Home
PAINTINGS
Poetry
Publications
Philosophy Physics
Physical Cosmology
Physics
Philosophy of Physics
Black Holes
The Big Bang
Anthropic Principle
Religion Atheism
Pantheism
Philosophy of Time
Metaphysics
Philosophy of Language
Linguistic Metarules
Mind Consciousness
Philosophy of Science
Hist. of Analytic Phil.
Ethics
Phenomenology
Felt Meanings 1986
Books/Book Comments
Press Releases
Biographical
Interview
Classical Music Lyricist
Students
Links

 

You can search this site:

 

Published in: Metaphilosophy, Volume 26, Nos. 1 and 2, January and April, 1995, pp. 97-106.

 

 

Page 97, Quentin Smith, “A Defense of a Principle of Sufficient Reason”,

Metaphilosophy, Vol. 26, NO. 1 & 2, January/April 1995, pp. 97-106

 

A DEFENSE OF A PRINCIPLE OF SUFFICIENT REASON

 

QUENTIN SMITH

 

I

 

The Principle of Sufficient Reason has very few contemporary defenders of any of its versions. (For a recent critique of this principle, see [Post 1991, 1987; Smith and Craig 1993, pp. 178—1911]). This is particularly true of some of its stronger versions, such as the principle that there is a sufficient reason why there are true propositions that entail that some contingent concrete objects exist. Most if not all contemporary philosophers believe this strong version of the principle is necessarily false, and some have presented an argument that it is necessarily false (e.g., [Rowe 1975]). The aim of this paper is to show that this principle is possibly true and is necessarily true if either (a) God necessarily exists or (b) space-time necessarily exists and contingently possesses a quantum mechanical vacuum. I will also distinguish this version of the principle from some other strong versions of PSR (principle of sufficient reason), all of which can be false consistently with the necessary truth of our version of the principle.

 

II

 

I begin by distinguishing several versions of PSR and defining my key terms. Four versions of PSR are:

 

PSR1:  Each true proposition that entails that some contingent concrete object (body or mind) begins to exist has a sufficient reason why it is true.

 

PSR2: Each true proposition that entails that some concrete object exists has a sufficient reason why it is true.

 

PSR3:  Each true proposition has a sufficient reason why it is true.

 

PSR4:  There is a sufficient reason why there are true propositions that entail that some contingent concrete object exists.

 

I shall show that PSR4 can be true and, moreover, can be true consistently with the falsity of PSR1, PSR2, and PSR3. This requires some key terms to be defined.

Some propositions are contingently the semantic content of sentence tokens and all propositions are necessarily bearers of truth values

 

 

Page 98, Quentin Smith, “A Defense of a Principle of Sufficient Reason”,

Metaphilosophy, Vol. 26, NO. 1 & 2, January/April 1995, pp. 97-106.

 

(assuming there are no true value gaps). I adopt a realist theory of propositions that implies propositions are abstract objects that have a sentence-like structure (but are not themselves sentences), and that propositions are neither reducible to nor dependent upon human mental phenomena (see [Smith 1993, pp. 133—224]). A contingent and positive truth is a proposition that entails some contingent concrete object exists. An object is contingent if and only if it exists in some but not all possible worlds. Whatever is a concrete object is a body (electron, star, etc.) or mind (e.g., a human mind).

A sufficient reason for the truth of a contingent and positive proposition p is another proposition q that meets two conditions; (i) q explains why p is true, (ii) q entails p, in the sense of relevance logic. Note that (ii) is a stronger condition than the condition that “q strictly implies p”, since the proposition that Alice is awake on November 4, 1994 strictly implies that triangles have three sides, but there is no relation of relevant entailment. (Each necessary truth is strictly implied by each contingent truth, but it is not the case that each necessary truth is relevantly entailed by each contingent truth.) Furthermore, condition (ii) about relevant entailment is not enough by itself to give a metaphysically interesting definition of sufficient reason, since condition (ii) by itself gives us many trivial cases of sufficient reasons. For example, the proposition that Alice is attentive most of the day on November 4, 1994 relevantly entails that Alice is awake on November 4, 1994, but the first proposition is a sufficient reason for the second only in a trivial and uninteresting sense. Condition (i) about explanation is not met by this pair of propositions, since Alice’s attentiveness does not explain why she is awake but is merely the mode in which she is awake. An example where conditions (i) and (ii) are both met is that the proposition, all bodies in the solar system at a distance from the sun are gravitationally attracted to the sun, and the earth is in the solar system, entails the earth is gravitationally attracted to the sun, The first proposition explains and relevantly entails the second proposition and thus is a “sufficient reason” for it in a metaphysically interesting sense.

