Ideas from 'Letters to Antoine Arnauld' by Gottfried Leibniz [1686], by Theme Structure

[found in 'The Leibniz-Arnauld Correspondence' by Leibniz,Gottfried (ed/tr Mason,HT/Parkinson,GHR) [Manchester UP 1967,]].

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1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Wisdom is the science of happiness
                        Full Idea: Wisdom is the science of happiness.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1690.03.23)
                        A reaction: That probably comes down to common sense, or Aristotle's 'phronesis'. I take wisdom to involve understanding, as well as the quest for happiness.
1. Philosophy / A. Wisdom / 2. Wise People
Wise people have fewer acts of will, because such acts are linked together
                        Full Idea: The wiser one is, the fewer separate acts of will one has and the more one's views and acts of will are comprehensive and linked together.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.04.12)
                        A reaction: [letter to Landgrave, about Arnauld] It is unusual to find a philosopher who actually tries to analyse the nature of wisdom, instead of just paying lipservice to it. I take Leibniz to be entirely right here. He equates wisdom with rational behaviour.
1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
Metaphysics is geometrical, resting on non-contradiction and sufficient reason
                        Full Idea: I claim to give metaphysics geometric demonstrations, assuming only the principle of contradiction (or else all reasoning becomes futile), and that nothing exists without a reason, or that every truth has an a priori proof, from the concept of terms.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.07.4/14 XI)
                        A reaction: For the last bit, see Idea 12910. This idea is the kind of huge optimism about metaphysic which got it a bad name after Kant, and in modern times. I'm optimistic about metaphysics, but certainly not about 'geometrical demonstrations' of it.
2. Reason / D. Definition / 4. Real Definition
Definitions can only be real if the item is possible
                        Full Idea: Definitions to my mind are real, when one knows that the thing defined is possible; otherwise they are only nominal, and one must not rely on them.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.07.4/14 XI)
                        A reaction: It is interesting that things do not have to actual to have real definitions. For Leibniz, what is possible will exist in the mind of God. For me what is possible will exist in the potentialities of the powers of what is actual.
3. Truth / A. Truth Problems / 1. Truth
The predicate is in the subject of a true proposition
                        Full Idea: In a true proposition the concept of the predicate is always present in the subject.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.07.4/14 X)
                        A reaction: This sounds very like the Kantian notion of an analytic truth, but Leibniz is applying it to all truths. So Socrates must contain the predicate of running as part of his nature (or essence?), if 'Socrates runs' is to be true.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
There is no multiplicity without true units
                        Full Idea: There is no multiplicity without true units.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1687.04.30)
                        A reaction: Hence real numbers do not embody 'multiplicity'. So either they don't 'embody' anything, or they embody 'magnitudes'. Does this give two entirely different notions, of measure of multiplicity and measures of magnitude?
7. Existence / A. Nature of Existence / 3. Being / g. Particular being
What is not truly one being is not truly a being either
                        Full Idea: What is not truly one being is not truly a being either.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1687.04.30), quoted by Alain Badiou - Briefings on Existence 1
                        A reaction: Badiou quotes this as identifying Being with the One. I say Leibniz had no concept of 'gunk', and thought everything must have a 'this' identity in order to exist, which is just the sort of thing a logician would come up with.
7. Existence / C. Structure of Existence / 5. Supervenience / a. Nature of supervenience
A thing 'expresses' another if they have a constant and fixed relationship
                        Full Idea: One thing 'expresses' another (in my terminology) when there exists a constant and fixed relationship between what can be said of one and of the other. This is the way that a perspectival projection expresses its ground-plan.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1687.10.09)
                        A reaction: Arnauld was puzzled by what Leibniz might mean by 'express', and it occurs to me that Leibniz was fishing for the modern concept of 'supervenience'. It also sounds a bit like the idea of 'covariance' between mind and world. Maybe he means 'function'.
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
A substance contains the laws of its operations, and its actions come from its own depth
                        Full Idea: Each indivisible substance contains in its nature the law by which the series of its operations continues, and all that has happened and will happen to it. All its actions come from its own depths, except for dependence on God.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1688.01.4/14)
                        A reaction: I take the combination of 'laws' and 'forces', which Leibniz attributes to Aristotelian essences, to be his distinctive contribution towards giving us an Aristotelian metaphysic which is suitable for modern science.
9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
Philosophy needs the precision of the unity given by substances
                        Full Idea: Philosophy cannot be better reduced to something precise, than by recognising only substances or complete beings endowed with a true unity, with different states that succeed one another; all else is phenomena, abstractions or relations.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1687.04.30), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 7
                        A reaction: This idea bothers me. Has the whole of modern philosophy been distorted by this yearning for 'precision'? It has put mathematicians and logicians in the driving seat. Do we only attribute unity because it suits our thinking?
