Jens Tomas Anfindsen

Department of Philosophy, Uppsala University

June 2005


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Leibniz on hypothetical necessity


It is one of the best known facets of Leibniz philosophy that it is compatibilistic with regard to necessity and freedom. Leibniz (1646-1716) persistently maintained (a) that every event is determined and that what happens is necessary, yet (b) that some acts are nonetheless free. An essential tenet of this compatibilistic account consists in its claiming that free acts are contingent in some sense which exclude absolute or metaphysical necessity, but not relative or hypothetical necessity.[1] Thus while free acts are contingent in one sense, they are necessary in another; they are metaphysically contingent, yet hypothetically necessary. This is a modal distinction, differentiating metaphysical from hypothetical modalities.[2]


This paper will explore the distinction between metaphysical and hypothetical modalities, and will especially aim at elucidating what it is for something to be hypothetically necessary.


Avicenna – an historical forerunner

The great Muslim philosopher Avicenna (980–1037) developed a distinction which essentially resembles that which we are exploring, and which, though somewhat crude, elucidates the subject matter neatly because it is so simple and clear. Avicenna says there are two kinds of existents:


1.      In one of them, when the thing itself is considered, its existence is not necessary; this is called “possible of existence”. In the second, when the thing itself is considered, its existence is necessary; this is called “necessary of existence” (from ‘Uyun al-masa’il, in: (Bosley 1997, p. 14)).   


A pertinent point here is that this distinction applies to things according as they are considered in themselves, which is like saying “considered essentially” or “considered intrinsically”. Avicenna is asserting that some things, what their essence or their intrinsic properties are concerned, are possible of existence, while others are necessary of existence. Further, he lays down a rationale for when, for any given thing, a thing instantiates one or the other kind of existence.


2.      Know that every existent has a cause for its existence or has no cause. If it has a cause, it is something possible [of existence]… If it has no cause in any way for its existence it is necessary of existence (from al-Risala al-‘arshiyya in Rasa’il Ibn Sina, in: (Bosley 1997, p. 14-15)). 


So things that are caused to exist are possible in themselves, things that exist but are not caused to exist are necessary in themselves.


Since there is evidently a distinction between considering a thing in itself – “when the thing itself is considered” – and considering a thing in relation to other things, there is logical room for asking whether something that is necessary or possible by itself, might simultaneously be necessary or possible in relation to something other. On reflection we realize that things that are uncaused and necessary cannot be influenced in their mode of existence by other things (since they will exist just as necessarily regardless). We also realize that something which is possible in itself and caused to exist by another, is at least possible in relation to something else, or else it could not have been caused to be. But the contentious question is whether things that are caused and possible can or must be necessary by another. Avicenna answers that in the positive. About the possible of existence he says:


3.      And if it does exist, it becomes necessary of existence by another thing; consequently it is something that is always possible of existence by itself and necessary of existence by another thing. (from ‘Uyun al-masa’il, in: (Bosley 1997, p14), cf. ibid. I.2.3).


So Avicenna envisions two contrary modalities actually pertaining to the same thing at the same time, though in different respects. A thing that is possible of itself not only can be but is necessary in relation to another – “is always possible of existence by itself and necessary of existence by another”. It is this basic distinction and the basic intuition underlying it that I wanted us to have in mind as we now proceed to investigate Leibniz notion of hypothetical necessity.


Necessary contingents in Leibniz


Leibniz’s philosophy was partly published in treatises and scholarly articles, but also largely expressed in correspondence with the learned elite of the time. The result is that the sources to Leibniz’s philosophy are dispersed over a very large number of different texts. In working with this paper, I have accessed Leibniz’s works primarily through a collection of texts edited by R.S. Woolhouse and Richard Franks (Woolhouse 1998), and through citations given by Robert Merrihew Adams in connection with a systematic exposition of the development of Leibniz theory of contingence (Adams 1994, chap. 1).



