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Preface by Anthony Harrison-Barbet
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Dr Anthony Harrison-Barbet In Memoriam
Philosophical Connections
Compiled by Anthony Harrison-Barbet
LEIBNIZ
RATIONAL IDEALISM (PLURALIST)
Gottfried Wilhelm von Leibniz was born in Leipzig, where his father was Professor of Moral Philosophy. He studied Aristotelian, Scholastic, and contemporary philosophy at Leipzig, mathematics at Jena, and then law at Altdorf, taking his doctorate in 1667. He entered the service of the Elector of Mainz and travelled in France and England, meeting many of the eminent thinkers of his day, including Malebranche and Spinoza. In 1676 he was appointed librarian in Hanover. In the same year he discovered the infinitesimal calculus; and this was to lead to an acrimonious dispute with Newton who had made the same discovery but whose results were published later. He was employed to write the history of the House of Brunswick, and he was also active in movements to reunite the Roman Catholic and Protestant churches, and to bring about an alliance of Christian states in Europe. He founded several learned societies and became the first president of the Berlin Academy of Sciences (later the Prussian Academy).
[Sources: References are to Leibniz's various works, such as The Monadology, The New System, and so on, but additionally there are some references to extracts provided in the Appendix to Russell's A Critical Exposition of the Philosophy of Leibniz. This book advantageously gives references to the standard Gerhardt edition of Leibniz's writings (Berlin, 1875-90) as well as to other compilations.]
PHILOSOPHY OF LOGIC AND LANGUAGE
[1] Leibniz's philosophy is grounded in a number of fundamental assumptions and principles. [See Monadology, 31-36; Discourse on Metaphysics, 8 -16.]
(1) He supposes (a) all propositions, including those expressing relations, to be expressible in the subject-predicate form; and (b) that singular may be assimilated to universal propositions. (For Leibniz, however, not all arguments are syllogistic). He also says that all true propositions the concept of the predicate is 'included' in that of the subject (either explicitly — as in 'identities' — or virtually) [see (3) below] [a].
(2) The Principle of Contradiction (or Identity): A is A and cannot be non-A. This is the basic truth of reason on which all other truths of reason are based. Truths of reason (whose opposites involve a contradiction and are necessary) are interconnected in a system. The propositions of logic and mathematics are typical [b]. They consist of self-evident axioms, real definitions, and deduced propositions.
(3) The Principle of Sufficient Reason. This provides a foundation for truths of fact. These are contingent and connected only accidentally; no contradiction is involved when they are denied. Now, necessary truths of reason are in a general sense analytic, their predicates being contained in their subjects. Contingent truths of fact, however, are synthetic; their predicates are not seen to be included in their corresponding subjects. However, Leibniz argues that given that God, as omniscient creator, exists, he (but not man) can know them; and to that extent, from His point of view, even these predicates too can be regarded as being contained in their subjects. Contingent truths are therefore also analytic, but only in a narrower sense. Thus the notion that Caesar will cross the Rubicon constitutes part of the subject Caesar. There is therefore a sufficient reason, located in God, for truths of fact [c].
(4) Definition for Leibniz is per genus et differentia. But he distinguishes between real and nominal definitions. Real definitions define the realm of the possible; nominal definitions define the realm of actualized possibles [d].
Given the feasibility of (a) analysing complex terms into simple ones or indefinable terms (to form an 'alphabet of human thoughts'), and (b) a complete deductive analysis of necessary or eternal truths, Leibniz hoped that it would be possible to construct a universal science incorporating mathematics, science, metaphysics, the study of law, and utilizing a universal language — a characteristica universalis [e] — consisting of mathematical symbolism, so that if we wished to discover new truths all we would have to do would be to perform the appropriate calculations. [See De Arte Combinatoria.]
METAPHYSICS
[2] Leibniz's metaphysics is closely connected with his logic. This is seen clearly in the parallels between the subject-predicate distinction appropriate to judgements an`d the substance-attribute distinction applicable to actual or possible existent things.
