86 ideas
| 19359 | Leibniz aims to give coherent rational support for empiricism [Leibniz, by Perkins] |
| Full Idea: Leibniz's philosophy largely serves to justify and enable a coherent empirical account of the world. | |
| From: report of Gottfried Leibniz (works [1690]) by Franklin Perkins - Leibniz: Guide for the Perplexed 4.I | |
| A reaction: A nice counter to the simplistic idea of Locke as empiricist and Leibniz as rationalist. Leibniz is explicit that science needs a separate 'metaphysics' to underpin it. Perkins says Locke constructs experience, and Leibniz analyses it. |
| 13086 | Metaphysics is a science of the intelligible nature of being [Leibniz, by Cover/O'Leary-Hawthorne] |
| Full Idea: For Leibniz, metaphysics is above all a science of the intelligible nature of being. | |
| From: report of Gottfried Leibniz (works [1690]) by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 4.3.1 | |
| A reaction: [Their footnote gives two quotes in support] I could take this as my motto. We are not studying the 'nature of being', because we can't. We are studying what is 'intelligible' about it; my thesis is that the need for intelligibility imposes an order. |
| 16710 | Leibniz tried to combine mechanistic physics with scholastic metaphysics [Leibniz, by Pasnau] |
| Full Idea: Leibniz made a sustained attempt to combine a mechanistic physics with something like a scholastic metaphysics. | |
| From: report of Gottfried Leibniz (works [1690]) by Robert Pasnau - Metaphysical Themes 1274-1671 20.1 | |
| A reaction: This seems to me clear enough, and a lot of current philosophers seem to underestimate how Aristotelian Leibniz was. |
| 16897 | Reason is the faculty for grasping apriori necessary truths [Leibniz, by Burge] |
| Full Idea: Leibniz actually characterises reason as the faculty for apprehending priori, necessary truths. | |
| From: report of Gottfried Leibniz (works [1690]) by Tyler Burge - Frege on Apriority (with ps) 2 | |
| A reaction: No wonder it is called the Age of Reason when the claims are this grandiose. |
| 3346 | For Leibniz rationality is based on non-contradiction and the principle of sufficient reason [Leibniz, by Benardete,JA] |
| Full Idea: Leibniz distinguished two fundamental principles of rationality - the principle of non-contradiction and the principle of sufficient reason. | |
| From: report of Gottfried Leibniz (works [1690]) by José A. Benardete - Metaphysics: the logical approach Ch.18 |
| 3347 | Leibniz said the principle of sufficient reason is synthetic a priori, since its denial is not illogical [Leibniz, by Benardete,JA] |
| Full Idea: Leibniz assigns synthetic a priori status to the principle of sufficient reason, readily conceding that one can deny it without fear of inconsistency. | |
| From: report of Gottfried Leibniz (works [1690]) by José A. Benardete - Metaphysics: the logical approach Ch.18 |
| 9847 | A contextual definition permits the elimination of the expression by a substitution [Dummett] |
| Full Idea: The standard sense of a 'contextual definition' permits the eliminating of the defined expression, by transforming any sentence containing it into an equivalent one not containing it. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.11) | |
| A reaction: So the whole definition might be eliminated by a single word, which is not equivalent to the target word, which is embedded in the original expression. Clearly contextual definitions have some problems |
| 8627 | Leibniz is inclined to regard all truths as provable [Leibniz, by Frege] |
| Full Idea: Leibniz has an inclination to regard all truths as provable. | |
| From: report of Gottfried Leibniz (works [1690]) by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §15 | |
| A reaction: Leibniz sounds like the epitome of Enlightenment optimism about the powers of reason. Could God prove every truth? It's a nice thought. |
| 9820 | In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett] |
| Full Idea: For sentential or first-order logic, the logical truths are represented by valid formulas; in higher-order logics, by sentences formulated in purely logical terms. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 3) |
| 9896 | A prime number is one which is measured by a unit alone [Dummett] |
| Full Idea: A prime number is one which is measured by a unit alone. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 7 Def 11) | |
| A reaction: We might say that the only way of 'reaching' or 'constructing' a prime is by incrementing by one till you reach it. That seems a pretty good definition. 64, for example, can be reached by a large number of different routes. |
| 18255 | Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett] |
| Full Idea: It is essential to a quantitative domain of any kind that there should be an operation of adding its elements; that this is more fundamental thaat that they should be linearly ordered by magnitude is apparent from cyclic domains like that of angles. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 22 'Quantit') |