Leibniz held a rather strong version of The Principle of Sufficient Reason (PSR) [3] leading him infer that all actual states of affairs have their ultimate cause in God’s benevolence. Leibniz argues that (a) “no fact could ever be true or existent … unless there were a sufficient reason why it was thus and not otherwise” (T19. 32; cf. TT1. 3; 18. 7; in: (Woolhouse 1998)), and that (b) since the reasons for things cannot continue to infinity, there must, outside the series of contingent things, be a “sufficient or final reason” … “and this we call God” (ibid. T19. 37 and T18. 8) (this answers to the classical structure of the cosmological argument). But there must, according to Leibniz, not only (c) be a sufficient reason for God’s creating a world at all, but also for his creating this world rather than some other (ibid. T19. 53-8; cf. T18. 8), and Leibniz identifies this reason as (d) a principle of the best: That “it follows from the supreme perfection of God that in producing the universe he chose the best possible” (ibid. T18. 10; cf. TT1. 1; 18. 9; 19. 53-8). So according to this line of reasoning it is necessarily the case that among all possible worlds, God chose, in accordance with his supreme perfection, to actualize the best possible one.


Now this philosophical stance gives rice to a bouquet of difficult questions concerning e.g. freedom and determinism, responsibility, evil, necessity and contingence. We are particularly concerned with the modal issue. A crucial question arising from the foregoing is whether everything actual is simply determined by Gods will in accordance with his perfection, in which case it will seem that the actual world is the only one possible, and in which case the actual world will be necessary. But what is then the sense of God’s choosing this among all possible worlds, and what is then the sense of postulating a final cause outside the series of contingent things, if nothing existent is contingent?


There is perhaps some vacillation in Leibniz as to the solution to this problem, but he was keenly aware of it. An excellent historical survey of the developments of Leibniz’s theory of contingency by Robert Merrihew Adams (Adams 1994, chap. 1), argues that some weak and early sources represent Leibniz as holding a position that would imply the annihilation of  contingency in favor of the absolute necessity of everything actual; but that Leibniz’s later, repeated, consistent and principal solution asserts (what I call) a “dual modality” pertaining to contingent things: That contingent things are contingent in themselves, but necessary on hypothesis of another (ex alterius hypotesi) (A VI, iii, 128). This claim of dual modality will be studied by us in some detail in what follows.


Dual modality

Leibniz claims there are two ways for things to have their modalities determined; either the thing through itself, or the thing through another. Thus distinguishing between (what I call) a “modal mode” on the hand side, and a “modal determinator” on the other, will yield the following schema.


Modal mode

Modal determinator


Through itself

Through another











Now, Leibniz claims that things that are contingent through themselves are also necessary through another. An illuminating angle of incidence to the intended meaning of this is found in the notion of the necessity of God’s choosing to actualize one particular world among all possible worlds.


4.      On the hypothesis of the divine will choosing the best, or operating most perfectly, certainly nothing but these things could have been produced; but according to the very nature of things considered per se, things could have been produced otherwise. (G I,149/L 204, in: (Adams 1994. p. 12)).


This passage contains reference to two ways in which the modal mode of actual things are determined.


Firstly, it refers to the aggregate of actual things as something that comes about as a necessary consequence of God’s immaculate choice of creation. The things or natures contained in the set of actual things are necessary consequences of the perfection of God’s creative act and thus in the class of the modally necessary, and necessary through another, namely God’s act. This refers to an external determinator.


Secondly, the passage makes reference to an internal modal determinator. It says that according to the per se nature of things, things could have been otherwise. So things are also modally determined by their per se nature. The per se nature of a thing is the same as the essence of a thing or ‘that which is expressed in a real definition of a thing’. To say that some nature, considered per se, could have been otherwise, is to say that that nature, considered per se, is not necessary. Things whose nature are not necessary considered per se, are modally determined through themselves as contingent.


Two principal points can be extracted from this passage. For one, the passage illustrates a difference between internal and an external modal determination. For another, the passage not only  claims that different modal determinators may yield different modal modes for the very same thing, yielding such things a dual modality (as I call it), it claims that it is the case that the things God created are necessary through another, viz. God.


