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Leibniz and the English-Speaking World, Liverpool, 3–6 September 2003
LEIBNIZ’S DEBT TO HOBBES (revised October 2004)
George MacDonald Ross (University of Leeds)
1. Introduction
My title might suggest that I am going to argue for a strong Hobbesian influence on
Leibniz’s philosophy. However, it is notoriously difficult to establish direct influences
in the history of philosophy, and especially so in Leibniz’s case. He was a voracious
reader, and even while developing the earliest versions of his system when he was still a
student, he had at his finger-tips an impressive range of authors — ancient, medieval,
and contemporary. In most cases, one and the same doctrine or concept can be found,
with greater or lesser variation, in a number of books Leibniz will have been familiar
with. It is therefore unclear which he will have been indebted to in particular — and the
more widely spread an idea, the more likely he is to have come under its influence. For
example, one of Leibniz’s aims was to reconcile Aristotelianism with the new
mechanistic philosophy; but it makes little sense to ask which modern philosopher in
particular converted him to the mechanistic worldview. On repeated occasions, Leibniz
himself merely provides a list, such as ‘Galileo, Bacon, Gassendi, Descartes, Hobbes,
and Digby’,1 without giving priority to any one author.
Leibniz was certainly eclectic, and he quite consciously set out to produce a system
which would incorporate what he believed to be true in different, conflicting
philosophical systems, while rejecting what was false. In his own words, his system
would be a ‘harmony of the philosophers’.2 As he wrote in his Clarification of Mr
Bayle’s Difficulties of 1698:3
Consideration of this system [of mine] makes it evident that when one comes
down to the basics, one finds that most philosophical schools have more of the
truth than one would have believed. . . . [They] come together as at a centre of
perspective, from which an object (confused if looked at from any other
position) displays its regularity and the appropriateness of its parts. The
commonest failing is the sectarian spirit in which people diminish themselves by
rejecting others.
Or as he put it more succinctly in a letter to Nicolas Remond of 1714:4
1 For example, Confessio naturae contra atheistas, A.VI.i.489–490.
2 For example, he uses the expression in a letter to Peter Moller/Müller of 2.1.1699: Eduard Bodemann,
Der Briefwechsel des Gottfried Wilhelm Leibniz in der Königlichen öffentlichen Bibliothek zu Hannover
(Hannover, 1895, reprinted Hildesheim, Olms, 1966), p.189. It so happens that, in this particular passage,
the ‘philosophers’ he is referring to are alchemists; but it is a frequent theme in Leibniz’s writings that he
is seeking to harmonise different philosophical schools.
3 G.IV.523-4: ‘La consideration de ce systeme fait voir aussi que lorsqu’on entre dans le fonds des choses,
on remarque plus de la raison qu’on ne croyoit dans la pluspart des sectes des philosophes. . . . [Ils] se
trouvent reunies comme dans un centre de perspective, d’où l’object (embrouillé en le regardant de tout
autre endroit) fait voir sa regularité et la convenance de ses parties: on a manqué le plus par un esprit de
Secte, en so bornant par la rejection des autres.’
4 G.III.607: ‘J’ay trouvé que la pluspart des Sectes ont raison dans une bonne partie de ce qu’elles
avancent, mais non pas tant en ce qu’elles nient.’
Most philosophical schools are largely right in what they assert, but not so much
in what they deny.
Although it is a fruitless project to champion one individual philosopher as the most
important influence on Leibniz, it is nevertheless worthwhile to explore similarities
wherever they may be found, in order to fill out the details of Leibniz’s eclecticism.
And sometimes there may be concrete evidence of a unique influence on a particular
doctrine. So, while I do happen to believe that Hobbes has been relatively neglected as a
source for Leibniz’s ideas, I should not be taken as championing Hobbes, in the way
that Catherine Wilson5 does, or that Christia Mercer6 champions Aristotle, Konrad Moll7
champions Gasssendi, or Ludwig Stein8 champions Spinoza as the main source for his
early philosophy.
In this paper, I shall concentrate on Hobbes’s and Leibniz’s metaphysics. This may
seem a surprising limitation, because Hobbes is now generally thought of as a political
philosopher. However, in his own lifetime, Hobbes was known (on the Continent, at
least) as first and foremost one of the leaders of the modern movement in theoretical
philosophy and science, and it is here where his influence on Leibniz is strongest.
Nevertheless, it is arguable that, even in his political philosophy, Leibniz was
significantly influenced by Hobbes. Patrick Riley9 and others may have been misled by
Leibniz’s repeated rejections of Hobbes’s political system as a whole into neglecting the
extent to which Leibniz was stimulated by an admiration of certain aspects of Hobbes’s
approach, while being repelled by its apparently10 atheistic conclusions.11 Ursula
Goldenbaum12 has unearthed evidence that Leibniz was perceived by those who knew
him best (in particular Christian von Boineburg) as a Hobbesian and Spinozist, rather
than being the traditionalist Aristotelian that Christia Mercer would have us believe.
Goldenbaum argues convincingly that Leibniz accepted the Hobbesian position that
humans act only for their own advantage, and that Leibniz’s problem was to reconcile
individual self interest with the common good. He found the solution in the non-
Hobbesian concept of love: ‘We love a thing whose happiness is pleasing to us.’13 In
other words, an individual who is motivated by Christian love will act altruistically,
because altruism is a source of pleasure.
5 Catherine Wilson, ‘Motion, Sensation, and the Infinite: the Lasting Impression of Hobbes on Leibniz’,
British Journal for the History of Philosophy 5.2, 1997, 339–351. Similarly Howard Bernstein, ‘Conatus,
Hobbes, and the Young Leibniz’, Studies in History and Philosophy of Science 11, 1980, 25–37.
6 Christia Mercer, Leibniz’s Metaphysics: Its Origins and Development (Cambridge, Cambridge
University Press, 2001).
7 Konrad Moll, Der junge Leibniz, 3 vols (Stuttgart, Fromann-Holzboog, 1968–1996).
8 Ludwig Stein, Leibniz und Spinoza (Berlin, Reimer, 1890).
9 Patrick Riley, Leibniz’ Universal Jurisprudence: Justice as the Charity of the Wise (Cambridge MS,
Harvard University Press, 1996), esp. pp. 91-98.
10 I say ‘apparently’, because Hobbes’s political writings, especially Leviathan and its Latin appendices,
are permeated by far more fundamentalist Christianity than anything written by Leibniz.
11 For example, in his Specimen quaestionum philosophicarum of 1664 (A.VI.i.84), he says that ‘the
otherwise very acute man, Thomas Hobbes . . . almost abandoned religion’ in holding that ‘our soul is
corporeal and by its nature mortal.’ ‘acutissimus alias Vir, Th. Hobbius, . . . religionem fere perdidit . . .
animam nostrum corpoream esse ac sua natura mortalem’.