| 9147 | Number cannot be defined as addition of ones, since that needs the number; it is a single act of abstraction [Fine,K on Leibniz] |
| Full Idea: Leibniz's talk of the addition of ones cannot define number, since it cannot be specified how often they are added without using the number itself. Number must be an organic unity of ones, achieved by a single act of abstraction. | |
| From: comment on Gottfried Leibniz (works [1690]) by Kit Fine - Cantorian Abstraction: Recon. and Defence §1 | |
| A reaction: I doubt whether 'abstraction' is the right word for this part of the process. It seems more like a 'gestalt'. The first point is clearly right, that it is the wrong way round if you try to define number by means of addition. |
| 9895 | A number is a multitude composed of units [Dummett] |
| Full Idea: A number is a multitude composed of units. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 7 Def 2) | |
| A reaction: This is outdated by the assumption that 0 and 1 are also numbers, but if we say one is really just the 'unit' which is preliminary to numbers, and 0 is as bogus a number as i is, we might stick with the original Greek distinction. |
| 9852 | We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett] |
| Full Idea: A child understands 'there are just as many nuts as apples' as easily by pairing them off as by counting them. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12) | |
| A reaction: I find it very intriguing that you could know that two sets have the same number, without knowing any numbers. Is it like knowing two foreigners spoke the same words, without understanding them? Or is 'equinumerous' conceptually prior to 'number'? |
| 19375 | The continuum is not divided like sand, but folded like paper [Leibniz, by Arthur,R] |
| Full Idea: Leibniz said the division of the continuum should not be conceived 'to be like the division of sand into grains, but like that of a tunic or a sheet of paper into folds'. | |
| From: report of Gottfried Leibniz (works [1690], A VI iii 555) by Richard T.W. Arthur - Leibniz | |
| A reaction: This from the man who invented calculus. This thought might apply well to the modern physicist's concept of a 'field'. |
| 18080 | A tangent is a line connecting two points on a curve that are infinitely close together [Leibniz] |
| Full Idea: We have only to keep in mind that to find a tangent means to draw a line that connects two points of a curve at an infinitely small distance. | |
| From: Gottfried Leibniz (works [1690]), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.1 | |
| A reaction: [The quote can be tracked through Kitcher's footnote] |
| 18081 | Nature uses the infinite everywhere [Leibniz] |
| Full Idea: Nature uses the infinite in everything it does. | |
| From: Gottfried Leibniz (works [1690]), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.1 | |
| A reaction: [The quote can be tracked through Kitcher's footnote] He seems to have had in mind the infinitely small. |
| 9829 | The identity of a number may be fixed by something outside structure - by counting [Dummett] |
| Full Idea: The identity of a mathematical object may sometimes be fixed by its relation to what lies outside the structure to which it belongs. It is more fundamental to '3' that if certain objects are counted, there are three of them. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 5) | |
| A reaction: This strikes me as Dummett being pushed (by his dislike of the purely abstract picture given by structuralism) back to a rather empiricist and physical view of numbers, though he would totally deny that. |
| 9828 | Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett] |
| Full Idea: The number 0 is not differentiated from 1 by its position in a progression, otherwise there would be no difference between starting with 0 and starting with 1. That is enough to show that numbers are not identifiable just as positions in structures. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 5) | |
| A reaction: This sounds conclusive, but doesn't feel right. If numbers are a structure, then where you 'start' seems unimportant. Where do you 'start' in St Paul's Cathedral? Starting sounds like a constructivist concept for number theory. |
| 9876 | Set theory isn't part of logic, and why reduce to something more complex? [Dummett] |
| Full Idea: The two frequent modern objects to logicism are that set theory is not part of logic, or that it is of no interest to 'reduce' a mathematical theory to another, more complex, one. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: Dummett says these are irrelevant (see context). The first one seems a good objection. The second one less so, because whether something is 'complex' is a quite different issue from whether it is ontologically more fundamental. |
| 9548 | A mathematical object exists if there is no contradiction in its definition [Waterfield] |