Given condition (i) about explanation, condition (ii) about relevant entailment is not redundant; explanation does not require entailment, let alone relevant entailment, since some explanations are probabilistic.

        The sufficient reason for the truth of any metaphysically necessary proposition p is p itself. In the case of any necessarily true proposition p, conditions (i) and (ii) are both met by the proposition p itself: the explanation for the truth of p lies in the nature of p itself (and not in some different proposition q that makes p true) and p relevantly entails p (each proposition relevantly entails itself).

        The above remarks suffice to define my key terms. I shall now argue that PSR3is necessarily false, and PSR1 and PSR2 contingently false, consistently with the necessary truth of PSR4. This involves

 

 

Page 99, Quentin Smith, “A Defense of a Principle of Sufficient Reason”,

Metaphilosophy, Vol. 26, NO. 1 & 2, January/April 1995, pp. 97-106.

 

examining the three false principles of sufficient reason and arguing that the fourth principle, PSR4 is possibly true and may reasonably be held to be necessarily true.

 

III

 

The third principle of sufficient reason I listed is:

 

    PSR3: Every true proposition has a sufficient reason why it is true.

 

There is a demonstration that PSR3  is necessarily false. Consider the actual world W. The actual world is the maximal proposition W, such that W (a) entails each proposition p or its negation and W (b) possesses only true conjuncts. Any merely possible world W* is a maximal proposition that meets condition (a) but not (b); at least one of W*s conjuncts is false. Thus, a world is a maximal proposition and the actuality of the world W is the being true of that proposition. (Note that the universe is not the actual world; the universe is the aggregate of all bodies and embodied minds.) Is it logically possible that there is a sufficient reason why the actual world W is actual? Suppose, for the sake of argument, that God actually exists and creates the universe. Thus, the proposition, God creates the universe, is one of the true conjuncts of the actual world W. This proposition about God is a sufficient reason for the truth of the universe exists, but it is not a sufficient reason for the truth of the proposition world W is actual. Assuming the classical definition of God as free in the libertarian sense, there is no sufficient reason for the truth of the proposition God creates the universe. God is not psychologically or logically determined to create a universe, let alone this universe, and thus there is no sufficient reason for the truth of the proposition God creates the universe. Given this, there is no sufficient reason for the truth of the proposition that world W is actual. If there is one conjunct (of the maximal proposition) whose truth has no sufficient reason, then the truth of the maximal proposition has no sufficient reason. The truth of a conjunction has a sufficient reason if and only if there is a sufficient reason for the truth of each of the conjuncts. If the building collapsed and Alice freely decided to write a book has a sufficient reason, then both of its conjuncts have a sufficient reason. If the conjunct about Alice’s free decision has no sufficient reason (because of libertarian free will), then the conjunction has no sufficient reason.

There is a more general proof that there can be no sufficient reason for the actuality of the actual world. For any conjunctive proposition p and for any proposition q that is a sufficient reason for p, q is a sufficient reason for p if and only if q is a sufficient reason for each conjunct of p. Thus, if the actual world W has a sufficient reason, this reason is a

 

 

Page 100, Quentin Smith, “A Defense of a Principle of Sufficient Reason”,

Metaphilosophy, Vol. 26, NO. 1 & 2, January/April 1995, pp. 97-106.