12 Ursula Goldenbaum, ‘Hobbes and Spinoza as the Heroes of the Young Leibniz. Leibniz as Belonging to
the Modern’, paper delivered at a conference on The Young Leibniz, at Rice University, Texas, Easter
13 Elementa iuris naturalis, A.VI.i.457: ‘Amamus rem cuius felicitas nobis jucunda est.’
2. Leibniz’s knowledge of Hobbes
Leibniz was sufficiently impressed by Hobbes’s philosophy to try to enter into
correspondence with him. Two letters survive: one written on 13/23 July 1670,14 and the
other around 1674.15 It is certain that Leibniz received no reply to the first,16 and it is
almost equally certain that the same is true of the second. Near the beginning of the
first, he makes the following significant claim:
I believe I have read most of your works, whether separately or in the collected
The collected edition which Leibniz refers to was published in Amsterdam in 1668.18
Hobbes’s motive was to boost his posthumous reputation as a major philosopher on the
Continent (he was already in his 80s), as a counterbalance to his uneasy mix of neglect
and notoriety at home. Although Leibniz had access to this edition soon after it was
published, he had already read some of Hobbes’s works in separate editions. Either way,
his claim is fully vindicated by the range of works he refers to explicitly in his early
writings: De corpore, De homine, De cive, Leviathan, De principiis et ratiocinatione
geometrarum, Examinatio et emendatio mathematicae hodiernae, and Problemata
physica.19 There can be no doubt that Leibniz had studied Hobbes with great care by the
end of the 1660s.
As I said earlier, many of the philosophical tenets Leibniz shared with Hobbes were
held in common by others. Examples are: that space is a plenum, that there are no
indivisible material atoms, that individual natural phenomena are to be explained in
terms of the laws of mechanics and not in terms of final causes, and so on. Such ideas
were generally in the air, even if not all the moderns espoused all of them. However,
other, more specific ideas were Hobbes’s own. I shall cover three clusters of such ideas
relatively briefly, and then discuss a fourth one in greater detail, since it has been
generally overlooked.
3. Ideas Leibniz derived from Hobbes
3.1. Logic as computation
In 1887, the Hobbes scholar, Ferdinand Tönnies, claimed that the basic idea of
Leibniz’s combinatory art, as well as his plan for a universal characteristic, could be
traced back to Hobbes.20 In 1901, the Leibniz scholar, Louis Couturat, published a
detailed rejection of this claim.21 In fact both writers ranged more widely than this, with
Tönnies looking for similarities between the two philosophers, and passages where
Leibniz praises Hobbes; and Couturat looking for dissimilarities, and passages where
14 A.II.i.56–59.
15 A.II.i.244–245.
16 According to Philip Bealey in a verbal communication, the letter was not forwarded to Hobbes, because
of his dispute with the Royal Society.
17 A.II.i.56: ‘Opera Tua partim sparsim partim junctim edita pleraqve me legisse credo.’
18 Thomae Hobbes Malmesburiensis opera philosophica, quae Latine scripsit, omnia (Amsterdam,
Ioannes Blaeu, 1668). This includes the Latin version of the Leviathan, the appendices to which are the
main sources for Hobbes’s materialist theology.
19 A.VI.ii, Schriftenverzeichnis zu VI.i und VI.i, p.684.
20 Ferdinand Tönnies, ‘Leibniz und Hobbes’, Philosophische Monatshefte 23, 1887, 557–573.
21 Louis Couturat, La logique de Leibniz d’après des documents inédits (Paris, PUF, 1901, reprinted
Hildesheim, Olms, 1969), Appendix 2, ‘Leibniz et Hobbes, leur logique, leur nominalisme’, 457–472.
Leibniz criticises him. However, both might be right in what they assert, and wrong in
what they deny.
The crucial passage in Hobbes is De corpore 1.2:
By ‘reasoning’ I mean computation. But to compute is to unite a number of things
added together into a single total, or to know the remainder when one thing is taken
away from another. So reasoning is the same as adding and subtracting. I do not mind
if you add multiplying and dividing, since multiplication is the same as the addition of
equals, and division is the same as the subtraction of equals as many times as is
possible. Consequently, all reasoning is reduced to two operations of the mind, namely
addition and subtraction.22
And again in 1.3:
Consequently, it would be wrong to confine computation (i.e. reasoning) to numbers, as
if humans were distinguished from other animate beings only by their ability to count
(as Pythagoras is said to have believed). This is because it is also possible to add a
magnitude to a magnitude, or to subtract a magnitude from a magnitude, and similarly
with bodies, motions, degrees of quality, actions, concepts, proportions, sentences, and
names — which cover all branches of philosophy. 23
Hobbes’s original and radical idea was that, instead of there being distinct kinds of
reasoning (syllogistic, arithmetical, geometrical, etc.), all human reasoning was
reducible to the single mental operation of adding or subtracting names, or propositions
consisting of names. Ultimately, logic was to be regarded as a species of arithmetic.
Leibniz approved of this. Referring to the first of the above passages, he wrote:
Thomas Hobbes, that most profound investigator of the principles of all things, rightly
laid down that every operation of the human mind is computation, and by this is to be
understood either adding a sum or subtracting a difference.24
What Tönnies rightly saw was that Leibniz was indebted to Hobbes for the central idea
that all reasoning was computation (or ‘calculation’ in Leibniz’s preferred terminology),
and hence a kind of arithmetic or algebra. Without this idea, Leibniz would never have
developed his combinatory art, nor his universal characteristic, which he envisaged as
an arithmetically notated system of all possible concepts. His vision was that, since all
reasoning was in principle computable, the day would come when inconclusive
argumentation would be a thing of the past. As he wrote in an undated note:
22 Opera Philosophica, ed. Molesworth (London, 1839-1845), vol. 1, p.3: ‘Per ratiocinationem autem
intelligo computationem. Computare vero est plurium rerum simul additarum summam colligere, vel una
re ab alia detracta, cognoscere residuum. Ratiocinari igitur idem est quod addere et substrahere, vel si
quis adjungat his multiplicare et dividere, non abnuam, cum multiplicatio idem sit quod aequalium
additio, divisio quod aequalium quoties fieri potest substractio. Recidit itaque ratiocinatio omnis ad duas
operationes animi, additionem et substractionem.’
23 Op.cit., pp.4–5: ‘Non ergo putandum est computationi, id est, ratiocinationi in numeris tantum locum
esse, tanquam homo a caeteris animantibus (quod censuisse narratur Pythagoras) sola numerandi
facultate distinctus esset, nam et magnitudo magnitudini, corpus corpori, motus motui, tempus tempori,
gradus qualitatis gradui, actio actioni, conceptus conceptui, proportio proportioni, oratio orationi, nomen
nomini (in quibus omne philosophiae genus continetur) adjici adimique potest.’
24 Dissertatio de arte combinatoria, G.IV.64: ‘Profundissimus principiorum in omnibus rebus scrutator
Th. Hobbes merito posuit omne opus mentis nostrae ese computationem, sed hac vel summam addendo
vel subtrahendo differentiam colligi.’
