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All the ideas for 'Thinking About Mathematics', 'On Nature Itself (De Ipsa Natura)' and 'The Philosophy of Art (2nd ed)'

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47 ideas

1. Philosophy / F. Analytic Philosophy / 3. Analysis of Preconditions
'Necessary' conditions are requirements, and 'sufficient' conditions are guarantees [Davies,S]
     Full Idea: A 'necessary' condition for something's being an X is condition that all Xs must satisfy. ...A 'sufficient' condition for something's being an X is a condition that, when satisfied, guarantees that what satisfies it is an X.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 2.1)
     A reaction: By summarising this I arrive at the requirement/guarantee formulation, which I am rather pleased with. What is required for rain, and what guarantees rain?
2. Reason / D. Definition / 1. Definitions
A definition of a thing gives all the requirements which add up to a guarantee of it [Davies,S]
     Full Idea: If we specify the 'necessary' conditions that are 'sufficient' for something's being an X, that is a combination of conditions such that all and only Xs meet them, which is the hallmark of a definition of X-hood.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 2.1)
     A reaction: There are, of course, many other ways to define something, as shown in the 2.D Reason | Definition section of this database. This nicely summarises the classical view.
2. Reason / D. Definition / 13. Against Definition
Feminists warn that ideologies use timeless objective definitions as a tool of repression [Davies,S]
     Full Idea: According to the feminist critique, ideologies that operate as tools of political repression are falsely represented as definitions possessing a timeless, natural, asocial, universal objectivity.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 2.2)
     A reaction: I suppose this does not just apply to definitions, but to all expressions of ideologically repressive strategy. I'm trying to think of an example of a specifically feminist problem case. Davies doesn't cite anyone.
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
     Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2)
     A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
     Full Idea: It is surely wise to identify the positions in the natural numbers structure with their counterparts in the integer, rational, real and complex number structures.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2)
     A reaction: The point is that this might be denied, since 3, 3/1, 3.00.., and -3*i^2 are all arrived at by different methods of construction. Natural 3 has a predecessor, but real 3 doesn't. I agree, intuitively, with Shapiro. Russell (1919) disagreed.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
Cauchy gave a formal definition of a converging sequence. [Shapiro]
     Full Idea: A sequence a1,a2,... of rational numbers is 'Cauchy' if for each rational number ε>0 there is a natural number N such that for all natural numbers m, n, if m>N and n>N then -ε < am - an < ε.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 7.2 n4)
     A reaction: The sequence is 'Cauchy' if N exists.
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Categories are the best foundation for mathematics [Shapiro]
     Full Idea: There is a dedicated contingent who hold that the category of 'categories' is the proper foundation for mathematics.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 10.3 n7)
     A reaction: He cites Lawvere (1966) and McLarty (1993), the latter presenting the view as a form of structuralism. I would say that the concept of a category will need further explication, and probably reduce to either sets or relations or properties.
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
     Full Idea: Zermelo said that for each number n, its successor is the singleton of n, so 3 is {{{null}}}, and 1 is not a member of 3. Von Neumann said each number n is the set of numbers less than n, so 3 is {null,{null},{null,{null}}}, and 1 is a member of 3.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2)
     A reaction: See Idea 645 - Zermelo could save Plato from the criticisms of Aristotle! These two accounts are cited by opponents of the set-theoretical account of numbers, because it seems impossible to arbitrate between them.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
     Full Idea: The structuralist vigorously rejects any sort of ontological independence among the natural numbers; the essence of a natural number is its relations to other natural numbers.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1)
     A reaction: This seems to place the emphasis on ordinals (what order?) rather than on cardinality (how many?). I am strongly inclined to think that this is the correct view, though you can't really have relations if there is nothing to relate.
A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
     Full Idea: A 'system' is a collection of objects with certain relations among them; a 'pattern' or 'structure' is the abstract form of a system, highlighting the interrelationships and ignoring any features they do not affect how they relate to other objects.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1)
     A reaction: Note that 'ignoring' features is a psychological account of abstraction, which (thanks to Frege and Geach) is supposed to be taboo - but which I suspect is actually indispensable in any proper account of thought and concepts.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
     Full Idea: The thesis that principles of arithmetic are derivable from the laws of logic runs against a now common view that logic itself has no ontology. There are no particular logical objects. From this perspective logicism is a non-starter.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 5.1)
     A reaction: This criticism strikes me as utterly devastating. There are two routes to go: prove that logic does have an ontology of objects (what would they be?), or - better - deny that arithmetic contains any 'objects'. Or give up logicism.