 

proposition q that relevantly entails and explains each conjunct of W. But if q is a contingently true proposition, q is a conjunct of W and does not explain itself, since only necessarily true propositions explain themselves. In this case, q cannot explain W, since there would be at least one conjunct of W, namely q, that q does not explain. On the other hand, if q is its own sufficient reason, q is necessarily true; but if q is necessarily true, it cannot be a sufficient reason for W, since if q were a sufficient reason for W it would entail W and an entailment of a necessary truth is itself a necessary truth, contradicting the fact that W is true contingently.

 

IV

 

We have seen that  PSR3 is necessarily false. We may reasonably regard  PSR1 as contingently false; PSR1  we recall, is:

 

PSR1: Every true proposition stating that some concrete object (body or mind) begins to exist has a sufficient reason why it is true.

 

This is reasonably regarded as false since some things, such as virtual particles that begin to exist in a quantum mechanical vacuum, begin to exist without a sufficient reason. (They have a probabilistic cause, but not a determining cause.) PSR1 may be regarded as false contingently, since there is some merely possible world in which every concrete object that begins to exist has a determining cause.

We may also plausibly suppose that PSR2 is contingently false:

 

PSR2:  Every true proposition stating that some concrete object exists has a sufficient reason why it is true.

 

        PSR2 is false if PSR1 is false; if there is no sufficient reason why a given virtual particle x begins to exist, there is no sufficient reason why x exists. PSR2 is false contingently, since there is some possible world in which every contingent concrete object that exists, both begins to exist and has a determining cause in some earlier contingent concrete object. In this world, PSR1 and PSR2 are both true.

 

V

 

Given that we have now explained why PSR1, PSR2 and PSR3 are false, we may present the main argument of this paper, that PSR4 can be true even if the aforementioned three versions of PSR  are false. I shall argue that, contrary to received opinion, PSR4  is possibly true, even if PSR1, PSR2 and PSR3 are false, and that PSR4 is necessarily true if God

 

 

Page 101, Quentin Smith, “A Defense of a Principle of Sufficient Reason”,

Metaphilosophy, Vol. 26, NO. 1 & 2, January/April 1995, pp. 97-106.

 

necessarily exists or a space-time necessarily exists and is contingently endowed with a quantum mechanical vacuum. PSR4 is:

 

PSR4: There is a sufficient reason why there are true propositions that entail that some contingent concrete object exists.

 

Our first observation about PSR4 is that the sufficient reason mentioned in PSR4 cannot be a necessary truth. The reason for this is not that a necessary truth cannot be a sufficient reason for there being contingent truths. There is a necessary truth that is a sufficient reason for the truth of the proposition there are contingent truths. The latter proposition, although about contingent truths, is itself a necessary truth and thus is a sufficient reason for its own truth. The fact that there are contingent truths is a necessary truth follows from the fact that there are at least two possible worlds. If there are at least two possible worlds W and W*, it follows that there is at least one proposition p that is true in W but not in W If W and W* contained all and only the same truths, then W is identical with W*. If the proposition p is true in W but not in W*, then p possesses its truth value contingently. If W is actual, then p is contingently true and if W* is actual, then the negation of p is contingently true. Therefore, there are contingent truths is true in each possible world, i.e., it is a necessary truth.

The reason that the sufficient reason mentioned in PSR4 cannot be a necessary truth is that PSR4 is not about all contingent truths, but only about all contingent positive truths. As we said, a contingent positive truth is a true proposition that entails that some contingent concrete object exists. The proposition that there are contingent positive truths is contingently true, since there is some possible world in which there exist no contingent concrete objects; in this world there exist only abstract objects (and perhaps God, if God is a necessarily existent concrete object). Thus, there are contingent positive truths is itself a contingent positive truth. Since it is not a necessary truth, it cannot have a necessary truth for its sufficient reason (if it has a sufficient reason at all). If there are contingent positive truths has a sufficient reason, this sufficient reason must itself be a contingent positive truth. Could there be such a sufficient reason? Most philosophers, following William Rowe, hold there could be no such sufficient reason. It seems to me, however, that Rowe’s argument is unsound and that there can be such a sufficient reason, as I shall argue in what follows.