But to return to the expression of thoughts by means of characters, I thus think that
controversies can never be resolved, nor sectarian disputes be silenced, unless we
renounce complicated chains of reasoning in favour of simple calculations, and vague
terms of uncertain meaning in favour of determinate characters.
In other words, it must be brought about that every fallacy becomes nothing other than a
calculating error, and every sophism expressed in this new type of notation becomes in
fact nothing other than a grammatical or linguistic error, easily proved to be such by
the very laws of this philosophical grammar.
Once this has been achieved, when controversies arise, there will be no more need for a
disputation between two philosophers than there would be between two accountants. It
would be enough for them to pick up their pens and sit at their abacuses, and say to each
other (perhaps having summoned a mutual friend): ‘Let us calculate.’25
This echoes Hobbes’s ambition to replace the disputes of ‘dogmatic’ philosophy with
the consensus characteristic of ‘mathematical’ philosophy, by applying the methods of
the latter to the natural and human sciences.26
If Tönnies had been more attuned to the latest developments in logic, he could have
gone further, and pointed out that Leibniz nearly succeeded in developing a complete
Boolean algebra — the final fulfilment of Hobbes’s dream of logic as a species of
What Couturat did was to show that none of the details of Leibniz’s logic are to be
found in Hobbes, and indeed that Hobbes lacked the logical and mathematical ability to
make any formal advances. However, this does not detract from Tönnies’ insight that
Leibniz was inspired by Hobbes’s unique vision, even if Hobbes himself was unable to
develop it. Couturat was wrong to dismiss Hobbes’s influence on Leibniz simply on the
grounds that Hobbes had failed to do what Leibniz subsequently achieved by standing
on his shoulders.
3.2. The definition of truth
One of the most distinctive features of Leibniz’s philosophy is his claim that in every
true proposition, the concept of the predicate is contained in the concept of the subject.27
When I say ‘distinctive’, I do not mean that he was the first to define truth in this way,
since the same definition is to be found in scholastic philosophy, at least as a definition
of universal truth.28 Leibniz’s originality lay in extending it to all truth, thus giving rise
to his principle that all truth is analytic, and its corollary that every individual has a
complete concept.
25 GP.VII.200: ‘Sed ut redeam ad expressionem cogitationum per characteres, ita sentio nunquam
controversias finiri neque sectis silentium imponi posse, nisi a ratiocinationibus complicatis ad calculos
simplices, a vocabulis vagae incertaeque significationis ad characteres determinatos revocemur.
Id scilicet efficiendum est, ut omnis paralogismus nihil aliud sit quam error calculi, et ut sophisma, in hoc
novae scripturae genere expressum, revera nihil aliud sit quam soloecismus vel barbarismus, ex ipsis
grammatices hujus philosophicae legibus facile revincendus.
Quo facto, quando orientur controversiae, non magis disputatione opus erit inter duos philosophos, quam
inter duos Computistas. Sufficiet enim calamos in manus sumere sedereque ad abacos, et sibi mutuo
(accito si placet amico) dicere: calculemus.’
26 cf. the Epistle Dedicatory to the Elements of Law, and (less succinctly) the Epistle Dedicatory to De
27 For example, in a letter to Arnauld of June/July 1686, G.II.52: ‘semper enim notio praedicati inest
subjecto in propositione vera.’ On other occasions he omits any reference to notions or concepts — for
example, the Specimen inventorum de admirandis naturae Generalis arcanis, G.VII.309, begins: ‘In
omni veritate universali affirmativa praedicatum inest subjecto . . .’
28 cf. Stuart Brown, Leibniz (Brighton, The Harvester Press, 1984), pp.74, 82.
Leibniz may have been encouraged by finding something very similar in Hobbes’s
writings. In De corpore 3.7 (‘True and False’), Hobbes writes:
A true proposition is one in which the predicate contains the subject, or in which the
predicate is the name of everything of which the subject is the name. For example, ‘A
human is an animal’ is a true proposition because whatever is called ‘human’ is also
called ‘animal’. And ‘Some human is sick’ is true, since ‘sick’ is the name of some
human. A proposition is called false if it is not true, or if its predicate does not include
its subject; for example ‘A human is a stone.’29
There is, however an important difference, namely that, whereas Leibniz’s definition is
intensional, Hobbes’s definition is extensional. That is to say, for Leibniz the predicate
‘animal’ is contained in the concept of ‘human’, because being an animal is part of the
concept of being a human (a human is a rational animal). For Hobbes, by contrast, the
concept of ‘human’ is contained in the predicate ‘animal’, because humans are a sub-set
of animals. In a sense the definitions are equivalent, since any proposition expressing
the predicate as contained in the subject intensionally can be replaced by one expressing
the subject as contained in the predicate extensionally.
One reason why Hobbes preferred the extensional approach was because it fitted the
traditional ‘tree of Porphyry’, according to which the lowest species, such as humans,
come under or are contained within a hierarchy of genera, with the highest genus of
substance (or in Hobbes’s system, body) at the top. He reproduces the ‘table of
predicaments of bodies’ in De corpore 2.15, and in 2.16 he comments:
Secondly, it should be observed that, in the case of positive names, the lower is always
contained in the higher; whereas in the case of negative names, the higher is contained
in the lower. For example, ‘animal’ is the name of every human, and therefore includes
the name ‘human’ in itself; but since ‘non-human’ is the name of everything which is
not an animal, the name ‘non-animal’ which is placed above it is contained by the lower
name ‘non-human’.30
In other words, there are more animals than humans, since there are some animals
which are not humans; and there are more non-humans than non-animals, since some
non-humans are animals.
However, a more important reason for Hobbes to prefer the extensional approach was
the metaphysical one that it was consistent with his nominalism. In Hobbes’s ontology
there was no room for anything other than individual bodies. Although names could
have universal import as human artefacts (sounds in the air, or marks on paper), there
were no concepts with an existence independent of human beings. So there was no
problem (on this account, at least) over saying that humans are a sub-set of the bodies to
which humans apply the name ‘animal’. Although an intensional approach is equivalent
in practice, it is ontologically very different, in that it implies the existence of real
29Vera [propositio] est cujus praedicatum continet in se subjectum; sive cujus praedicatum nomen est
uniuscujusque rei, cujus nomen est subjectum; ut homo est animal, vera propositio est, propterea quod
quicquid vocatur Homo, idem vocatur quoque Animal. Et quidam homo est aegrotus vera est, cum sit
cujusdam hominis nomen Aegrotus. Quae autem vera non est, sive cujus praedicatum non continet
subjectum, ea Falsa appellatur, ut homo est saxum.’
30 ‘Secundo observandum est, quod nominum positivorum inferius semper continetur a superiore,
nagativorum vero superius ab inferiore. Nam exempli gratia, animal nomen est uniuscujusque hominis, et
ideo continet in se nomen homo, cum contra non-homo nomen sit uniuscujusque rei quod non est animal,
ideoque nomen non-animal quod ponitur superius continetur ab inferiore nomine non-homo.’
essences or independently existing concepts which can be said to be contained within
one another.