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
     Full Idea: Term Formalism is the view that mathematics is just about characters or symbols - the systems of numerals and other linguistic forms. ...This will cover integers and rational numbers, but what are real numbers supposed to be, if they lack names?
     From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.1)
     A reaction: Real numbers (such as pi and root-2) have infinite decimal expansions, so we can start naming those. We could also start giving names like 'Harry' to other reals, though it might take a while. OK, I give up.
Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
     Full Idea: Game Formalism likens mathematics to chess, where the 'content' of mathematics is exhausted by the rules of operating with its language. ...This, however, leaves the problem of why the mathematical games are so useful to the sciences.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.2)
     A reaction: This thought pushes us towards structuralism. It could still be a game, but one we learned from observing nature, which plays its own games. Chess is, after all, modelled on warfare.
Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
     Full Idea: The Deductivist version of formalism (sometimes called 'if-thenism') says that the practice of mathematics consists of determining logical consequences of otherwise uninterpreted axioms.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 6.2)
     A reaction: [Hilbert is the source] More plausible than Term or Game Formalism (qv). It still leaves the question of why it seems applicable to nature, and why those particular axioms might be chosen. In some sense, though, it is obviously right.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
     Full Idea: Critics commonly complain that the intuitionist restrictions cripple the mathematician. On the other hand, intuitionist mathematics allows for many potentially important distinctions not available in classical mathematics, and is often more subtle.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 7.1)
     A reaction: The main way in which it cripples is its restriction on talk of infinity ('Cantor's heaven'), which was resented by Hilbert. Since high-level infinities are interesting, it would be odd if we were not allowed to discuss them.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
     Full Idea: I classify conceptualists according to what they say about properties or concepts. If someone classified properties as existing independent of language I would classify her as a realist in ontology of mathematics. Or they may be idealists or nominalists.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 2.2.1)
     A reaction: In other words, Shapiro wants to eliminate 'conceptualist' as a useful label in philosophy of mathematics. He's probably right. All thought involves concepts, but that doesn't produce a conceptualist theory of, say, football.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
'Impredicative' definitions refer to the thing being described [Shapiro]
     Full Idea: A definition of a mathematical entity is 'impredicative' if it refers to a collection that contains the defined entity. The definition of 'least upper bound' is impredicative as it refers to upper bounds and characterizes a member of this set.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2)
     A reaction: The big question is whether mathematics can live with impredicative definitions, or whether they threaten to be viciously circular, and undermine the whole enterprise.
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
Substance is a force for acting and being acted upon [Leibniz]
     Full Idea: The very substance in things consists of a force for acting and being acted upon.
     From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §08)
     A reaction: Garber places this text just before the spiritual notion of monads took a grip on Leibniz. He seems to have thought that only some non-physical entity, with appetite and perception, could generate force. Wrong.
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
     Full Idea: Rationalism is a long-standing school that can be characterized as an attempt to extend the perceived methodology of mathematics to all of knowledge.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 1.1)
     A reaction: Sometimes called 'Descartes's Dream', or the 'Enlightenment Project', the dream of proving everything. Within maths, Hilbert's Programme aimed for the same certainty. Idea 22 is the motto for the opposition to this approach.
14. Science / D. Explanation / 2. Types of Explanation / h. Explanations by function
Final causes can help with explanations in physics [Leibniz]
     Full Idea: Final causes not only advance virtue and piety in ethics and natural theology, but also help us to find and lay bare hidden truths in physics itself.
     From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §04)
     A reaction: This rearguard action against the attack on teleology is certainly aimed at Spinoza. The notion of purpose still seems to have a role to play in evolutionary biology, but probably not in physics.
17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism
Something rather like souls (though not intelligent) could be found everywhere [Leibniz]
     Full Idea: Nor is there any reason why souls or things analogous to souls should not be everywhere, even if dominant and consequently intelligent souls, like human souls, cannot be everywhere.