What are substances? Leibniz says they are the basic elements or 'atoms' of nature, out of which are made the individual things of our universe — the one reality God has actually created. They are simple 'spiritual' entities: Leibniz calls them 'monads' [Monadology, 1; Discourse, 8; see also Principles of Nature and Grace]. They have no shape or extension and hence cannot be divided either practically or theoretically. Leibniz thinks of them as metaphysical points. (Physical points are divisible; mathematical points do not exist.) [See also Russell, p. 254.] They can be created or annihilated only by God. They are entities which both persist and provide 'support' for qualities or ideas of colour, shape, and so on. In so far as these qualities inhere in or belong to a substance, the monad can be regarded as a subject of which attributes may be predicated and as a 'centre of change' [a], as it were. Successive predicates included in the subject then correspond to changes of 'accidents' occurring in the substance. No two monads are alike. This is in accord with his Principle of the Identity of Indiscernibles ['Fifth Paper to Clarke', 24-26], which asserts that no two individuals can be perfectly alike or equal; it would be contrary to the Principle of Sufficient Reason to suppose that two indiscernible substances exist, and if there were, we should have no principle of individuation [b]. Although he is not always consistent, Leibniz's general view seems thus seems to be that it is both inconceivable and metaphysically impossible that there should be two indistinguishable substances. Every position in the created world is therefore occupied. There are, as it were, no gaps. Likewise there are no discontinuities in the changes substances undergo — though we do not actually see them or are unaware of them. As he says, "nature does not make leaps" (natura non facit saltum) (he calls this the Law of Continuity) [New Essays, Preface]. The universe is thereby complete and harmonious — and indeed exhibits simple mathematical ratios. It is truly infinite in that, as the 'Absolute', it exists prior to all composition and is not formed by the addition of parts [c]. (By contrast what he refers to as an infinite aggregates by virtue of divisibility [see sec. 4] are not actually infinite; 'infinite' aggregates are not truly wholes. However, he continues to use the concept to the extent that it does not lead to infinite number — which he rejected. [see New Essays I, xvii, and Russell, pp. 109-10] ) Monads differ from each other in the degrees of perception and appetition they possess [Monad., 14ff.]. By 'perception' Leibniz means an internal condition of the monad in so far as it represents external bodies. (Our consciousness of our internal states he refers to as 'apperception'.) By 'appetition' he means the action of an internal principle that monads also possess which enables them to change from one perception to the next. Leibniz says there are therefore degrees of clarity and distinctness in perception. (Accordingly he allows validity to the Cartesian 'cogito' but says it is not a fundamental principle.) Appetition is a manifestation of a general inner capacity for activity and self-development, that is, for action. It is a 'living force' (vis viva), energy, or 'drive' (conatus) [d]. Leibniz thinks of the monads as 'entelechies' — first principles of perfection, and as substantial forms [Monad., 18; also New System]. Simple monads are thus in a sense 'spiritual' substances. However, they must also have a potential or passive aspect as their 'essence'. He calls this prime matter. This is not corporeal, although monads are supposed to possess, by virtue of their prime matter, impenetrability and inertia — capacities to resist respectively penetration and motion. Leibniz's position leads to the postulation of mind-body as a unity of monads — with the substantial soul monad as dominant. And, consistently with his concept of continuity [e], he seems to minimize the differences between spirit and matter within the monads. He certainly wishes to preserve the notion of man as a unitary being [e]. The human soul is immortal but requires memory [Discourse, 34; see also Russell, pp. 265, 294]. But unlike other substances it cannot have pre-existence; And Leibniz rejected the idea of the soul's being absorbed and reunited with the "ocean of Divinity" (which he supposed to be Averroes' position): there can be no transmigration [f], on account of the lack of contact between monads [g] [New Essays, Introduction].
[3] How does Leibniz account for extended physical bodies if simple monads are non-extended metaphysical points? Corporeal substances, he says, are 'aggregates' of an infinite number of inferior monads under the control of a dominant superior monad. Whereas each monad comprises active entelechy and passive prime matter, corporeal substances constitute secondary matter or mass [see Russell, p. 226]. Bodies are nevertheless regarded as 'organic'. As for extension, Leibniz thinks of this in terms of the way in which bodies appear to us: it is a phenomenon, a product of "plurality, continuity, and simultaneous existence of many parts" represented as if they were similar and indiscernible [a]. It follows that space and time are relative and not absolute. Space is "an order of coexistences", time "an order of successions". They too are therefore phenomenal and unreal (in the sense that they exist 'subjectively' as orders of appearances). Nevertheless, Leibniz calls them "well-founded phenomena" in so far as they are objectively grounded in relations) [see 'Third Paper to Clarke', 2-6; 'Fourth Paper', 7-18; 'Fifth Paper'] [b].