It is true that Leibniz had a brief flirtation with nominalism,31 and one which left a
lasting mark in the form of his lifelong and fruitful concern with the importance of
notation in areas such as the universal characteristic, logic, and the calculus. However,
even at his most nominalist he regarded Hobbes’s version of nominalism as
unacceptably extreme, and he always retained a belief in the objective existence of
concepts, which made an intensional approach to the issue of concept inclusion more
There is a further question as to whether Hobbes anticipated Leibniz in making his
definition of truth apply to all truths, or only to universal truths. Although the passage
from De corpore 3.7 quoted above seems to apply to all truths, it is a general feature of
Hobbes’s writings that he is thinking mainly of ‘scientific’, or necessary and universal
knowledge, and not of ‘historical’, or merely empirical knowledge. Thus in De corpore
3.10 (‘Necessary and Contingent Propositions’), he writes:
Again, in every necessary proposition, the predicate is either equivalent to the subject
(as in ‘A human is a rational animal’), or part of an equivalent name (as in ‘A human is
an animal’). . . . But this is not the case with contingent propositions. Even if it were
true that ‘Every human is a liar,’ the word ‘liar’ is not part of the compound name to
which the name ‘human’ is equivalent. So the proposition will not be called necessary,
but contingent, even if it is contingently the case that it is always true.32
So, although Leibniz may well have been influenced by Hobbes’s definition of truth, he
developed it far further than Hobbes could have envisaged.
A corollary of Hobbes’s definition, reinforced by his nominalism, is a stress on the
importance of verbal definitions as the foundation of all logical reasoning. One of the
characteristics of Hobbes’s writing is that he prefaces his arguments with long lists of
definitions of key terms — a particularly good example being Chapter VI of Leviathan.
Leibniz adopted a similar approach in many of his early writings, such as the Theoria
motus abstracti, and his private notes include long lists of definitions of terms relating
to particular topics.33 These were a preliminary to Leibniz’s ultimate goal of
constructing a universal characteristic, in which concepts would be notated
arithmetically, in such a way that their logical relations would be patent. This would
make it possible to calculate mechanically whether any given proposition was true of
false. Yet again, Leibniz’s ambitions far outstripped those of Hobbes; but the central
idea that the definition of names lies at the root of all reasoning is something Leibniz
owed to Hobbes, who was unique among early modern philosophers for his stress on
3.3. The concept of Conatus
One of the key concepts in Hobbes’s system is that of conatus or ‘endeavour’. Its
primary occurrence is in his physics, where it serves to make up one of the many
31 See in particular the Preface to Nizolio, G.IV.127–162.
32 ‘Rursus in omni propositione necessaria, praedicatum vel aequivalet subjecto, ut in hac homo est
animal rationale, vel pars aequivalentis est, ut in hac homo est animal. . . . At in contingente hoc non fit,
nam etsi vera esset omnis homo est mendax, quoniam tamen vox mendax, non est pars nominis compositi,
cui aequivalet nomen homo, non dicetur illa propositio necessaria sed contingens, etiamsi semper ita
33 For example, Leibniz, Textes inédits, ed. Gaston Grua (Paris, PUF, 1948), 512–545.
deficiencies of Cartesian physics. Descartes had tried to explain everything in terms of
the two fundamental concepts of extension and motion; but it soon became evident that
more concepts were needed to account for the phenomena — in particular, the concepts
of mass and of force. Hobbes implicitly recognised the conceptual difference between a
massy object and an equal volume of empty space by making size and shape accidents
of body, as something existing in its own right, independently of its extensional
properties. Even though he agreed with Descartes that there was no empty space, this
was a contingent fact, rather than a necessary truth following from Descartes’ thesis that
the essence of matter was extension, and hence that there could be no extension without
Force was more problematic, because, unlike matter and motion, it was not directly
observable, and therefore uncomfortably close to the occult virtues which the moderns
were so concerned to eliminate from the description of nature. Hobbes got round this
problem by postulating conatus as a limiting case of motion, which is observable. In De
corpore 15.2, he writes:
I shall define conatus as a motion through a space and time which is less than is given,
i.e. is determined, whether by being displayed, or by being assigned a number; in other
words, it is a motion through a point. In order to explain this definition, I must remind
you that by ‘point’ I do not mean that which has no quantity, or which cannot
conceivably be divided, since there is no such thing in the real world. Rather, it is that
the quantity of which is entirely disregarded, in other words, that of which neither the
quantity nor any part of it enters into the calculation for the purposes of demonstration.
So a point should not be taken as indivisible, but as undivided.34
Just as a real point is an infinitesimal — greater than a mathematical point, but smaller
than any given quantity — so a conatus is an infinitesimal motion. Conceptually it is
still a motion, but its primary function is not to be the smallest component of a
macroscopic motion, but to be the force35 which initiates a motion. Thus, in the same
chapter he says:
I define resistance, when two moving bodies come into contact, as a conatus contrary to
a conatus, whether wholly, or in a particular part.36
to define what it is to push: We say that one of two moving bodies pushes the other,
when its conatus brings it about that the whole or part of the other leaves its place.37
34 ‘definiemus conatum esse motum per spatium et tempus minus quam quod datur, id est, determinatur,
sive expositione vel numero assignatur, id est, per punctum. Ad cujus definitionis explicationem
meminisse oportet, per punctum non intelligi id, quod quantitatem nullam habet, sive quod nulla ratione
potest dividi (nihil enim est ejusmodi in rerum natura); sed id cujus quantitas non consideratur, hoc est,
cujus neque quantitas neque pars ulla inter demonstrandum computatur; ita ut punctum non habeatur pro
indivisibili, sed pro indiviso’. Hobbes’s contemporary translator glosses ‘id est, per punctum’ as ‘that is,
motion made through the length of a point, and in an instant or point in time.’ J.W.N. Watkins, Hobbes’s
System of Ideas (London, Hutchinson, 2nd ed., 1973), pp.87–88, treats the translation as if it were
Hobbes’s own words.
35 Hobbes does not himself call conatus a force. Instead, he uses the word vis or ‘force’ in the
idiosyncratic sense of ‘impetus multiplied either by itself, or by the magnitude of the moving body, by
virtue of which a moving body exerts more or less action on a body resisting it.’ De corpore 15.2: ‘vim
definiemus esse impetum multiplicatum sive in se, sive in magnitudinem moventis, qua movens plus vel
minus agit in corpus quod resistit.’
36 ‘definiemus resistentiam esse, in contactu duorum mobilium, conatum conatui, vel omnino vel ex
aliqua parte, contrarium.’
As a force, a conatus is importantly different from an ordinary motion in that any given
body can have only one motion at a time, but it will be subject to a variety of
conatuses,38 of which its actual motion is the resultant. Indeed, Hobbes held that every
conatus is propagated to infinity through the plenum,39 from which it follows that every
body is subject to an infinity of forces. A corollary is that no body is absolutely at rest.