     From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §12)
     A reaction: He is always flirting with panpsychism, though he doesn't seem to offer any account of how these little baby souls can be built up to create one intelligent soul, the latter being indivisible. 'Souls' are very different from things 'analous to souls'!
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
Aesthetic experience involves perception, but also imagination and understanding [Davies,S]
     Full Idea: It was suggested that aesthetic experience isn't solely perceptual. It's infused by a cognitive but non-conceptual process described by Kant as involving the free play of the imagination and the understanding.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 1.2)
     A reaction: This fits literature very well, painting quite well, and music hardly at all.
21. Aesthetics / A. Aesthetic Experience / 3. Taste
The faculty of 'taste' was posited to explain why only some people had aesthetic appreciation [Davies,S]
     Full Idea: To explain why not everyone who is prepared to encounter a thing's aesthetic properties can recognise them, ...eighteenth century theorists posited the existence of a special faculty of aesthetic perception, that of taste.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 1.2)
     A reaction: But there seem to be two aspects to taste - first the capacity to enjoy some sorts of art, and second the ability to discriminate the good from the bad. The latter is 'standards' of taste (Hume's title). Do non-musical people lack taste?
21. Aesthetics / A. Aesthetic Experience / 6. The Sublime
The sublime is negative in awareness of insignificance, and positive in showing understanding [Davies,S]
     Full Idea: An example of the sublime is the vastness of the night sky. ...It includes negative feelings of insignificance in the face of nature's indifference, power and magnitude, but is positive in that we are capable of comprehending such matters.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 1.2)
     A reaction: The negative part seems to be a very intellectual experience, with close links to religion, and may be the experience that leads to deism (belief in God's indifference).
21. Aesthetics / B. Nature of Art / 1. Defining Art
The idea that art forms are linked into a single concept began in the 1740s [Davies,S]
     Full Idea: The first to link the art forms together explicitly and to separate them from other disciplines and activities were the authors of encyclopedias and books in the 1740s and 1750s.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 1.2)
     A reaction: Intriguing that no individual seems to get the credit (or blame). Presumably our modern Aesthetics (applied to art) couldn't exist before this move was made - and yet there is plenty of aesthetic discussion in early Greek philosophy.
Defining art as representation or expression or form were all undermined by the avant-garde [Davies,S]
     Full Idea: The avant-garde art of the twentieth century played a significant role in defeating definitions that had prevailed in earlier times, such as ones maintaining that art is representation, expression or significant form
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 2.2)
     A reaction: I really think the first rule of philosophical aesthetics is 'ignore Marcel Duchamp'. We wouldn't give up our idea of philosophy if someone managed to publish a long string of expletives in a philosophy journal. Would we??
'Aesthetic functionalism' says art is what is intended to create aesthetic experiences [Davies,S]
     Full Idea: 'Aesthetic functionalism' maintains that something is an artwork if it is intended to provide the person who contemplates it for its own sake with an aesthetic experience of a significant magnitude on the basis of its aesthetic features.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 2.5)
     A reaction: [Beardsley is cited as having this view] For this you need to know what an aesthetic 'feature' is, and you'd have to indepdently recognise aesthetic experience.
21. Aesthetics / B. Nature of Art / 4. Art as Expression
Music may be expressive by being 'associated' with other emotional words or events [Davies,S]
     Full Idea: One view explains music's expressiveness as 'associative'. Through being regularly associated with emotionally charged words or events, particular musical ideas become associated with emotions or moods.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 6.4)
     A reaction: This is a more promising theory. I take the feeling in music to be parasitic on other feelings we have, and other triggers that evoke them. I'm particularly struck with story-telling (which Levinson and Robinson also like).
It seems unlikely that sad music expresses a composer's sadness; it takes ages to write [Davies,S]
     Full Idea: The 'expression theory' holds that if music is sad that is because it expresses the composer's sadness, ...but composers take a long time composing sad works, and may even been gleeful at receiving payment for it.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 6.4)
     A reaction: [compressed] Pretty conclusive. I see composing as like acting. Just as you can put on a happy or sad face, so a composer can discover music that feels sad or happy. Three movement sonatas don't fit expression at all.