 

VI

 

Rowe has mounted a prima facie plausible argument that it is logically impossible for there to be a sufficient reason why there are positive and contingent truths. Rowe uses the terminology of “states of affairs”

 

 

Page 102, Quentin Smith, “A Defense of a Principle of Sufficient Reason”,

Metaphilosophy, Vol. 26, NO. 1 & 2, January/April 1995, pp. 97-106.

 

rather than “propositions” and focuses his discussion on the state of affairs t:

 

(t) there obtain positive, contingent states of affairs.

 

Rowe holds that a state of affairs is positive and contingent if and only if it entails that at least one contingent concrete object exists. According to Rowe, states of affairs are abstract objects that exist even if they do not obtain. They are isomorphic to propositions, which exist even if they are false. “Propositions either are true or false and exist even if they are false” is logically equivalent to “states of affairs either obtain or do not obtain and exist even if they do not obtain.” It is arguable that states of affairs as Rowe defines them are in fact identical with propositions (see [Smith 1993, pp. 156--158]), but even if they are only isomorphic, there is a sufficient similarity for an argument about propositions to be logically equivalent to a corresponding argument about states of affairs.

        Rowe adopts the assumptions that t is contingent, which is arguably a true assumption, given our foregoing consideration that there is some possible world in which there exist abstract objects but no contingent concrete objects. Rowe argues that if t is positive and contingent, then no state of affairs can be a sufficient reason for the obtaining of t and thus that it is impossible for there to be a sufficient reason why there obtain positive and contingent states of affairs. If q is a state of affairs that supposedly explains t and if “actual state of affairs” means “obtaining state of affairs”, then we have the requisite terminology to understand Rowe’s argument. Rowe writes:

 

Suppose that q is the state of affairs that explains t and that ‘q explains t’ is made true by the fact that the actual state of affairs q stands in a certain relation R to t. The actual state of affairs qRt must entail the state of affairs t, otherwise the fact that qRt would not make it true that q explains t. . . . Now the actual state of affairs qRt is either necessary or contingent. It cannot be necessary, for t would then be necessary . . . This means that the actual state of affairs qRt is a positive, contingent state of affairs. This being so, it is clear that qRt cannot make it true that q explains t. For to explain t, q must explain why there are positive, contingent states of affairs — and clearly q cannot serve this explanatory role by virtue of standing in relation R to t, if the fact that q stands in relation R to t is itself a positive contingent, state of affairs. (Rowe 1975, p. 105.)

           

I do not agree that it is “clear” that q cannot explain t if qRt is contingent. Rowe offers no further argument but offers a theistic example. He asks us to suppose that “God willed that positive contingent states of affairs be actual” (Rowe 1975, p. 106). Thus, God wills that positive contingent states of affairs be actual is a positive, contingent state of affairs: it obtains contingently and entails that some contingent concrete object exist. Rowe reasons that this prevents this

 

 

Page 103, Quentin Smith, “A Defense of a Principle of Sufficient Reason”,

Metaphilosophy, Vol. 26, NO. 1 & 2, January/April 1995, pp. 97-106.

 

state of affairs from explaining why t is actual. “Clearly, the fact that accounts for why there are positive contingent state of affairs cannot itself be a positive, contingent state of affairs” (Rowe 1975, P. 106). However, Rowe’s statement may be doubted. Rowe is willing to countenance that God necessarily exists and thus that God exists is a necessarily obtaining state of affairs; accordingly, God exists is not one of these state of affairs needing to be explained by the fact of God’s willing that positive, contingent states of affairs obtain. What needs to be explained is merely that there obtain positive contingent states of affairs, which is logically equivalent to explaining there are contingent concrete objects. However, this state of affairs does have an explanation; it is explained by:

 

(1) God wills that there be contingent concrete objects.

 

(1) is a sufficient reason for t, since (1) meets the two conditions for being a sufficient reason: The state of affairs (1) relevantly entails t and explains t. Consequently, Rowe does not appear to be correct in holding that there can be no sufficient reason or explanation for t.