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
Accidental unity has degrees, from a mob to a society to a machine or organism
                        Full Idea: There are degrees of accidental unity, and an ordered society has more unity than a chaotic mob, and an organic body or a machine has more unity than a society.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1687.04.30)
                        A reaction: This immediately invites questions about the extremes. Why does the very highest degree of 'accidental unity' not achieve 'true unity'? And why cannot a very ununified aggregate have a bit of unity (as in unrestricted mereological composition)?
9. Objects / B. Unity of Objects / 1. Unifying an Object / c. Unity as conceptual
We find unity in reason, and unity in perception, but these are not true unity
                        Full Idea: A pair of diamonds is merely an entity of reason, and even if one of them is brought close to another, it is an entity of imagination or perception, that is to say a phenomenon; contiguity, common movement and the same end don't make substantial unity.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1687.04.30), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 7
                        A reaction: This invites the question of what you have to do to two objects to give them substantial unity. The distinction between unity 'of reason' and unity 'of perception' is good.
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
A body is a unified aggregate, unless it has an indivisible substance
                        Full Idea: One will never find a body of which it may be said that it is truly one substance, ...because entities made up by aggregation have only as much reality as exists in the constituent parts. Hence the substance of a body must be indivisible.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.11)
                        A reaction: Leibniz rejected atomism, and he evidently believed that pure materialists must deny the real existence of physical objects. Common sense suggests that causal bonds bestow a high degree of unity on bodies (if degrees are allowed).
Unity needs an indestructible substance, to contain everything which will happen to it
                        Full Idea: Substantial unity requires a complete, indivisible and naturally indestructible entity, since its concept embraces everything that is to happen to it, which cannot be found in shape or motion.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.11.28/12.8)
                        A reaction: Hence if a tile is due to be broken in half (Arnauld's example), it cannot have had unity in the first place. To what do we refer when we say 'the tile was broken'?
Every bodily substance must have a soul, or something analogous to a soul
                        Full Idea: Every bodily substance must have a soul, or at least an entelechy which is analogous to the soul.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1687.10.09)
                        A reaction: He routinely commits to a 'soul', and then pulls back and says it may only be an 'analogy'. He had deep doubts about his whole scheme, which emerged in the late correspondence with Des Bosses. This not monads, says Garber.
9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance
Aggregates don’t reduce to points, or atoms, or illusion, so must reduce to substance
                        Full Idea: In aggregates one must necessarily arrive either at mathematical points from which some make up extension, or at atoms (which I dismiss), or else no reality can be found in bodies, or finally one must recognises substances that possess a true unity.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1687.04.30), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 2
                        A reaction: Garber calls this Leibniz's Aggregate Argument. Leibniz is, of course, talking of physical aggregates which have unity. He consistently points out that a pile of logs has no unity at all. But is substance just that-which-provides-unity?
9. Objects / D. Essence of Objects / 1. Essences of Objects
Basic predicates give the complete concept, which then predicts all of the actions
                        Full Idea: Apart from those that depend on others, one must only consider together all the basic predicates in order to form the complete concept of Adam adequate to deduce from it everything that is ever to happen to him, as much as is necessary to account for it.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.06)
                        A reaction: This (implausibly) goes beyond mere prediction of properties. Eve's essence seems to be relevant to Adam's life. Note that the complete concept is not every predicate, but only those 'necessary' to predict the events. Cf Idea 13082.
Essences exist in the divine understanding
                        Full Idea: Essences exist in the divine understanding before one considers will.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.07.4/14 X)
                        A reaction: This is a sort of religious neo-platonism. The great dream seems to be that of mind-reading God, and the result is either Pythagoras (it's numbers!), or Plato (it's pure ideas!), or this (it's essences!). See D.H.Lawrence's poem on geranium and mignottes.
9. Objects / D. Essence of Objects / 6. Essence as Unifier
Bodies need a soul (or something like it) to avoid being mere phenomena
                        Full Idea: Every substance is indivisible and consequently every corporeal substance must have a soul or at least an entelechy which is analogous to the soul, since otherwise bodies would be no more than phenomena.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], G II 121), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 2
                        A reaction: There is a large gap between having 'a soul' and having something 'analogous to a soul'. I take the analogy to be merely as originators of action. Leibniz wants to add appetite and sensation to the Aristotelian forms (but knows this is dubious!).