21. Aesthetics / B. Nature of Art / 6. Art as Institution
The 'institutional' theory says art is just something appropriately placed in the 'artworld' [Davies,S]
     Full Idea: The 'institutional' theory says to be an artwork, an artwork must be appropriately placed within a web of practices, roles and frameworks that comprise an informally organised institution, the artworld.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 2.5)
     A reaction: [He cites George Dickie] This theory seems to entirely developed to cope with the defiant gesture of Marcel Duchamp. Once I am an established artist, I have the authority to label anything I like as a work of art. Silly.
21. Aesthetics / B. Nature of Art / 8. The Arts / a. Music
Music is too definite to be put into words (not too indefinite!) [Davies,S]
     Full Idea: Mendelssohn said that what music expresses is not too indefinite to put into words but, on the contrary, it is too definite.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 6.4)
     A reaction: Not sure whether that is true, but it is a lovely remark. It certainly challenges the naive philosophical view that words are the most precise mode of expression.
21. Aesthetics / C. Artistic Issues / 1. Artistic Intentions
The title of a painting can be vital, and the artist decrees who the portrait represents [Davies,S]
     Full Idea: The title as given by the artist is something we might need to know (Brueghel's 'Icarus', for example), ...and if a painting depicts one of two twins, it will be the artist's intention that settles which one it is.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 3.5)
     A reaction: Those two points strike me as conclusively in favour of the importance of an artist's perceived intentions.
We must know what the work is meant to be, to evaluate the artist's achievement [Davies,S]
     Full Idea: Learning that a work is a copy of an earlier work, or is done in the style of some other artist, is relevant to an evaluation of what its creator has achieved.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 3.6)
     A reaction: A simple but powerful point. We evaluate a forgery as an achievement, and the original plate of a great print as the focus of the achievement. We can assess the achievement of a poem in any printed copy. But what about perfect painting replicas?
Intentionalism says either meaning just is intention, or ('moderate') meaning is successful intention [Davies,S]
     Full Idea: 'Actual intentionalism' holds that work's meaning is what its author intended, ...while 'moderate actual intentionalism' allows that the author's intention determines the work's meaning only if that intention is carried through successfully.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 5.3)
     A reaction: [He cites Noel Carroll for the moderate version] D.H. Lawrence, probably with a dose of Freud, said 'trust the work, not the artist' (of Moby Dick, I think). The thought is that authors only half know intentions, and works reveal them.
The meaning is given by the audience's best guess at the author's intentions [Davies,S]
     Full Idea: According to the 'hypothetical intentionalist', the work's meaning is determined by the intentions the audience is best justified in attributing to the author, whether or not these are the ones the author actually had.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 5.4)
     A reaction: [Nehamas, Levinson and Jenefer Robinson are cited] This opens the door for psychiatric interpretations of 'Hamlet', and so on. The experts disagree over the nature of the audience needed to do the job.
21. Aesthetics / C. Artistic Issues / 2. Copies of Art
If we could perfectly clone the Mona Lisa, the original would still be special [Davies,S]
     Full Idea: If we could duplicate 'Mona Lisa', we're likely to be concerned to track the original and keep it separate from its clones, even if we judge that the clone isn't inferior to the original when the goal is art appreciation.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 4.3)
     A reaction: But why? Is it just a sentimental attachment to what Leonardo worked on? Does the original manuscript of a work of literature have the same importance? We treasure such things, but not for aesthetic reasons.
Art that is multiply instanced may require at least one instance [Davies,S]
     Full Idea: Some multiply instanced artworks, such as novel and poems, must have at least one instance.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 4.4)
     A reaction: This is a comment on the idea that all artworks, even oil paintings and buildings are potentially multiply instanced (so the work is the type - Wollheim's view, not one of the tokens).
21. Aesthetics / C. Artistic Issues / 4. Emotion in Art
Music isn't just sad because it makes the listener feel sad [Davies,S]
     Full Idea: The 'arousal' theory says music is sad because it moves the hearer to sadness, ...but this seems to get things back to front, because we normally think it is because the music is sad that it moves the listener to sadness.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 6.4)
     A reaction: The objection is right. If Beethoven's 'Ode to Joy' always makes me feel sad (because it is so hopelessly optimistic), then that makes the music sad. Is the theory saying that there are no feelings in the music?