To explore this matter further, note that (1) is itself a positive, contingent state of affairs. If the libertarian theory of free will applies to God, as it is normally thought to, then there is no sufficient reason why (1) obtains. Consequently, there is at least one positive contingent state of affairs that obtains for no sufficient reason. Does this imply that t obtains for no sufficient reason? If so, (1) cannot be the sufficient reason for t.

However, this implication does not hold, even though it may appear to hold at first glance. The appearance that (1) cannot be a sufficient reason for t is due to a failure to appreciate that the following two states of affairs are mutually consistent:

 

(2) There are some positive, contingent states of affairs that obtain for no sufficient reason.

(3) There is a sufficient reason why there are positive, contingent states of affairs that obtain.

 

These two states of affairs are consistent since (3) does not entail that each obtaining positive, contingent state of affairs has a sufficient reason why it obtains. If (3) obtains, then there is at least one positive, contingent state of affairs that has a sufficient reason for obtaining; at least the state of affairs t obtains for the sufficient reason mentioned in (3). However, if (3) obtains, it need not be the case that every obtaining positive, contingent state of affairs obtains for a sufficient reason, be it the reason mentioned in (3) or some other reason. This is because a proposition of the form:

 

 

Page 104, Quentin Smith, “A Defense of a Principle of Sufficient Reason”,

Metaphilosophy, Vol. 26, NO. 1 & 2, January/April 1995, pp. 97-106.

 

(4) There is a sufficient reason why there are Fs does not entail a proposition of the form

 

(5) For each x that is F, there is a sufficient reason why it exists.

 

For example, there may be a sufficient reason why there are particles rather than no particles at all. But that does not imply there is a sufficient reason for the existence of each particle. It may be that there is a sufficient reason for the existence of some particles, the so-called “real particles” (the long lasting electrons, protons, etc.), which entails there is a sufficient reason for there existing some particles rather than no particles at all, and yet that there is no sufficient reason for the existence of other particles, virtual particles (the short lasting electrons and protons, etc., that probabilistically begin to exist in a quantum mechanical vacuum). Consequently, God’s willing that there obtain positive contingent states of affairs is a sufficient reason for there obtaining positive contingent states of affairs, even though there is at least one positive contingent state of affairs, namely, the mentioned state of affairs about God’s willing, that obtains for no sufficient reason.

These considerations are consistent with the fact that it is logically impossible for there to be a sufficient reason for the conjunction of all obtaining positive, contingent states of affairs. There is a sufficient reason for the conjunction of all obtaining positive, contingent states of affairs if and only if each positive, contingent state of affairs that obtains, obtains for a sufficient reason. But it is logically impossible for each obtaining positive, contingent state of affairs to have a sufficient reason. The conjunction of all obtaining positive, contingent states of affairs is itself a positive, contingent state of affairs and it obtains for no sufficient reason. If it obtained for a sufficient reason SR, then SR is either a positive contingent state of affairs or is not. If SR is a positive contingent state of affairs, then SR is one of the conjuncts of the conjunction of all obtaining positive contingent states of affairs. In this case, SR can at best be a sufficient reason for the obtaining of every other conjunct; it cannot be a sufficient reason for its own obtaining, for then it would be a necessary state of affairs. But if it cannot be a sufficient reason for its own obtaining, then it cannot be a sufficient reason for the obtaining of the conjunction of all obtaining positive, contingent states of affairs. On the other hand, if SR is not itself a positive, contingent state of affairs, it is either a necessary state of affairs or a negative contingent state of affairs. If SR is a necessary state of affairs, it cannot be a sufficient reason for the conjunction of all positive, contingent states of affairs; if it were such a reason, SR’s necessity would be inherited by this conjunction, contradicting the fact that the conjunction is contingent. If SR is a negative, contingent state of affairs, it cannot explain the conjunction of all obtaining positive,

 

 

Page 105, Quentin Smith, “A Defense of a Principle of Sufficient Reason”,

Metaphilosophy, Vol. 26, NO. 1 & 2, January/April 1995, pp. 97-106.

 

contingent states of affairs, since no state of affairs of the form. It is not the case that Fs exist can be a suitable explanatory state of affairs.