| Full Idea: A mathematical object exists provided there is no contradiction implied in its definition. | |
| From: Robin Waterfield (Introduction to 'Hippias Minor' [1987], p.44), quoted by Charles Chihara - A Structural Account of Mathematics 1.4 | |
| A reaction: A rather bizarre criterion for existence. Not one, for example, that you would consider applying to the existence of physical objects! But then Poincaré is the father of 'conventionalism', rather than being a platonist. |
| 7565 | Leibniz proposes monads, since there must be basic things, which are immaterial in order to have unity [Leibniz, by Jolley] |
| Full Idea: Leibniz believes in monads because it would be contrary to reason or divine wisdom if everything was compounds, down to infinity; there must be ultimate unified building-blocks; they cannot be material, for material things lack genuine unity. | |
| From: report of Gottfried Leibniz (works [1690]) by Nicholas Jolley - Leibniz Ch.3 | |
| A reaction: It is hard to discern the basis for the claim that only immaterial things can have unity. The Greeks proposed atoms, and we have no reason to think that electrons lack unity. |
| 9884 | The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett] |
| Full Idea: The distinction between concrete and abstract objects, or Frege's corresponding distinction between actual and non-actual objects, is not a sharp dichotomy, but resembles a scale upon which objects occupy a range of positions. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: This might seem right if you live (as Dummett chooses to) in the fog of language, but it surely can't be right if you think about reality. Is the Equator supposed to be near the middle of his scale? Either there is an equator, or there isn't. |
| 9869 | Realism is just the application of two-valued semantics to sentences [Dummett] |
| Full Idea: Fully fledged realism depends on - indeed, may be identified with - an undiluted application to sentences of the relevant kind of straightforwards two-valued semantics. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: This is the sort of account you get from a whole-heartedly linguistic philosopher. Personally I would say that Dummett has got it precisely the wrong way round: I adopt a two-valued semantics because my metaphysics is realist. |
| 10419 | If relations can be reduced to, or supervene on, monadic properties of relata, they are not real [Leibniz, by Swoyer] |
| Full Idea: Leibniz argued that relations could be reduced to monadic properties and so were dispensable, and some still agree, saying relations supervene on monadic properties of the relata, and are not actually real. | |
| From: report of Gottfried Leibniz (works [1690]) by Chris Swoyer - Properties 7.4 | |
| A reaction: At the very least a background of space and/or time seem required, in addition to any properties the relata may have. y only becomes 'to the left of x' when x appears to its right, so the relation doesn't seem to be intrinsic to y. |
| 13078 | Relations aren't in any monad, so they are distributed, so they are not real [Leibniz] |
| Full Idea: The relations which connect two monads are not in either the one or the other, but equally in both at once; and therefore properly speaking, in neither. I do not think you would wish to posit an accident which would inhere simultaneously in two subjects. | |
| From: Gottfried Leibniz (works [1690], G II:517), quoted by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 2.4.3 | |
| A reaction: Where Russell affirms relations as universals, and scholastics make them properties of individuals, Leibniz denies their reality entirely. It seems obvious that once the objects and properties are there, the relations come for free. |
| 12713 | Forms have sensation and appetite, the latter being the ability to act on other bodies [Leibniz, by Garber] |
| Full Idea: Leibniz's form contains both sensation and appetite, and he seems to associate appetite with the ability a body has to act on another. | |
| From: report of Gottfried Leibniz (works [1690]) by Daniel Garber - Leibniz:Body,Substance,Monad 3 | |
| A reaction: It strikes me (you may be surprised to hear) that this concept is not unlike Nietzsche's all-mastering 'will to power'. I offer Idea 7140 in evidence. |
| 13087 | The essence of a thing is its real possibilities [Leibniz, by Cover/O'Leary-Hawthorne] |
| Full Idea: In Leibniz's view, the essence of a thing is fundamentally the real possibilities of that thing. | |
| From: report of Gottfried Leibniz (works [1690]) by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 4.3.3 | |
| A reaction: Note that the essences are individual. On the whole I would prefer Leibniz in his own words, but this is too good to lose (..but see Idea 12981). It is the aspect of Leibniz that fits perfectly with modern scientific essentialism. |
| 9880 | Nominalism assumes unmediated mental contact with objects [Dummett] |