Quite apart from the lack of a fixed point of reference in an infinite universe, even
bodies which are apparently at rest relative to their neighbours are internally vibrating
because of the conatuses acting on them. Rest is a state in which the forces are in
equilibrium, and a body will spring into motion as soon as the balance is disturbed.
Leibniz draws heavily on Hobbes’s concept of conatus, both in his letter to Hobbes of
1670, and in his Theoria motus abstracti of 1671. Although Leibniz diverges from
Hobbes on points of detail, his broad position is that the smallest components of the
material world are infinitesimals; that they are endowed with conatuses which are
infinitesimal motions; that conatuses are propagated to infinity in the plenum; that a
given body is subject to a multiplicy of conatasus at one and the same time; and that
nothing is absolutely at rest.40
While this is by no means yet Leibniz’s mature system, the seeds of it are clearly
present, and it is equally clear that he stood on the shoulders of Hobbes for many
aspects of it. Hobbes had gone as far as he could, and he was not mathematician enough
to develop his concept of conatus into the calculus, as Leibniz did a few years later. Nor
could Hobbes resolve the ambiguity of conatus being at the same time nothing other
than a motion, and yet also the cause of motion. Leibniz resolved the problem by
spiritualising Hobbes’s infinitesimal atoms into non-spatial monads characterised by
active and passive powers, and relegating motion itself to the realm of phenomena
perceived by monads. Nevertheless, there is still a striking similarity between Hobbes’s
material universe, consisting of a dynamically interconnected plenum of infinitesimal
particles, each pulsating with motion, and Leibniz’s mature vision of a spiritual
universe, consisting of unities striving for perfection, and accommodating themselves to
each other through the universal harmony.
However, conatus as force is only one half of the story. Hobbes also used the concept of
conatus to solve the mind/body problem. In the pre-modern period, the predominantly
Aristotelian worldview fudged the issue by postulating mind and body as different
aspects or components of one and the same individual substance (form and matter).
Both Hobbes and Descartes independently sharpened the issue in their own distinctive
ways: Hobbes with his uncompromising materialism, which excluded mind as a distinct
ontological category; and Descartes with his uncompromising dualism, which made any
interaction between mind and matter problematic.41 Although Hobbes’s first published
37 ‘ut definiamus quid sit premere: duorum mobilium alterum alterum premere dicimus, quando conatu
suo unum eorum facit ut alterum vel pars ejus loco cedat.’
38 I know that the plural of conatus in Latin is conatus; but if it is used as an English word, the plural
needs to be the inelegant ‘conatuses’ in order to avoid ambiguity. I wish we could agree to use the word
‘conation’ instead, since it does have a plural.
39 De corpore 15.7.
40 Theoria motus abstracti, G.IV.221–240, esp. pp.228–230. I have merely sketched the points of
similarity. Much more detailed comparisons of Hobbes and Leibniz on conatus are to be found in
Watkins, op. cit., and Bernstein, op. cit.
41 I say ‘uncompromising’ in accordance with the popular view of Descartes; but there are places where
he seems to proposes a trialistic ontology, with the union of mind and body as a third kind of substance.
See The Principles of Philosophy I.48 (Adam & Tannery, VIII-1, 23), and the letters to Princess Elizabeth
of 21st May and 28th June 1643 (Adam & Tannery, III, 664ff., and 680ff.). However, postulating the
human being as a distinct substance sui generis does nothing to make mind/body interaction more
philosophical work was his objections to Descartes’ Meditations, it is unlikely that his
own account of the relation between mind and body was a reaction to Descartes,
because he regarded Descartes’ concept of immaterial substance as totally absurd.42
Nevertheless, Hobbes did have to explain how our everyday experience of consciously
controlling the behaviour of our bodies is compatible with a materialist ontology.
In Leviathan 6, Hobbes takes it for granted that, since human beings are material
objects, all their activities are motions. He distinguishes between purely physical or
‘vital’ motions such as the circulation of the blood or breathing, and ‘animal’ or
‘voluntary’ motions, in which the imagination stimulates a new motion which would not
otherwise have occurred. As with the inanimate realm, where a conatus is an
infinitesimal motion giving rise to a macroscopic motion, in the animate realm, a
volition is likewise an infinitesimal motion giving rise to a macroscopic motion:
These small beginnings of Motion, within the body of Man, before they appear in
walking, speaking, striking, and other visible actions, are commonly called
So there is an exact parallel between conatus or endeavour in the inanimate and the
animate realms. Just as there is no need to appeal to occult forces to account for motion
in the inanimate realm, there is no need to appeal to similar forces in the animate realm.
Volitions are nothing other than small beginnings of motion, and they do not imply a
separate, immaterial substance which stimulates the body into action.
Leibniz was fully aware of the significance of Hobbes’s concept of conatus for
overcoming the Cartesian problem of how mind can influence matter (and vice versa) if
they are totally different categories of entity. His solution was to avoid Cartesian
dualism in the first place, by locating minds at unextended points, and equating conatus
with volition. Thus in the Theoria motus abstracti, he says that this concept of conatus
opens the door to arriving at the true distinction between body and mind, which no-one
has hitherto discovered.43
He explains this further in an undated letter to Arnauld. After summarising the Theoria
motus abstracti, he writes:
Further, from these propositions I reaped a huge harvest, not only in demonstrating the
laws of motion, but in the philosophy of mind. For having demonstrated that the true
location of our mind is a sort of point or centre, from this I deduced some surprising
consequences about the indissolubility of mind, about the impossibility of refraining
from thinking, about the impossibility of forgetting, and about the true and hitherto
unknown difference between motion and thought — that thought consists in conatus,
just as body consists in motion.44
42 Leviathan 34: ‘And according to this acceptation of the word, Substance and Body, signifie the same
thing; and therefore Substance incorporeall are words, which when they are joined together, destroy one
another, as if a man should say, an Incorporeall Body.’
43 G.IV.230: ‘hic aperitur porta prosecuturo ad veram corporis mentisque discriminationem, hactenus a
nemine explicatam.’
44 G.I.72–73: ‘Ex his porro propositionibus cepi fructum ingentem, non tantum in demonstrandis motus
legibus, sed et in doctrina de mente. Cum enim sit a me demonstratum, locum verum mentis nostrae esse
punctum quoddam seu centrum, ex eo deduxi consequentias quasdam mirabiles de mentis
incorruptibilitate, de impossibilitate quiescendi a cogitando, de impossiblitate obliviscendi, de vera atque
intima differentia inter motum et cogitationem; cogitationem consistere in conatu, ut corpus in motu.’
So we have Leibniz’s own word for it that many of his key metaphysical doctrines
originated in the concept of conatus, which he owed to Hobbes.
3.4. All bodies perceive
For the rest of this paper, I shall focus on a related point of similarity between Hobbes
and Leibniz which has not received much attention,45 namely their both holding that all
bodies perceive, and that the difference between inanimate bodies and animals is that
the latter remember their perceptions.