The notion of being modally determined through another is, I think, intuitively much more edible to us than then the notion of internal modal determination. Although passage (4) contains a non-empirical and extra-mundane reference to external determination through God (the whole reasoning there depending on the cosmological argument and the principle of the best), there are other and mundane examples of external determination which are much more readily accessible to an empirically inclined imagination. Take some state of affairs; say, “a pig traversing the air-space of northern Bretagne in a speed of 180 km/h”. I assume it will appear prima facie plausible, even for non-zoologists, to contend that such activity is no intrinsic part of the per se nature of pigs, or put in other words, that such activity is not a necessary condition for being a pig, not something pigs necessarily do. Yet I think there would be some prima facie probability in the contention that a pig could not but do this if it was shot out from a pig-catapult ejector properly geographically placed (assuming proper set-up conditions and the general laws of physics). That is, I think we would be inclined to recognize that there are conditions under which pig-flying over northern Bretagne is necessitated. So I think the notion of external modal determination is at least prima facie understandable to us.


The notion of internal modal determination is not only less intuitive to us, I think, but also more controversial philosophically. I deem great the likelihood that even just a little philosophical training will clarify at least the intended meaning of the notion, but the philosophical objections to it are likely to be more persistent. The major gist of objections towards the notion of internal modal determination is likely to focus on the notion of a “per se nature” or “essence”. Many modern philosophers are persuaded by epistemic considerations that our conceptualizations of things do not mirror the objective reality of things in the manner required for philosophy to be able to construct ontological arguments which presuppose insight into real essences [cf. Audi, 1995 #2, s.v. “essentialism”]. This objection gives rise to a problematic which constitutes quite an enigma in the history of philosophy, and it falls outside the limits of this paper to evaluate it (though I intend to discuss at least one facet of this problem in an upcoming essay on necessary existence). For our purposes now I will contend myself with submitting that Leibniz proceeds on a reasoned assumption that our concepts of things do mirror the reality of things at least sufficiently well for us to be able to engage in speculative, ontological argumentation.[4] More specifically, he is committed to holding that our definition of essences do truly reflect their real modal mode.[5] We shall now investigate the rationale for that commitment.


Based on citation (4) above, we know that the modal mode a thing has through itself is epistemically accessed by us through considering the essence of the thing per se. The passage also states that other worlds than the actual world are possible in themselves. Yet the consideration leading to the establishment of the possibility of other possible worlds cannot itself be based on an empirical examination. One may justifiably infer that an empirically given object is possible (or else it would not be empirically given), but the principal determination of whether an essence is possible or not cannot consist in an empirical investigation, for according to Leibniz it is possible to determine whether things that do not exist, never have and never will, are possible in themselves. What is the criterion for such a determination?


5.      - [Is a] contradiction implied by the nonexistence of that which God wills to exist?

I deny that that proposition is absolutely true. Otherwise those things which God does not will would not be possible. For they remain possible, even if they are not chosen by God. It is possible indeed even for that to exist which God does not will to exist.

- But God cannot will that it exist [, you might object].

I agree; yet it remains possible in its own nature, even if it is not possible in respect to the divine will. For we have defined possible in its own nature as that which does not imply a contradiction in itself even if its coexistence with God can be said in some way to imply a contradiction. Therefore I say: that is possible, of which there is some essence or reality, or which can be distinctly understood. (Gr 289f./AG 20-22, in: (Adams 1994, p 12)).


So Leibniz maintains that even natures which are not compossible with God, and which thus cannot possibly exist, are nonetheless possible in their own nature. (NB! I understand “possible in its own nature” as wholly synonymous with “possible through itself”). Leibniz gives an example of such a case in the Theodicy, where he argues that it can be said that it is possible that a man who will in fact be damned (assuming God knows he will be damned, so there is no way it could turn out to be true that he will not be damned) can be saved (my source in: (Adams 1994)); but this is not a possibility with respect to what might happen or what might turn out true, but a possibility with respect to human nature, which is capable of salvation. So here is a vivid example of an actual impossibility which is simultaneously an intrinsic possibility.


This same passage also gives a definition of what it takes for something to be possible in its own nature.