 

VII

 

The fact that there can be a sufficient reason for the truth (obtaining) of positive, contingent propositions (states of affairs) does not hinge upon the possibility of theism being true. Suppose that Richard Gale (1976) is correct that space-time necessarily exists, and suppose that God doe3 not exist. Suppose further than a quantum cosmology of the sort envisaged by Tryon, Gott, Pagels, Brout, and others is true, at least in broad outline (see Smith, 1986). According to these cosmologies, there exists an empty background space-time that contains a quantum mechanical vacuum. This vacuum is regularly emitting virtual particles, and in some cases the emitted virtual particles produce a distortion of the background space-time that leads to the production of real particles and a “big bang” that ensues in an expanding universe, such as our own. Suppose in some possible worlds the background space-time contains a quantum mechanical vacuum and in others it does not. In the worlds where there is no quantum mechanical vacuum, no virtual or real particles are emitted and there are no positive contingent truths. However, in the worlds where the background space-time contains a quantum mechanical vacuum, there are virtual and real particles emitted from the vacuum and it is the case that in these worlds some positive contingent propositions are true, namely, the propositions asserting that the relevant particles exist. Suppose the actual world is one of the worlds in which the background space-time contains a quantum mechanical vacuum. Given this, there actually is a sufficient reason why there are positive and contingent truths. The sufficient reason is that there exists a space-time that contains a quantum mechanical vacuum. This is a contingent positive truth. There exists a space-time is the naturalistic analog to the theistic proposition God exists (both are considered to have the modal status of necessary truths) and there exists a space-time that contains a quantum mechanical vacuum is analogous to God wills that there be contingent concrete objects (both are positive contingent truths that have no sufficient reason, and yet are the sufficient reason why there are positive contingent truths at all). The proposition there exists a space-time that contains a quantum mechanical vacuum meets the two conditions for being a sufficient reason for there are contingent concrete objects (which, we recall, is logically equivalent to there are positive contingent truths). Since the concept of a quantum mechanical vacuum analytically entails that it is a source of virtual particles, which are a species of contingent concrete objects, the sufficient reason mentioned relevantly entails there are contingent concrete objects. Further, the sufficient reason explains why there are

 

 

Page 106, Quentin Smith, “A Defense of a Principle of Sufficient Reason”,

Metaphilosophy, Vol. 26, NO. 1 & 2, January/April 1995, pp. 97-106.

 

contingent concrete objects (the explanation of virtual particles in terms of the presence of a quantum mechanical vacuum is standard in quantum mechanics). Observe that there exists a space-time that contains a quantum mechanical vacuum does not give a sufficient reason for the existence of any given virtual particle; for any given virtual particle x, x has a merely probabilistic reason for existing. However, if there is a quantum mechanical vacuum, there is a sufficient condition of there being some virtual particles. “Each F that exists has a probability of less than one of existing” is consistent with “There is a probability of one that some Fs exist”.

In conclusion, I have argued that one version of the principle of sufficient reason, PSR4 is possibly true and may be true even if PSR1, PSR2 and PSR4 are false. Indeed, PSR is necessarily true if God necessarily exists or if space-time necessarily exists and contingently contains a quantum mechanical vacuum. If PSR4 is necessarily true, part of the “mystery of being” is unveiled, namely, the mystery of why there are any positive, contingent truths at all, rather than no positive, contingent truths.

 

 

References

 

Gale, Richard. (1976). Negation and Non-Being. American Philosophical Quarterly, monograph no. 10.

Post, John. (1991). Metaphysics. New York: Paragon House.

Post, John. (1987). The Faces of Existence: An Essay in Nonreductive Metaphysics. Ithaca: Cornell University Press.

Rowe, William. (1975). The Cosmological Argument. Princeton: Princeton University Press.

Smith, Quentin. (1993). Language and Time. New York: Oxford University Press.

Smith, Quentin (1986). “World Ensemble Explanations”, Pacific Philosophical Quarterly 67: 73-86.

Smith, Quentin and Craig, William Lane. (1993). Theism, Atheism and Big Bang Cosmology. Oxford: Clarendon Press.