Hobbes’s account of sensation is briefly as follows. Changes take place only when one
body moves against a body adjacent to it. So a change in the sensory state of a sentient
being can take place only if a body sets up a motion in a sense organ. In the case of
touch, the motion is direct. In the case of vision, the brightness of a luminous body
consists in a pulsating motion, which causes a vibration in the ether; and the part of the
ether adjacent to the eye causes a motion in the eye. Again, sound consists in a
vibration, which causes the air to vibrate, and the part of the air closest to the ear sets up
a motion in the ear — and similarly with the other senses. But as yet there is no
sensation. Once a motion is set up in the sense organ, it propagates a similar motion
along the nerves, through the brain, and down to the heart. In the heart, it meets with an
equal and opposite reaction, which travels back along the same route until it arrives
back at the sense organ. Then and only then a ‘phantasm’ is generated by the opposition
between the two motions. This phantasm is the sensory image of which we are directly
aware, and it appears to be external to us because of the outward motion from the heart
and brain. 46
There are, of course, many problems with this account. But what concerns me here is
the difference between three kinds of being: human beings, sentient beings or animals,
and non-sentient beings or inanimate matter.
Hobbes is quite explicit that sensation is the same in animals as in humans.47 In this he
differs from Descartes, for whom animals are automata, with no awareness of their
sensations. Indeed, it is a corollary of Hobbes’s materialism that he makes much less of
a divide between humans and other animals, since he does not explain consciousness as
the function of an immaterial soul (in fact he does not discuss consciousness as such at
all). For Hobbes, what distinguishes humans is their possession of reason, and reason
consists in nothing more than the ability to name things so as to construct a language,
and to perform computations involving names. So if a human and an animal observe the
same scene, the only difference is that the human can add a linguistic running
commentary. As Hobbes says in the sixth objection to Descartes’ Meditations (and bear
in mind that he uses the word ‘thought’ both for perceptions and for rational
but thought can be similar in humans and in animals. For when we assert that a person
is running, we do not have a thought which is any different from that had by a dog
watching its owner running. So the only thing that assertion or negation adds to simple
thoughts is perhaps the thought that the names which the assertion consists of are the
names of the same thing in the mind of the person doing the asserting. This is not to
45 Exceptions are Milič Čapek, ‘Leibniz on Matter and Memory’, in Ivor Leclerc (ed.), The Philosophy of
Leibniz and the Modern World (Nashville, Vanderbilt University Press, 1973), 78–113, and Catherine
Wilson, op. cit., esp. p.343.
46 Hobbes’s main account of perception is in De corpore 25.2.
47 Chapter 25 is entitled ‘Animal sensation and motion’, and he refers to ‘sentient beings’ in general, not
just to humans.
involve in a thought anything more than its resemblance to its object, but to involve that
resemblance twice over.48
If we now turn to the difference between animals and inanimate matter, Hobbes has a
problem. His account of sensation in sentient beings is purely mechanical, as it has to be
if he is to avoid appealing to animal souls. But the crux of his explanation is that
phantasms occur spontaneously at the meeting point between two equal and opposite
motions. Or, one might say, a phantasm is nothing other than this meeting of motions,
since no new matter can come into being, and there can be no such thing as an
immaterial sensory image. If so, there is no justification for restricting phantasms to
sense organs. Why should not a billiard ball be said to ‘sense’ the impact of the white,
and therefore to have a phantasm of it? All Hobbes’s account of sensation does is to
describe the route taken by a pressure wave so that there is an equal and opposite
reaction at the surface of the sense organ; it does not explain why only sense organs
should have phantasms.
Hobbes considers this question in De corpore 25, Article 5, headed ‘Not all bodies are
endowed with sensation’. He says:
Even though, as I have said, all sensation occurs by reaction, it is not necessarily the
case that whatever reacts has a sensation. I know there have been philosophers, and
learned ones at that, who have held that all bodies are endowed with sensation; nor do I
see how they could be refuted, if the nature of sensation consisted in reaction alone. But
even if bodies other than sentient ones had some sort of phantasm whenever they
reacted, it would cease as soon as the object went away. Unless they had organs capable
of retaining an impressed motion even after the object had gone away, as animals have,
their sensation would be unaccompanied by any memory that they had sensed — and
this has nothing to do with the sort of sensation we are talking about here.49
He doesn’t quite say that all reactions result in a phantasm, but he comes very close to
it. What he does say is that having a phantasm is not sufficient for sensation, because
sensation requires memory. In other words, bodies are consciously aware of what
impinges on them, or have sensations, only if they have a memory in which they can
retain the phantasm beyond the instant in which it occurs. This is identical to Descartes’
explanation of how we can sleep, given that the soul must always think, since thought is
the essence of the soul. When we are awake, we remember our previous thoughts; but
when we are asleep, we forget our thoughts from one instant to the next. Both Descartes
and Hobbes hold that memory is integral to consciousness, whether or not
consciousness requires a separate immaterial substance.
But Hobbes goes further in explaining why memory is necessary. In the same Article he
48 Adam & Tannery, Oeuvres de Descartes, vol.7 (Paris, Vrin, 1973), 182: ‘attamen cogitatio similis
potest esse in homine et bestia. Nam, cum affirmamus hominem currere, non habemus aliam cogitationem
ab ea quam habet canis videns currentem dominum suum; nihil igitur addit affirmatio vel negatio
cogitationibus simplicibus, nisi forte cogitationem quod nomina, ex quibus constat affirmatio, sint nomina
ejusdem rei in affirmante; quod non est complecti cogitatione plus quam rei similitudinem, sed eandem
similitudinem bis.’
49 ‘Etsi autem sensio, uti diximus, omnis fiat per reactionem, ut tamen quicquid reagit sensiat necessarium
non est. Scio fuisse philosophos quosdam, eosdemque viros doctos, qui corpora omnia sensu praedita esse
sustinuerunt; nec video, si natura sensionis in reactione sola collocaretur, quo modo refutari possint. Sed
etsi ex reactione etiam corporum aliorum phantasma aliquod nasceretur, illud tamen remoto objecto
statim cessaret; nam nisi ad retinendum motum impressum, etiam remoto objecto, apta habeant organa, ut
habent animalia, ita tantum sentient, ut nunquam sensisse se recordentur; id quod ad sensionem, de qua
nunc sermo institutus est, nihil attinet.’
By ‘sensation’, we customarily mean a sort of judgment, based on phantasms, about the
things which are the objects of sensation. More specifically, we compare and
distinguish phantasms; and this is possible only if the motion in the organ which gave
rise to a phantasm continues for some time, and the phantasm itself is brought back
during that time. So the sort of sensation I am talking about (which is what is meant by
‘sensation’ in ordinary language) is necessarily accompanied by a memory, which
enables us to compare earlier sensations with later ones, and to distinguish one from
Here, Hobbes seems to have forgotten that he is talking about animals as well as
humans, since he says that sensation is a form of judgment, and he talks of ‘us’.
Nevertheless, animals do have memories, and inanimate objects do not. Moreover,
Hobbes’s point that sensation is necessarily accompanied by memory is a good one,
since sense organs would be without a function unless they enabled animals to make
comparisons and discriminations.