That is possible in its own nature (= through itself) whose definition does not imply a contradiction in itself (by cit 5).


But what is involved in the definition of “a nature”? According to Robert M. Adams, “This theory requires …


… a relatively narrow understanding of the nature, essence or concept of a thing or a world. The essence of a substance, in the narrow sense, contains information about such things as the perceptions the substance has, and perhaps the geometrical configurations and motions expressed by those perceptions, and about the substance’s powers and tendencies to produce perceptions in itself – but not about other substances [my emphasis] (Adams 1994, p. 13).


The reason for distinguishing a narrow from a complete notion of an essence, is to safeguard Leibniz’s doctrine of monads (monads are the substantial entities in Leibniz’s philosophy). In the Monadology Leibniz claims that the whole “monadic universe” is reflected in each individual monad (T 2. 19 § 77, in: (Woolhouse 1998)). This means that in a wide or complete sense, knowledge of a real essence is such that it contains knowledge of a monad’s relation to all other essences, even to God, and so contains all truth. This is not the sense of nature or essence that we are after when we talk of an essence as possible through itself. We are after the narrow sense defining only the essence as it is in relation to itself, in abstraction from its actual relations or compossibility with other things. So in this narrow sense which is relevant for us now and which is the topic of (5), the possibility of an essence consists solely in that the definition of the essence in itself does not contain a contradiction in itself.


According to Leibniz, this means that “that is possible of which there is some essence” (Gr 289, in (Adams 1994, p. 13)) (manifestly, a definition containing a contradiction describes no essence; impossible essences aren’t possible). A standard example of a a definition containing a contradiction is that of the non-essence “squircle”: ‘a squircle’ is ‘a square circle’. The definiens here contains two contrary terms and hence the definition is contradictory. This means that the predicate “square circle” is not just something nothing has, it is also something nothing can have, exactly because its two terms are contrary (assuming the principle of contradiction). In making this inference, we need make no reference to God’s order of creation, nor any actual states of affairs at all, the definition in itself reveals that we are dealing with a non-essence and an impossibility. The point now is that in order to determine whether or not some essence is possible through itself, Leibniz believes we can proceed analogously. If a definiens of an essence narrowly defined contains no contradiction, then the essence is possible – considered in itself.


To construe an example, let us assume that the definition of ‘a unicorn’ is ‘a solid-hoofed, herbivorous quadruped with one straight and spirally twisted horn in the forehead’. Let us also assume that no unicorn exists, has existed or ever will exist – unicorns are quite simply no part of the best possible world. Nonetheless, since the definiens here contains no contradiction, a unicorn-essence is possible in itself according to Leibniz’s definition of it. Leibniz’s position here would imply that unicorns are a real possibility which God chose not to actualize in the best possible world.


This much is sufficient, I believe, to explain what Leibniz means by saying that things are impossible or possible through themselves. It is quite another question whether this notion of internal modal determination reflects any ontological reality. For why does the fact that a definition of some essence is non-contradictory reveal anything more than that a string of concepts is without contradiction; what does this tell us about real possibilities?[6] The philosophically interesting question being evoked here, I think, is whether it has any ontological relevance to talk of possibilities in abstraction from powers that could actually actualize them.


Calvin Normore has given a very thoughtful exposition of how modal notions in John Duns Scotus are ultimately justified through their relation to real powers (Normore 2003). On that model, there is no real possibility which could not be actualized. This is not evidently so in Leibniz. For Leibniz holds that many things which God would not create on account of his supreme perfection, and which thus cannot be real, are nonetheless possibilities in themselves. So then the question arises anew: what does such possibility have to do with ontology?