[4] While, consistently with his concept of continuity, Leibniz seems to minimize the differences between spirit and matter within the monads, he wants to keep a distinction between 'rational' souls and souls of all other organic bodies. [See New System.] Rational souls or spirits are those which, he thinks, are capable of reasoning and can have knowledge of immaterial things and truths. The motion of bodies can be explained in terms of efficient, mechanical causes — in accordance with the laws of natural philosophy (that is, science). Such causes are thus systematic regularities in the phenomenal world 'Souls', however, act according to the laws of final causation [a], relating to appetition, ends and means. Because what each monad is and how it acts is a consequence of its 'entelechy', there can be no causal interaction between souls and bodies. But Leibniz argues that God, when He created the universe, so arranged things that the seemingly reciprocal activity of each monad corresponds perfectly with what happens in all the others. Souls as dominant monads are thus also in agreement with the operations of their respective 'bodies'. Leibniz compares monads to clocks which have been constructed by the eternal clockmaker so that they all keep the same time. No intervention is needed. Indeed it would be incompatible with his perfection and 'uneconomical' were he to do so. Leibniz calls his theory the Theory of Pre-established Harmony [b]; and he sees it also as reconciling the two different causal realms [New System; also Monad., 78ff.]. This is because the totality of all that occurs in all monads is ultimately attributable to God's choice in creating this particular world [see sec. 5]. In effect, therefore, for Leibniz contingent mechanical causation, is subsumed under final causation [c] — and we can assume that for Leibniz the proposition 'all events have causes' is a restatement of the principle of sufficient reason. It follows also from Leibniz's account of the pre-established harmony of the system of corresponding monads that he is committed to a coherence theory of truth [d].
[5] God, for Leibniz, is pure Being, the primary monad, pure activity, and distinct from His creation [a] (which is corporeal and subject to mechanistic laws). He is not the One substance. Leibniz's account of the world clearly presupposes that God exists; and he offers a number of different arguments designed to prove this.
(1) The ontological argument [Monad., 45]. Taking existence to be a perfection, Leibniz says that God — possessing all perfections — must necessarily exist. This can be seen as soon as the idea of God is understood. However, for this proof to be valid Leibniz said that the concept of God would have to be possible, that is, not self-contradictory [b]; and it must be because no incompatibility can be shown between the simple qualities (the perfections), which are essentially unanalysable. So, although 'God is a possible being' is a truth of reason, it entails that God exists. 'God exists' is thus the single existential statement which is a truth of reason.
(2) Eternal and necessary truths must be grounded in something absolutely and metaphysically necessary [c]. This must be God; and such truths exist in His understanding.
(3) Truths of fact also demonstrate God's existence, in that a succession, even to infinity, of contingent causes must have a sufficient reason for their existence [d]. There must therefore be a necessary being [Principles of Nature and Grace, 8].
(4) Given his definition of monads as entities which do not interact, Leibniz says that the need for a pre-established harmony itself proves that God exists. This is reinforced by the moral certainty provided by the order and beauty we perceive in nature. (Leibniz attributes our feelings of beauty to harmony and proportion [ibid. 17] [e].
Leibniz said that our world is the one that God has actually created out of the infinite number of 'compossible' worlds. Why then did he do so? Leibniz's answer is that it was seen by God to be the best of all possible worlds — the one in which the greatest amount of good would be realized [Discourse, 6]. There are number of difficulties with this view, which he addresses [especially in Theodicy].
(1) God is not compelled to create this world. It is a world which is necessary physically but not metaphysically. God, says Leibniz, has free choice [f].
(2) But although the world may be "the best of all possible worlds", surely it is not perfect? Leibniz accepts the existence of evil though he thinks of it as a 'privation'. He in fact distinguishes three kinds. (a) There is metaphysical evil, in that individuals are necessarily limited in their being and knowledge and can therefore err. This gives rise to (b) moral evil or sin; and thence to (c) physical evil or suffering. But Leibniz says that all these can be a means of bringing about good; and God therefore permits but does not will evil as such. Individual souls can progress towards perfection and happiness in the next world through a partial vision and knowledge of God. Thus the world as a whole becomes more perfect, as "the physical kingdom of nature" is brought into closer harmony with "the moral kingdom of grace" [g].