Hobbes then draws a further conclusion, which is that we must have a successive
variety of phantasms in order to be said to sense anything, otherwise we have nothing to
compare our present phantasm with. He gives the example of someone confronted with
an unchanging perceptual state:
I might say that you were absorbed in the thing, and perhaps that you were looking at it;
but that you were oblivious. I would not say that you saw it. So it comes to the same
thing whether you sense one thing all the time, or do not sense anything at all.51
On the same grounds, in the Ten Dialogues,52 he says that a new-born baby does not
sense when it first opens its eyes, but only after it has had enough phantasms to be able
to distinguish one from another.
In short, there are three levels of awareness, and everything in the universe is aware at
one or other of these levels. At the lowest level, inanimate objects have phantasms when
they interact, but they do not have sensation. Animals do have sensation, because they
can remember previous phantasms, and compare and distinguish them. Humans have
the additional capacity to reflect on their sensations using language.
Coming back to Leibniz, he too, at least in his mature philosophy, holds that everything
in the universe is a perceiver. Monads that are not souls of animals perceive
unconsciously (they only have petites perceptions);53 animals perceive consciously; and
humans have the additional capacity for apperception, which includes reason, self-
awareness, and a moral sense.
Of course, there are still many differences between the two philosophers. The biggest
difference is that for Leibniz all substances are essentially perceivers and are not
50 ‘Nam per sensionem vulgo intelligimus aliquam de rebus objectis per phantasmata judicationem;
phantasmata scilicet comparando, et distinguendo; id quod, nisi motus in organo ille a quo phantasma
ortum est, aliquandiu maneat, ipsumque phantasma quandoque redeat, fieri non potest. Sensioni ergo, de
qua hic agitur, quaeque vulgo ita appellatur, necessario adhaeret memoria aliqua, qua priora cum
posterioribus comparari et alterum ab altero distingui possit.’
51 ‘attonitum esse et fortasse aspectare eum, sed stupentem dicerem, videre non dicerem; adeo sentire
simper idem, et non sentire, ad idem recidunt.’
52 English Works, ed. Molesworth (London, 1839–45 ), VII.83.
53 Catherine Wilson (op. cit., p.346) suggests that Leibniz may have derived the concept of a petite
perception from Hobbes. Although Hobbes doesn’t use the term, in De corpore 29.2 he gives the example
of our being able to hear the roar of the sea without consciously hearing individual waves — precisely the
same example as Leibniz later gives in the Nouveaux Essais, A.VI.6, p.54.
extended, whereas for Hobbes all substances are essentially extended, and are
perceivers only in so far as they interact with other substances (though they are in fact
doing this all the time). Nevertheless, it is remarkable that a materialist such as Hobbes
could talk of inanimate matter as perceiving at all.
As I hinted above, the reason for this is that Hobbes is a monist. As a materialist monist,
he is committed to denying any absolute difference in kind between inanimate bodies,
animal bodies, and human bodies. Even God is a body, or body in general.54 Their basic
ingredients are the same, and they operate in accordance with the same mechanical
laws. Consequently, both the animal function of sensation and the human function of
rational thought must be reducible to elements which are found throughout the material
world. For Hobbes the common element is the mutual action and reaction of colliding
bodies; and if this is describable in terms of phantasms in the case of sense perception,
then it ought to be describable in these same terms in the case of non-sentient bodies.
That is why the difference between the animate and the inanimate must be attributed to
something else, namely memory. Of course, memory in turn must be reducible to
mechanical interactions of bodies; but it is reasonable to suppose that only some bodies
are sufficiently complex to be able to store copies of phantasms (namely animal bodies),
whereas the majority are not.
But Leibniz is also a monist, albeit a spiritualist one. Consequently, he too must reduce
all the phenomena of nature to items of the same kind. He starts from the other end, by
making something analogous to human and animal perception the essential property of
substances, and he explains phenomena such as the extension and mass of bodies in
terms of these perceptions. So, paradoxically, although the two philosophies seem
diametrically opposed, they have it in common that if anything perceives, then in some
sense everything must perceive.
I am not going to argue that Leibniz got the idea that inanimate objects perceive from
Hobbes. Hobbes himself is quite cautious about it, and in the passage from De corpore
25.5 quoted above, he remarks that other philosophers have held that ‘all bodies are
endowed with sensation’. He doesn’t say which philosophers in particular he has in
mind, but vitalism was widespread in the seventeenth century. Indeed, one way of
looking at Leibniz’s philosophy is to see him as bringing about a reconciliation between
vitalism on the one hand, and mechanism on the other.
However, although Leibniz cannot be said to have got his vitalism from Hobbes, he
does seem to have been influenced by Hobbes’s theory that the difference between
inanimate bodies and animals is that the latter have memory. In his Theoria motus
abstracti, the work which owes more to Hobbes than any other, he writes as follows:
No conatus which does not result in motion lasts more than an instant, except in minds.
For what happens at an instant is a conatus, whereas what happens over time is the
motion of a body. This opens the door to arriving at the true distinction between body
and mind, which no-one has hitherto discovered. For every body is a momentary mind,
or a mind that lacks memory, because it does not retain its own conatus together with
the contrary conatus of another body beyond an instant. But two things are required for
there to be sensation, namely action and reaction, or in other words comparison, and
hence harmony — and also pleasure or pain, without which there is no sensation. So a
54 In the Appendix to the Latin version of Leviathan, chapter 3 (LW 3.561), Hobbes states boldly that
Deus est corpus; but it is ambiguous whether this should be read as ‘God is body’ (in general), or ‘God is
a body’. I prefer the former reading.
body lacks memory; it lacks any sensation of its actions and passions; and it lacks
The concept of a non-sentient body as a ‘momentary mind’ lacking memory is
absolutely crucial for his later conception of primitive monads as unconscious
perceivers belonging to the same ontological category as conscious perceivers. This is
clearly a debt he owes to Hobbes.
In his later writings, Leibniz lays more stress on the idea of distinctness, and he
sometimes implies that the difference between the perceptions of bare monads at one
extreme, and humans at the other, is one of degree, namely the extent to which they are
obscure and confused or clear and distinct. Indeed the main function of sense organs is
to focus the infinitely confused mass of forces acting on us into a distinct representation
of reality. However, he never abandoned the idea that memory is also essential for
distinguishing between bare monads and animals. For example, in Monadalogy §19 he
If we are willing to give the name ‘soul’ to everything which has perceptions and
appetites . . . , then all created simple substances (monads) could be called ‘souls’. But
since sensation is something more than simple perception, I am prepared to accept that
the general name ‘monad’ or ‘entelechy’ is sufficient for simple substances which only
have simple perceptions, and that we should reserve the name ‘soul’ for those which
have more distinct perceptions accompanied by memory.56
And a little later, in §25, he makes it clear that he is talking about all animals, and not
just human beings:
We also see that Nature has given heightened perceptions to animals, through the care it
has taken to supply them with sense organs . . .57
He then goes on to say how memory enables animals to reason in an empirical way
through the association of ideas. What distinguishes humans from animals is not a
superior consciousness of what we experience, but the ability to know necessary and
eternal truths over and above what is given in experience (§29)58 — another point in
common with Hobbes.