There is perhaps no clear cut answer to this question, or perhaps it can eventually be answered straightforwardly, but that that would require a deeper investigation than what I am able to undertake here. According to Robert Adams, Leibniz defended a moral as opposed to brute or blind necessity in God, and held that this preserves a real choice in God’s creation (Adams 1994, p. 22-25). If God’s choice between possible worlds is real, this must mean that God has the power to actualize other worlds than the best possible one. This will further imply that Leibniz is committed to hold that the actual world is somehow necessary on account of God’s supreme perfection, yet contingent on account of God’s powers to create. If this is a correct implication of Leibniz’s position, it raises the difficult theological-philosophical objection that, on account of the unity and simplicity of God (a basic theorem in any philosophical theology I know of), God’s powers and God’s perfections are nothing distinct. So if it is morally necessary that God creates the best, that will be a necessity inhering just as much in God’s creative powers. A distinction between God’s moral perfection and God’s power cannot be but conceptual, for (on the theorem of God’s simplicity) there are no real distinctions in God. As far as I can see, this yields a deep problem, and I do not see Leibniz’s way out of it.


Infinite analysis

Leibniz thought that an important element in defense of the contingency of the world was a proof that it is contingent that this, rather than any other world, is the best possible one. For Leibniz, this proof consists in showing that it cannot be demonstrated that this world is the best.[7] For Leibniz, showing that consists in demonstrating that it cannot be proven by analysis in a finite number of steps precisely which world is the best one; that would require a comparison with infinitely many possible worlds, something which is humanly impossible. Another way of expressing this same realization is to say that, though false, a denial of the predicate “best possible world” of the actual world, cannot be proven in a finite number of steps to be in contradiction with the definition of the subject (my sources in: (Adams 1994, p. 25-30); (Audi 1995, s.v. “Leibniz”); (Ishiguro 1990, p. 193-99)).


What Leibniz presents us with here is a proof-theoretical notion. But even if we accept that it cannot be proven in a finite number of steps what is best, and even if we were to assume that the reason why that cannot be proven, is that it is in fact contingent that this world is the best, that would still not sidestep the objection launched in the previous paragraph. For if the sense of other worlds that the actual being possible is supposed to reflect a real as opposed to mere conceptual possibility, it seems at least God must have the potency to create them. But as argued above, positing God as having such a potency seem to be incompatible with his moral perfection.  


Modal distribution

We have seen that Leibniz simultaneously holds (a) that every finite being as well as the actual aggregate of all finite beings (the world) are contingent in themselves, and (b) that their actual existence is necessary relative to God’s act of creation. So the world is contingent through itself, but necessary through God. In the two previous paragraphs we dealt with a philosophical-theological objection that can be raised against this position. But is another and very rigorous objection to Leibniz’s position here which does not presuppose any postulates of theology, but which argues that Leibniz’s contention that God necessarily creates the best possible world can be shown by modal logic to be in contradiction with the claim that that world is contingent.


According to the so called “distribution axiom” (hereafter “DA”) of modal logic, an axiom which even holds in K, the most basic and least contentious of modal paradigms (named “K” after Saul Kripke), that which is entailed by something necessary is itself necessary:

DA:  □(AB) (□A□B).[8]

DA says that if it is necessary that if A then B, then if necessarily A then necessarily B.

Assuming DA and, as Leibniz does, that it is the case that God, a necessary being, necessarily creates the best of all possible worlds, it seems that world must be necessary, not contingent. That may bee seen by substituting “God”  for “A” and “the actual world” for “B” in the formula above: “If it is necessary that (if God, then the actual world), then (if God is necessary, then the actual world is necessary)”. The problem is particularly acute because it has the actual world appear to be necessary absolutely and in itself, not merely hypothetically. Let’s investigate that appearance a little closer.


An implication contains three elements: (a) an antecedent, (b) a consequence, and (c) a consequent. What Leibniz means by hypothetical necessity is what we might call necessity of the consequence, it is for it to be the case that some form of the relation “if p then q” is necessarily true. Necessity by necessity of the consequence may be distinguished from a relation of the form, “if p, then q is necessary”, which makes a claim about the necessity of the consequent, not the consequence. Now, in a case where an antecedent is necessary, and necessarily has a consequence, then (this is what DA stipulates) the consequent is necessary too. So that necessity of the antecedent + necessity of the consequence (hypothetical necessity) = necessity of the consequent. Since Leibniz held it to be necessarily true that ““God is the creator of the actual world” (antecedent) necessarily implies (consequence) that “the actual world is the best of all possible worlds”” (consequent), it seems Leibniz is actually committed to hold, on pain of rejecting DA, that the actual world is absolutely, not merely hypothetically necessary. Does Leibniz have any reply to this?