(3) How can people be called free if God has chosen to create monads all the actions of which are contained within that concept even before they are actualized? [Discourse, 13]. Leibniz's answer is that while there are always moral reasons that "incline without necessitating", our choices are not absolutely, that is, metaphysically necessary [Discourse, 30; see also New Essays, II, xxi; Correspondence with Arnauld; Russell, pp. 292-3] [h].
Implicit in Leibniz's philosophy is the assumption that there is no incompatibility between reason and faith [i]. Indeed he regarded his metaphysics as a natural theology which could be utilized by any Christian regardless of denomination. However, in his later years he came to espouse a 'natural' religion rather than one grounded in revelation and the teachings of an authoritative church.
KNOWLEDGE
[6] [See Discourse, 23-29; Monad., 56-62; New Essays, Book IV.] As monads contain within themselves the totality of their future states [Monad., 22 — the present state of a simple substance is "big with the future"], or, as subjects, contain implicitly all their own predicates, there is no causal connection between them. Strictly therefore no monad can have any knowledge of another. Monads have no 'windows', says Leibniz. But because of the pre-established harmony the unfolding perceptions of one monad mirrors that occurs in each of the others [a]. Thus we may talk of perceptual knowledge in a limited sense — as "the internal state of each monad representing external things". However, Leibniz says that there are degrees of perception. In some monads and in the case of human beings (when asleep, for example) perception is confused or absent altogether. Higher levels are attainable when perception is accompanied successively by memory, feeling, and finally consciousness. He tends therefore to think in terms of a continuum between passive and confused sense experience and increasingly clear understanding as the mind (the dominant monad) becomes ever more active. At the higher levels of reflection we may have general knowledge of eternal truths (the principles of contradiction, sufficient reason, truths of mathematics and logic), all of which are derivable by the mind from within itself through the exercise of reason [b]; and inference is possible (at least in theory) from an analysis of one substantial monad to the predicates of all the others, thereby giving us potentially knowledge of the whole universe. In a wide sense, therefore, all ideas for Leibniz are (virtually) innate. However, using the term more narrowly he applies it to clear and distinct ideas such as those of substance, cause, God, as well as space and time, and perception itself. Confused perceptions, which mirror external aggregates of monads and thus constitute 'knowledge' of the phenomenal world, are therefore not strictly innate [c]. Both senses of 'innate' are implicit in Leibniz's observation: "There is nothing in the understanding which was not first in the senses — except for the intellect itself' [New Essays, II, i].
CRITICAL SUMMARY
Leibniz was a thinker of great brilliance who encompassed an extraordinarily wide range of interests. The fragmentary nature of his writings, many of which were incomplete or published after his death, have made interpretation difficult and contentious. There is undoubtedly a close connection between his logic and metaphysics (perhaps more apparent in his earlier work). However, many commentators would now reject Russell's view that the latter is grounded in the former. Of many important issues in his philosophy the following deserve comment.
(1) Truths of reason, governed by the Principle of Non-contradiction, are analytic — necessary in all possible worlds (thus all analytic propositions are true); while truths of fact, governed by the Principle of Sufficient Reason, are synthetic and contingent. Nevertheless, Leibniz also says that all true propositions (including 'contingent' ones) are analytic, in the sense that their predicates are contained in the 'complete notions' of their subjects. There are difficulties with this so-called 'predicate-in-subject' principle. Complete notions of subjects, and thus their unique individualities, can be known only by God. Moreover, while analytic in this wider sense, such propositions are also contingent in that the existence of their subjects is dependent on God's will. He had a sufficient reason for creating them; they might not have existed actually. These concepts of analyticity and contingency, particular in relation to 'possible worlds' are the subject of much discussion today.