9. Objects / D. Essence of Objects / 10. Essence as Species
Truths about species are eternal or necessary, but individual truths concern what exists
                        Full Idea: The concept of a species contains only eternal or necessary truths, whereas the concept of an individual contains, regarded as possible, what in fact exists or what is related to the existence of things and to time.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.06)
                        A reaction: This seems to be what is behind the preference some have for kind-essences rather than individual essences. But the individual must be explained, as well as the kind. Not all tigers are identical. The two are, of course, compatible.
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
If varieties of myself can be conceived of as distinct from me, then they are not me
                        Full Idea: I can as little conceive of different varieties of myself as of a circle whose diameters are not all of equal length. These variations would all be distinct one from another, and thus one of these varieties of myself would necessarily not be me.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.05.13)
                        A reaction: This seems to be, at the very least, a rejection of any idea that I could have a 'counterpart'. It is unclear, though, where he would place a version of himself who learned a new language, or who might have had, but didn't have, a haircut.
If someone's life went differently, then that would be another individual
                        Full Idea: If the life of some person, or something went differently than it does, nothing would stop us from saying that it would be another person, or another possible universe which God had chosen. So truly it would be another individual.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.07.14)
                        A reaction: Plantinga quotes this as an example of 'worldbound individuals'. This sort of remark leads to people saying that Leibniz believes all properties are essential, since they assume that his notion of essence is bound up with identity. But is it?
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
I cannot think my non-existence, nor exist without being myself
                        Full Idea: I am assured that as long as I think, I am myself. For I cannot think that I do not exist, nor exist so that I be not myself.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.05.13)
                        A reaction: Elsewhere he qualifies the Cogito, but here he seems to straighforwardly endorse it.
11. Knowledge Aims / B. Certain Knowledge / 5. Cogito Critique
I can't just know myself to be a substance; I must distinguish myself from others, which is hard
                        Full Idea: It is not enough for understanding the nature of myself, that I feel myself to be a thinking substance, one would have to form a distinct idea of what distinguishes me from all other possible minds; but of that I have only a confused experience.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.07.4/14)
                        A reaction: Not a criticism I have encountered before. Does he mean that I might be two minds, or might be a multitude of minds? It seems to be Hume's problem, that you are aware of experiences, but not of the substance that unites them.
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
Nothing should be taken as certain without foundations
                        Full Idea: Nothing should be taken as certain without foundations.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1687.04.30)
                        A reaction: This might leave open the option, if you were a modern 'Fallibilist', that something might lack foundations, and so not be certain, and yet still qualify as 'knowledge'. That is my view. Knowledge resides somewhere between opinion and certainty.
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
Nature is explained by mathematics and mechanism, but the laws rest on metaphysics
                        Full Idea: One must always explain nature along mathematical and mechanical lines, provided one knows that the very principles or laws of mechanics or of force do not depend upon mathematical extension alone but upon certain metaphysical reasons.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.07.4/14 X)
                        A reaction: I like this, and may even use it as the epigraph of my masterwork. Recently Stephen Hawking (physicist) has been denigrating philosophy, but I am with Leibniz on this one.
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
To fully conceive the subject is to explain the resulting predicates and events
                        Full Idea: Even in the most contingent truths, there is always something to be conceived in the subject which serves to explain why this predicate or event pertains to it, or why this has happened rather than not.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.06)
                        A reaction: The last bit, about containing what has happened, seems absurd, but the rest of it makes sense. It is just the Aristotelian essentialist view, that a full understanding of the inner subject will both explain and predict the surface properties.
15. Nature of Minds / A. Nature of Mind / 1. Mind / b. Purpose of mind
Mind is a thinking substance which can know God and eternal truths
                        Full Idea: Minds are substances which think, and are capable of knowing God and of discovering eternal truths.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1687.10.09)
                        A reaction: 'God' is there because the ability to grasp the ontological argument is seen as basic. Note a firm commitment to substance-dualism, and a rationalist commitment to the spotting of necessary truths as basic. He is not totally wrong.
15. Nature of Minds / A. Nature of Mind / 7. Animal Minds
It seems probable that animals have souls, but not consciousness
                        Full Idea: It appears probable that the brutes have souls, though they are without consciousness.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.12.08)
                        A reaction: This will be a response to Descartes, who allowed animals sensations, but not minds or souls. Personally I cannot make head or tail of Leibniz's claim. What makes it "apparent" to him?