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
If the depiction of evil is glorified, that is an artistic flaw [Davies,S]
     Full Idea: One case when the depiction of immorality becomes an artistic flaw …is when it is presented in brutal detail in a way that glorifies it. The celebration of evil corrodes the work's artistic value.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 8.7)
     A reaction: This doesn't allow for the case where the evil is celebrated in one part of a novel, yet the novel as a whole does not endorse the evil. The Marquis de Sade seems to have fully celebrated what we take to be evil.
It is an artistic defect if excessive moral outrage distorts the story, and narrows our sympathies [Davies,S]
     Full Idea: The positive moral stance of a story can be an artistic defect where it shapes the story in an inappropriate fashion. If it displays disproportionate moral outrage, …it reveals a lack of toleration, compassion, or insight into its subject-matter.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 8.7)
     A reaction: There could be narrative irony in a story told by an angry and puritanical person, which continually condemns wickedness, with the reader expected to have a more tolerant attitude. Hard to think of any examples of this problem.
A work which seeks approval for immorality, but alienates the audience, is a failure [Davies,S]
     Full Idea: A work that looks for the audience's sympathetic approval and alienates them instead, because it's both morally repulsive and incoherent in what it requires them to suppose, isn't an artistic success.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 8.7)
     A reaction: The implication seems to be that works are only successful if they achieve what the creator consciously intended. Lawrence said trust the novel, not the novelist. Milton's Satan is a famous example of heroism not intended by the author.
Immorality may or may not be an artistic defect [Davies,S]
     Full Idea: Immorality in art is sometimes an artistic defect and sometimes not.
     From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 8.7)
     A reaction: Davies seems to avoid the 'immoralist' view, that immorality in a work of art can sometimes be a strength. A sharp distinction is needed, I think, between the morality of what is depicted, and the morality of the whole artwork.
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
There are atoms of substance, but no atoms of bulk or extension [Leibniz]
     Full Idea: Although there are atoms of substance, namely monads, which lack parts, there are no atoms of bulk [moles], that is, atoms of the least possible extension, nor are there any ultimate elements, since a continuum cannot be composed out of points.
     From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §11)
     A reaction: Leibniz has a constant battle for the rest of his career to explain what these 'atoms of substance' are, since they have location but no extension, they are self-sufficient yet generate force, and are non-physical but interact with matter.
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / a. Early Modern matter
Secondary matter is active and complete; primary matter is passive and incomplete [Leibniz]
     Full Idea: I understand matter as either secondary or primary. Secondary matter is, indeed, a complete substance, but it is not merely passive; primary matter is merely passive, but it is not a complete substance. So we must add a soul or form...
     From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §12), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 4
     A reaction: It sounds as if primary matter is redundant, but Garber suggests that secondary matter is just the combination of primary matter with form.
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
If there is some trace of God in things, that would explain their natural force [Leibniz]
     Full Idea: If the law of God does indeed leave some vestige of him expressed in things...then it must be granted that there is a certain efficacy residing in things, a form or force such as we usually designate by the name of nature, from which the phenomena follow.
     From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §06)
     A reaction: I wouldn't rate this as a very promising theory of powers, but it seems to me important that Leibniz recognises the innate power in things as needing explanation. If you remove divine power, you are left with unexplained intrinsic powers.
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
It is plausible to think substances contain the same immanent force seen in our free will [Leibniz]
     Full Idea: If we attribute an inherent force to our mind, a force acting immanently, then nothing forbids us to suppose that the same force would be found in other souls or forms, or, if you prefer, in the nature of substances.
     From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §10)
     A reaction: This is the kind of bizarre idea that you are driven to, once you start thinking that God must have a will outside nature, and then that we have the same thing. Why shouldn't such a thing pop up all over the place? Only Leibniz spots the slippery slope.
28. God / C. Attitudes to God / 2. Pantheism
To say that nature or the one universal substance is God is a pernicious doctrine [Leibniz]
     Full Idea: To say that nature itself or the substance of all things is God is a pernicious doctrine, recently introduced into the world or renewed by a subtle or profane author.
     From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], 8)
     A reaction: The dastardly profane author is, of course, Spinoza, whom Leibniz had met in 1676. The doctrine may be pernicious to religious orthodoxy, but to me it is rather baffling, since in my understanding nature and God have almost nothing in common.