4. Conclusion
To sum up, Leibniz’s relationship with Hobbes is an excellent example of his
willingness to incorporate into his own philosophical system any good features he found
in other philosophers, however much he might disagree with them in other respects. He
55 G.IV.230: ‘Nullus conatus sine motu durat ultra momentum praeterquam in mentibus. Nam quod in
momento est conatus, id in tempore motus corporis: hic aperitur porta prosecuturo ad veram corporis
mentisque discriminationem, hactenus a nemine explicatam. Omne enim corpus est mens momentanea,
seu carens recordatione, quia conatum simul suum et alienum contrarium (duobus enim, actione et
reactione, seu comparatione ac proinde harmonia, ad sensum et sine quibus sensus nullus est, voluptatem
vel dolorem opus est) non retinet ultra momentum: ergo caret memoria, caret sensu actionum
passionumque suarum, caret cogitatione.’ Cf. the letter to Arnauld, G.I.73.
56 G.VI.610: ‘Si nous voulons appeller Ame tout ce qui a perceptions et appetites dans le sense que je
viens d’expliquer, toutes les substances simples ou Monades creées pourroient être appellées Ames; mais,
comme le sentiment est quelque chose de plus qu’une simple perception, je consens, que le nom general
de Monades et d’Entelechies suffise aux substances simples, qui n’auront que cela, et qu’on appelle Ames
seulement celles, dont la perception est plus distincte et accompagnée de memoire.’
57 G.VI.611: ‘Aussi voyons nous que la Nature a donné des perceptions relevées aux animaux par les
soins, qu’elle a pris de leur fournir des organes.’
58 G.VI.611.
completely rejected Hobbes’s materialism, alleged atheism, and most of his political
philosophy. There is no way Leibniz could be described as a Hobbesian, even in the
early 1670s when he was most immersed in Hobbes’s writings. Yet, despite their
differences, he found much to admire in Hobbes — not least his approach to logic and
truth, his concept of conatus, and the way he distinguished between the perceptions of
inanimate bodies, animals, and humans.
Full-text available
Dániel Schmal’s paper poses the question of why Leibniz assigned no reality to the infinitely small numbers used in the infinitesimal calculus. He argues that Leibniz’s position can be understood not so much from his mathematics but rather from his metaphysics and epistemology. Seen from this perspective, it is a common feature of the phenomena of everyday life and infinitely small numbers that they lack unity, therefore they are both categorized as well supported fictions without reality in Leibniz’s philosophy.
The study of algorithms, computations, and computability offers a major contact point between mathematics, technology, and philosophy. This chapter begins with a brief history of computations and the technical means used to support them. Summary accounts are given of two scholarly developments that provided much of the intellectual background for modern computation: attempts to express all reasoning as mathematics and attempts to reduce all of mathematics to simple, rule-bound symbol manipulation. This is followed by a discussion of the Turing machine, including a detailed explanation of why it can be said to cover all systems of rule-bound symbol manipulation. The universal Turing machine and its philosophical implications are also discussed. A two-dimensional classificatory scheme is offered for proposed constructions of computing devices with stronger computing powers than a Turing machine. This categorization serves to highlight the weaknesses of current proposals for such devices. In conclusion, it is emphasized that computation has to be understood as an intentional input-output process with high demands on reliability and lucidity. The study of computations and algorithms has much to learn from other studies of intentional human action, not least in the philosophy of technology.
This volume presents two Leibnizian writings, the Specimen of Philosophical Questions Collected from the Law and the Dissertation on Perplexing Cases. These works, originally published in 1664 and 1666, constitute, respectively, Leibniz’s thesis for the title of Master of Philosophy and his doctoral dissertation in law. Besides providing evidence of the earliest development of Leibniz’s thought and amazing anticipations of his mature views, they present a genuine intellectual interest, for the freshness and originality of Leibniz’s reflections on a striking variety of logico-philosophical puzzles drawn from the law. The Specimen addresses puzzling issues resulting from apparent conflicts between law and philosophy (the latter broadly understood as comprising also mathematics, as well as empirical sciences). The Dissertation addresses cases whose solution is puzzling because of the convoluted logical form of legal dispositions and contractual clauses, or because of conflicting priorities between concurring parties. In each case, Leibniz dissects the problems with the greatest ingenuity, disentangling their different aspects, and proposing solutions always reasonable and sometimes surprising. And he does not refrain from peppering his intellectual acrobatics with some humorous comments. bbbbbb
p class="p1">En este trabajo examinaremos la evolución del tratamiento de la noción de “espacio” en los escritos de juventud de Leibniz. Distinguiremos tres momentos del desarrollo de esta noción. En un primer momento, consideraremos la concepción del espacio como un “lugar universal” que el filósofo de Leipzig presentó entre 1669 y 1671. En segundo lugar, abordaremos algunos escritos físicos de 1672 en los que introdujo el movimiento en la definición de cuerpo. Esto lo llevó a rechazar su concepción anterior del espacio como “lugar universal”. En tercer lugar, consideraremos algunos textos redactados entre 1675 y 1676 en los que elaboró un examen de la noción de “espacio universal” que difiere de la concepción desarrollada en el periodo preparisino y que se vincula con el surgimiento de la noción de extensión como atributo de Dios.</p
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Markku Roinila (University of Helsinki, Finland), in Affects and Activity in Leibniz’s De affectibus, discusses the doctrine of substance that emerges from Leibniz’s unpublished early memoir De affectibus of 1679. The memoir marks a new stage in Leibniz’s views of the mind. The motivation for this change can be found in Leibniz’s rejection of the Cartesian theory of passion and action in the 1670s. Leibniz’s early Aristotelianism and some features of Cartesianism persisted, to which Leibniz added influences from Hobbes and Spinoza. His nascent dynamical concept of substance is seemingly a combination of old and fresh influences, representing a characteristically eclectic approach. The author argues that the influence of Hobbes is especially important in the memoir. To do that, he examines Leibniz’s development in the 1670s up to the De affectibus and considers the nature of affects in the memoir, especially the first affect which starts the thought sequence. This first affect of pleasure or pain is the key to Leibniz’s theory of active substances and in this way to the whole of Leibniz’s moral psychology and ethical metaphysics.
Here the young Leibniz (he was only 18 years old when writing the Specimen) advances his original and bold thesis that, despite the jurists’ contempt for philosophy, the law without the guidance of philosophy “would be an inextricable labyrinth”. On the other hand, as he argues deploying an impressive array of sources, both canonical law and civil law contain a considerable amount of philosophical content, pertaining not only to practical philosophy, but also to logic, physics, and other disciplines, including mathematics and metaphysics (a point on which Leibniz will insist, with an explicit reference to the Specimen, in the preface to the Nova methodus [A VI/1 265]).
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