16. Persons / F. Free Will / 7. Compatibilism
Everything which happens is not necessary, but is certain after God chooses this universe
                        Full Idea: It is not the case that everything which happens is necessary; rather, everything which happens is certain after God made choice of this possible universe, whose notion contains this series of things.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.05)
                        A reaction: I think this distinction is best captured as 'metaphysical necessity' (Leibniz's 'necessity'), and 'natural necessity' (his 'certainty'). 'Certainty' seems a bad word, as it is either certain de dicto or de re. Is God certain, or is the thing certain?
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
Concepts are what unite a proposition
                        Full Idea: There must always be some basis for the connexion between the terms of a proposition, and it is to be found in their concepts.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.07.4/14 X)
                        A reaction: We face the problem that bothered Russell, of the unity of the proposition. We are also led to the question of HOW our concepts connect the parts of a proposition. Do concepts have valencies? Are they incomplete, as Frege suggests?
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
Beauty increases with familiarity
                        Full Idea: The more one is familiar with things, the more beautiful one finds them.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1688.01.4/14)
                        A reaction: This is always the reply given to those who say that science kills our sense of beauty. The first step in aesthetic life is certainly to really really pay attention to things.
22. Metaethics / B. The Good / 2. Happiness / a. Nature of happiness
Happiness is advancement towards perfection
                        Full Idea: Happiness, or lasting contentment, consists of continual advancement towards a greater perfection.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1690.03.23)
                        A reaction: To the modern mind this smacks of the sort of hubris to which only the religious mind can aspire, but it's still rather nice. The idea of grubby little mammals approaching perfection sounds wrong, but which other animal has even thought of perfection?
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
I think the corpuscular theory, rather than forms or qualities, best explains particular phenomena
                        Full Idea: I still subscribe fully to the corpuscular theory in the explanation of particular phenomena; in this sphere it is of no value to speak of forms or qualities.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 14.07.1686)
                        A reaction: I am puzzled by Garber's summary in Idea 12728, and a bit unclear on Leibniz's views on atoms. More needed.
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
Each possible world contains its own laws, reflected in the possible individuals of that world
                        Full Idea: As there exist an infinite number of possible worlds, there exists also an infinite number of laws, some peculiar to one world, some to another, and each individual of any one world contains in the concept of him the laws of his world.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.06)
                        A reaction: Since Leibniz's metaphysics is thoroughly God-driven, he will obviously allow God to create any laws He wishes, and hence scientific essentialism seems to be rejected, even though Leibniz is keen on essences. Unless the stuff is different...
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
Motion alone is relative, but force is real, and establishes its subject
                        Full Idea: Motion in itself separated from force is merely relative, and one cannot establish its subject. But force is something real and absolute.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1688.01.4/14)
                        A reaction: The striking phrase here is that force enables us to 'establish its subject'. That is, force is at the heart of reality, and hence, through causal relations, individuates objects. That's how I read it.
28. God / B. Proving God / 3. Proofs of Evidence / e. Miracles
Miracles are extraordinary operations by God, but are nevertheless part of his design
                        Full Idea: Miracles, or the extraordinary operations of God, none the less belong within the general order; they are in conformity with the principal designs of God, and consequently are included in the notion of this universe, which is the result of those designs.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.05)
                        A reaction: Some philosophers just make up things to suit themselves. What possible grounds can he have for claiming this? At best this is tautological, saying that, by definition, if anything at all happens, it must be part of God's design. Move on to Hume…
Everything, even miracles, belongs to order
                        Full Idea: Everything, even miracles, belongs to order.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.07.4/14 X)
                        A reaction: This is very reminiscent of Plato, for whom there was no more deeply held belief than that the cosmos is essentially orderly. Coincidences are a nice problem, if they are events with no cause.
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
Immortality without memory is useless
                        Full Idea: Immortality without memory would be useless.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.07.4/14 X)
                        A reaction: I would say that having a mind of any sort needs memory. The question for immortality is whether it extends back to human life. See 'Wuthering Heights' (c. p90) for someone who remembers Earth as so superior to paradise that they long to return there.
29. Religion / D. Religious Issues / 2. Immortality / b. Soul
The soul is indestructible and always self-aware
                        Full Idea: Not only is the soul indestructible, but it always knows itself and remains self-conscious.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.11)
                        A reaction: Personally I am not even self-aware during much of my sleeping hours, and I would say that I cease to be self-aware if I am totally absorbed in something on which I concentrate.
29. Religion / D. Religious Issues / 2. Immortality / c. Animal Souls
Animals have souls, but lack consciousness
                        Full Idea: It appears probable that animals have souls although they lack consciousness.
                        From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1686.11)
                        A reaction: Personally I would say that they lack souls but have consciousness, but then I am in no better position to know the answer than Leibniz was. Arnauld asks what would happen to the souls of 100,000 silkworms if they caught fire!