(2) Leibniz's Principle of the Identity of Indiscernibles, which he derives from the Principle of Sufficient Reason and the 'predicate-in-subject' principle, underlies his views on appearance and reality. Whereas, in response to Descartes, Spinoza posited one substance, for Leibniz the universe consists of an infinite plurality of monads. This gives rise to further problems. (a) Given the impossibility of interaction between monads, Leibniz has to postulate the pre-established harmony. This is not easy to reconcile with human freedom; there would seem to be an inconsistency between his logic/ metaphysics and his ethics/ theology. His solution involving the notion of inclination without necessitation is not convincing. Moreover an individual's perception and knowledge have to be understood as being derived from within himself and ultimately attributable to God. Leibniz is thus committed to the characteristically rationalist criterion of 'clarity' to determine truth. (b) His account of space and time as 'well-founded phenomena' sits uneasily between Newtonian absolutism and Kant's 'forms of intuition' theory. (c) The only real individuals are souls (characterized by 'active force'). This gives rise to a difficulty concerning the individuality of composites. As against these difficulties, it can be argued that Leibniz's 'organicism' offers a way towards overcoming the Cartesian problem of interaction.
(3) God is obviously central to Leibniz's metaphysics. His suggested proofs — the (modified) ontological argument and his appeal to a sufficient reason — are, however, unsatisfactory. Further, Leibniz's view that this created world is the best of all possible worlds, and his solution to the problem of evil have not been found convincing by many thinkers; and they would question also his assumption that reason and faith are in harmony.
READING
Leibniz: Discours de Métaphysique (1686) (Discourse on Metaphysics); Système Nouveau de la Nature et de la Communication des Substances (1695) (New System of Nature and of the Interaction of Substances); Principes de la Nature et de la Grce fondés en raison (1714) (The Principles of Nature and of Grace founded in Reason); Monadologie (1714) (Monadology). Nouveaux Essais sur l'Entendement Humain (New Essays on the Human Understanding (1765). These, with the exception of the New Essays, can be found in R. Ariew and G. Garbner (eds), Philosophical Essays. A good edition of the New Essays is that of P. Remnant and J. Bennett. Leibniz's important correspondence with Arnauld is translated by H. T. Mason and with Clarke by S. Clarke and H. G. Alexander. (There is also a useful overall selection in Russell's book on Leibniz — see below.)
Studies:
Introductory
C. D. Broad, Leibniz: An Introduction.
N. Rescher, Leibniz: An Introduction to his Philosophy.
G. MacDonald Ross, Leibniz.
More advanced
B. Mates, The Philosophy of Leibniz.
G. H. R. Parkinson, Logic and Reality in Leibniz's Metaphysics.
B. Russell, A Critical Exposition of the Philosophy of Leibniz, 2nd edn.
Collections of essays
H. G. Frankfort (ed.), Leibniz: A Collection of Critical Essays.
N. Jolley (ed.), The Cambridge Companion to Leibniz.
CONNECTIONS
Leibniz
Note: Leibniz was widely read in the writings of the Scholastics, for example, Aquinas and Suarez, and much of the influence on him of Aristotle would have been mediated through these (though he had of course also studied Aristotle's own writings).
Logic and metaphysics [1a] All propositions in subject-predicate form; singular assimilable to universal propositions; not all arguments in syllogistic form; predicates 'included' in subjects →Kant
[1b]
[4a]
[1a]
[1d]
[1b] The Principle of Contradiction; truths of reason are necessary; propositions of logic and mathematics →Kant
[1e]
[1g]
[1a 1b]
[1c]
[1c; cf. 2b 4c 5d] The principle of Sufficient Reason; truths of fact are contingent; synthetic and analytic propositions (in a wide sense of the latter even 'contingent' propositions are analytic — because of God's foreknowledge) →Kant
