time. It is a relation of a subject to a conceptual (or intellectual) representation. The fourth concerns the conditions of acting on some object. It is a relation of a subject to a “motive”, or desire broadly construed. The second and third principles correspond to Kant’s distinction between real and logical grounds. The first principle seems closest to Crusius’s notion of a real existential ground.

What about the status of the principles themselves (or the general version of the PSR)? Schopenhauer denies that there is any explanation to be had here.

The principle of reason is the principle of all explanation: to explain a thing means to trace its given existence or connection back to some form of the principle of reason, according to which form the existence or connection must be as it is. Accordingly, the principle of reason itself, i.e., the connection that it expresses in any of its forms, cannot be further explained because there is no principle to explain the principle of all explanation – like an eye, which sees everything except itself. (§50 p. 148)

On the one hand, and like Kant’s principles of experience and the categories from which they are derived, there is no further explanation to the law of connection of representations between subject and object. This law (or laws) is simply constitutive of what it is to be the subject-object relation. But one might also wonder here why this doesn’t end up counting as a form of explanation. If one wants to know why the PSR applies, one need only look to the (fourfold) nature of the subject-object relation. Does this fact fall withing Schopenhauer’s fourfold framework?

4 Explanatory Parallelism

Schopenhauer contends that each version of the PSR excludes the others. This is not to say that in any form of inquiry only one form of the PSR is present, but only that there is only one “dominant” PSR for any form of enquiry.

in each science one of the forms of our principle is the guiding thread more so than the others, although in each science the others also apply, but in a subordinate role. Thus the ground of being is the principal guiding thread in pure mathematics (although in proofs the exposition proceeds only through cognitive grounds); at the same time, the law of causality appears in applied mathematics, and this law completely dominates in physics, chemistry, geology, and the like. (§51, p. 149)

So while the various principles might be at play in a single form of inquiry, it is nevertheless the case that with respect to any particular why question there is just one principle according to which that question may be answered. To think otherwise is to be led into confusion.

So, for example, the problem with the ontological argument is that it mistakes a ground of knowing, which is concerns a conceptual relation, with a ground of being or becoming, which concerns what has spatial or temporal form. Hence Descartes goes wrong in his ontological argument because,

He should have said, the immensity of God is a cognitive ground from which it follows that God requires no cause. However, he mingles the two [i.e. ground and cause], and one sees that he is not clearly aware of the great distinction between cause and cognitive ground. (§7, p. 14)

Similarly, Spinoza’s conception of a causa sui is incoherent, because causation is a principle of becoming, and thus inherently temporal. Hence, there cannot be a first cause, since the temporal chain is infinite, and there cannot be a self\–cause, since this would require that the effect already exist temporally prior to its cause – a contradiction in adjecto.

Of course, this would only be persuasive to Descartes or Spinoza if they agreed with the underlying framework according to which the various forms of the PSR are rooted in the laws of the intellect and in the subject-object relation. But why would they accept those latter arguments? Perhaps though Schopenhauer does not intend these observations to count as internal objections to their positions.

5 Limitations of the PSR

Schopenhauer is also clear that the PSR is limited in its application. It may not be applied unrestrictedly, but only to possible objects of experience.

the general sense of the principle of sufficient reason may be reduced to the fact that always and everywhere each thing is only by means of another thing. Now, however, the principle of reason is a priori in all its forms, thus rooted in our intellect; therefore, this principle cannot be applied to the totality of all existing things – the world including this intellect in which the world resides. For such a world, presenting itself by means of a priori forms, is for just this reason mere appearance; therefore, what applies to this world as a consequence of just these forms can have no application to the world itself; i.e. to the thing in itself presenting itself in the world. Therefore, one cannot say ‘the world and all things in it exist by means of something else’ – which proposition is simply the cosmological proof. (§52, p. 150)

Since the PSR is a generalization of the laws connecting representations, this limitation should come as no surprise. In this sense it allows Schopenhauer to limit scientific inquiry to the empirical in much the way that Kant did, but without relying on Kant’s conception of cognition as requiring intuition.



Schopenhauer, Arthur. 2012. On the Fourfold Root of the Principle of Sufficient Reason and Other Writings. Translated by David E. Cartwright, Edward E. Erdmann, and Christopher Janaway. The Cambridge Edition of the Works of Schopenhauer. Cambridge: Cambridge University Press.
Watkins, Eric. 1998. “The Argumentative Structure of Kant’s Metaphysical Foundations of Natural Science.” Journal of the History of Philosophy 36 (4): 567–93.
Wolff, Christian. 1730. Philosophia prima sive Ontologia methodo scientifica pretractata, qua omnis cognitionis humanae principia continentur. Frankfurt.

  1. (Wolff 1730, sec. 70 p. 47). ↩︎

  2. See (Watkins 1998) for representative discussion. ↩︎