6.      I reply that it is false that whatever follows from what is necessary through itself is necessary through itself. From truths, to be sure, nothing follows that is not true. Yet since a particular [conclusion] can follow from purely universal [premises], as in [the syllogistic figures] Darapti and Felapton, why may not something contingent, or necessary on the hypothesis of something else, follow from something that is necessary through itself? (From The Philosopher’s Confession, A VI, iii, 127f.; my source: (Adams 1994, p. 17)).


Leibniz further explains:


7.      In this place we call necessary only that which is necessary through itself – that is, which has the reason of its existence and truth within itself. Such are the geometrical truths, and of existing things only God. The others, which follow from the supposition of this series of things – that is, from the harmony of things – or from the existence of God, are contingent through themselves and only hypothetically necessary. (Ibid 128).


Leibniz’s reply in these passages is very simple; he just cuts the issue in two by reference to the two kinds of modal determinators. A consequent which is necessary by necessity of the consequence is surely necessary, he admits; i.e., when a consequent is necessary by necessity of the consequence, the consequent itself is necessary, too. It is necessary in the sense that it cannot fail to be true or to obtain given that the antecedent is true or obtains. But that does still not say anything about whether the consequent is true in virtue of itself or of another. For Leibniz, settling that question will depend on the criteria for “contingency in itself” which we explored in the two previous sections. The point in Leibniz’s response is simply that even if some consequent is necessary, if it is necessary by necessity of the consequence, it is not the kind of necessity that interest us when we say that something is contingent in itself. A thing may well be necessary by the necessity of a relation of entailment, yet contingent in itself.


I believe Leibniz’s answer, here, is totally valid. Just to enhance his point, I will add that for something to be necessary in a modal logical paradigm like K, is simply and solely for something to be true in all possible worlds. This implies nothing as to why something is true in all possible worlds; that is a matter of extra-logical considerations. In the case of something which is necessary by necessity of the consequent, one may, from a purely logical point of view, say this much, that the consequent is true in all possible worlds because its being true is implied by an antecedent which is true in all possible worlds. Yet that does still not inform us about the underlying ontological reason for the obtainment of that truth or that relation of entailment. So being necessary by necessity of the consequence is matter of something being necessarily on the hypothesis of a certain relation of entailment, but this is an entirely different matter than being necessary or contingent in one’s own nature. Three lessons can be drawn from this.


Firstly, Leibniz’s distinction between things necessary through themselves and things necessary through another, is not identical to the traditional distinction between that which is necessary or contingent by necessity or contingency of the consequence. Secondly, the two distinctions are such that they can be operated on the same subject matter, being different, overlapping distinctions within the same set of entities, but defining different properties within that set and without, so to speak, “interfering” with one another. Thirdly, from these points we can further infer that, unless we have overlooked something, there just is no formal objection to asserting that things that are necessary by necessity of the consequence are simultaneously contingent through themselves. This means that Leibniz’s commitment that things that are necessary by necessity of the consequent are contingent through themselves, does not contradict the Distribution Axiom of modal logic.


Conclusion and summary

I divide my conclusions under three headings.


1. Terminology

In this paper we have explored Leibniz’s distinction between absolute and hypothetical modality, and we have seen that this distinction is borne out of a theory of modal determinators, of how a thing’s modal mode is determined either through the thing itself or through another. My assessment is that these distinctions are well defined and comprehensible, something which I take to justify that albeit non-trivial philosophical objections connected to the use of these terms in ontological speculation, it is at least clear what Leibniz means by claiming that some things have a dual modality, being contingent through themselves and necessary through another.