[1e]
[1c]
[1c]
[CSa]
[1g]
[1a]
[1a]
[5a]
[1d] Definition per genus et differentia; real and nominal definitions [5a-c]
[1c]
[1e] Universal science and language [sec.1]
[2b]
[2e]
[2a; cf. 1a 2d e] Substances as 'monads' — as logical subjects and centres of change in which attributes (predicates of subjects) inhere; infinite number and variety of simple substances — 'spiritual', indivisible, unextended metaphysical points →Kant
[1b]
[1c]
[1a]
[4a 4b 13b c]
[2a]
[2a]
[2h]
[1h]
[3a]
[2b]
[2d]
[1i]
[3d]
[2e]
[4g]
[2b; cf. 1c] Indiscernible substances conceivable but do not exist (contrary to principle of sufficient reason & need for principle of individuation); individuals as infima species, sum of attributes known by God [14a]
[2g]
[3d]
[2g]
[2c e; cf. 3a] Principle of continuity — no gaps in change or space; the world as 'absolute' as really infinite; harmony and mathematical ratios [1a]
[4d]
[2j]
[1h]
[1b]
[1a]
[2d; also 6b c] Monads differ; degrees of perception; apperception and consciousness; clarity and distinctness; 'cogito' valid but not fundamental principle; appetition and 'vis viva' ('conatus') (force) [2g]
[5b]
[2a]
[3a]
[1b]
[1a]
[1b]
[1b e]
[7g]
[4d e 5a]
[2e; cf. 2a d 3a] Monads as substantial forms (entelechies), spiritual substances with passive aspect (prime matter); unity of mind and body; soul as principal monad; man as unitary →Kant
[8d 13c d 14a b 5b]
[3a b]
[5a]
[3d e g]
[2g]
[2e]
[3b 5a]
[1a 1b]
[1a c]
[4h]
[2f; cf. 4b] The human soul is immortal (requires memory), but unlike other substances cannot pre-exist; no transmigration for any substance →Kant
[2b]
[3c]
[3e]
[3g]
[2h]
[5b]
[2g — see 4b]
[3a; cf. 2e] Corporeal substances (secondary matter) as aggregates of monads; extension as phenomenal [2a]
[3e]
[3b] Space and time — relative; well-founded phenomnena grounded in relations →Kant
[4a]
[3f]
[4a]
[2b]
[3b]
[4a; cf. 2d] Efficient/ mechanical causes (bodies) and final causes (souls) not incompatible →Kant
[6a sec. 9 11b]
[2c]
[1a 1d]
[4a]
[3d e]
[1b]
[10d]
[1c]
[4b 2g; cf. 5e 6a] No causal interaction between monads (and therefore between souls and bodies: account of apparent reciprocal activity in terms of God's pre-established harmony →Kant
[1e]
[3g]
[2b g]
[1c d]
[3e 5b]
[1c]
[4c; cf. 1c] Mechanical causation is final causation (when considered from God's point of view); cf. principle of sufficient reason →Kant
[3e 10c d]
[1c]
[4d] Coherence theory of truth [Contrast, for example,]
[Cf. the following:]
[2a]
[2c]
[6a]
[1b]
[5a] God as pure Being, the primary monad, distinct from his creation; not the One substance [3a]
[3a]
[2b]
Arguments for God's existence: [5b] i. The ontological argument (provided concept possible) →Kant
[3d]
[3a]
[3c]
[2c]
[5d]
[5c] ii. Necessary, eternal truth must be grounded in necessary being →Kant
[3a]
[5d]
[5d; cf. 1c] iii. Sufficient reason for existence of truths of fact →Kant [5d]
[5e] iv. Need for pre-established harmony — proof for God's existence; reinforced by moral certainty from order in nature; feeling of beauty derives from harmony and proportion →Kant
[3h 11b]
[4a]
[5d]
[5f; cf. 5i] God free — not compelled to create [2b]
[3c]
[5g] Evil (metaphysical, physical, moral) as 'privation': all can bring about best of all possible worlds (the moral within the natural; nature and grace; perfection and happiness as end →Hume
→Kant
[2c 5b 8a]
[2b 3e]
[5a]
[5d]
[6a]
[5h; cf. 1c 5g] Individual freedom; logical/ metaphysical necessity; moral choice (reasons only 'incline') →Kant
[4a]
[5a]
[2e 3c]
[5c]
[2c]
[5i] Reason compatible with faith but has limits Aquinas→ [1a]
Knowledge [6a; cf. 4b] Monads have no knowledge of each other: 'mirroring' [2h]
[1h]
[6b] Knowledge and degrees of perception: continuum from passive confused sense to clear understanding to knowledge of eternal truths through reason →Kant
[2b]
[4b]
[2a d 4a]
[1a]
[2a]
[2b]
[6c] Innate ideas — wide and narrow sense; latter as clear and distinct (substance, God); knowledge of phenomenal world innate in wide sense →Kant
[6c 6f]
[2b]
[2a]
[2c 3a]
[6c]