2. Impossible possibles

Following the exposition of modal determinators and dual modality, we investigated a difficult dilemma. If the notion of a nature’s being possible through itself is to express something more than the non-contradictory combination of the concepts contained in its definition, i.e. if it is to express something more than mere conceptual possibility, then it seems that such possibility must be related to its possible actualization by a real power. If not, “being possible considered in its own nature” is a statement of logic, not ontology. On the other hand, if being possible in its own nature is something which is only displayed or epistemically accessed through a definition of its essence, yet a real possibility precisely because it could be actualized, implying that at least God must have the power to actualize it, then we enter into conflict with Leibniz’s “principle of the best”. For assume it possible for God to actualize all possible worlds. We have now assumed that it is possible for God to create other worlds than the best possible one, but Leibniz says that this is impossible on account of God’s supreme perfection. But on the theorem of God’s absolute simplicity, God’s supreme perfection is nothing distinct from God’s power. So it seems we cannot hold that God has the power to create something which contradicts his supreme perfection. If this reasoning is right, no other world than the best possible one is really possible, and if that is right, “being possible in one’s own nature” designates a conceptual possibility with no ontological import. I dare not deem this problem insurmountable, but I do not know its solution, and I think Leibniz is in serious trouble here.


3. Infinite analysis

In a little section on infinite analysis, I argued that even if we suppose Leibniz right in supposing that the proof-theoretical notion of something being provable only through infinite analysis is revelatory of the contingent mode of the subject of proof, Leibniz’s position is still vulnerable to the objection I raised in the previous section.


3. The distribution axiom

Based on the distribution axiom of modal logic, one can construct a rigid argument appearing to demonstrate the impossibility of something’s being implied by something necessary being contingent in its own nature. This argument, however, fails, for the reason that Leibniz’s notion of “being possible through itself” designates something else than de dicto necessity or necessity by necessity of the consequence, which is what is relevant with respect to the distribution axiom. Leibniz can and does admit that actuals which are contingent in their own nature, are necessary de dicto, i.e. cannot fail to be true, and necessary by necessity of the consequence, i.e. on hypothesis of another.





Adams, R. M. (1994). Leibniz - Determinist, Theist, Idealist. New York, Oxford University Press.


Audi, R., Ed. (1995). The Cambridge Dictionary of Philosophy, Cambridge University Press.


Bosley, R. N. T., Martin, Ed. (1997). Basic Issues in Medieval Philosophy. Ontario, Broadview Press.


Garson, J. (2003). Modal Logic. The Stanford Encyclopedia of Philosophy,  Edward N. Zalta (ed.).


Ishiguro, H. (1990). Leibniz's Philosophy of Logic and Language. Cambridge, Cambridge University Press.


Kauppi, R. (1985). Über die Leibnizsche Logik. New York & London, Garland Publishing.


Normore, C. (2003). Duns Scotus's Modal Theory. The Cambridge Companion to Duns Scotus. T. Williams. Cambridge, Cambridge University Press: 129-160.


Pruss, A. R. (2004). Ex Nihilo Nihil Fit - A Study of The Principle of Sufficient Reason, Work in progress.


Woolhouse, R. S., Franks, Richard, Ed. (1998). G.W. Leibniz. Oxford Philosophical Texts. Oxford, Oxford university Press.





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[1] This theme rather permeates Leibniz’s writings, but a compact overview of his position on it, and with Leibniz answering some common objections, can be found in Correspondence with Arnauld, T2 in: (Woolhouse 1998).

[2] What we here call ”metaphysical” modality is often designated by philosophers as ”absolute” or ”intrinsic”. What we call ”hypothetical” modality is often designated by philosophers as ”relative”.

[3] To see how Leibniz version of the PSR is stronger than versions of the principle which conceives of “sufficient reasons” merely in terms of “that which makes something true”, see (Pruss 2004, p 33-36).

[4] See ”Essence and constitution” in (Ishiguro 1990, p. 65 ff.).

[5] See especially ”Die Definition” in (Kauppi 1985, p. 101 ff.).


[6] Leibniz is careful to qualify that modalities are ontological, ”not a chimera which we create”, Letter to Foucher. My source in: (Ishiguro 1990, p. 171).

[7] The belief that the actual is in fact best, flows from the principle of the best (se above), but constitutes no proof of what the best is.


[8] See a fuller exposition of this axiom in: (Garson 2003).