| Full Idea: The nominalist superstition is based ultimately on the myth of the unmediated presentation of genuine concrete objects to the mind. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: Personally I am inclined to favour nominalism and a representative theory of perception, which acknowledges some 'mediation', but of a non-linguistic form. Any good theory here had better include animals, which seem to form concepts. |
| 9885 | The existence of abstract objects is a pseudo-problem [Dummett] |
| Full Idea: The existence of abstract objects is a pseudo-problem. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: This remark follows after Idea 9884, which says the abstract/concrete distinction is a sliding scale. Personally I take the distinction to be fairly sharp, and it is therefore probably the single most important problem in the whole of human thought. |
| 9858 | Abstract objects nowadays are those which are objective but not actual [Dummett] |
| Full Idea: Objects which are objective but not actual are precisely what are now called abstract objects. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: Why can there not be subjective abstract objects? 'My favourites are x, y and z'. 'I'll decide later what my favourites are'. 'I only buy my favourites - nothing else'. |
| 9859 | It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett] |
| Full Idea: If someone argued that assuming the existence of the Equator explains nothing, and it has no causal powers, so everything would be the same if it didn't exist, so we needn't accept its existence, we should gape at the crudity of the misunderstanding. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: Not me. I would gape if someone argued that latitude 55° 14' (and an infinity of other lines) exists for the same reasons (whatever they may be) that the Equator exists. A mode of description can't create an object. |
| 9860 | 'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett] |
| Full Idea: 'We've crossed the Equator' is judged true if we are nearer the other Pole, so it not for philosophers to deny that the Earth has an equator, and we see that the Equator is not a concept or relation or function, so it must be classified as an object. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: A lovely example of linguistic philosophy in action (and so much the worse for that, I would say). A useful label here, I suggest (unoriginally, I think), is that we should label such an item a 'semantic object', rather than a real object in our ontology. |
| 9872 | Abstract objects need the context principle, since they can't be encountered directly [Dummett] |
| Full Idea: To recognise that there is no objection in principle to abstract objects requires acknowledgement that some form of the context principle is correct, since abstract objects can neither be encountered nor presented. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.16) | |
| A reaction: I take this to be an immensely important idea. I consider myself to be a philosopher of thought rather than a philosopher of language (Dummett's distinction, he being one of the latter). Thought connects to the world, but does it connect to abstracta? |
| 12701 | Leibniz moved from individuation by whole entity to individuation by substantial form [Leibniz, by Garber] |
| Full Idea: By 1680 Leibniz had clearly abandoned the 'whole entity' conception of individuation, for a conception grounded in substantial form alone. | |
| From: report of Gottfried Leibniz (works [1690]) by Daniel Garber - Leibniz:Body,Substance,Monad 2 | |
| A reaction: In other words, Leibniz became more of an Aristotelian, and more of an essentialist. |
| 13105 | The laws-of-the-series plays a haecceitist role [Leibniz, by Cover/O'Leary-Hawthorne] |
| Full Idea: Leibniz takes the laws-of-the-series to play a haecceitistic role. | |
| From: report of Gottfried Leibniz (works [1690]) by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 7.5 | |
| A reaction: Idea 13092 for law-in-the-series. He thinks that a law-in-a-series is unique to a substance, and so can individuate it. That is a pretty good proposal, if anything is going to do the job. Perhaps I do believe in haecceities, as unique bundles of powers? |
| 16513 | Identity of a substance is the law of its persistence [Leibniz] |
| Full Idea: For there to be a certain persisting law which involves the future states of that which we conceive as one and the same continuant, this is what I say constitute's a substance's identity. | |
| From: Gottfried Leibniz (works [1690], G II:264), quoted by David Wiggins - Sameness and Substance 3.1 | |
| A reaction: This is a key remark for those who thing 'persistence conditions' are basic to metaphysics. I'm not so sure. |
| 12035 | Leibniz bases pure primitive entities on conjunctions of qualitative properties [Leibniz, by Adams,RM] |
| Full Idea: Leibniz is committed with apparent consistency to both a purely qualitative character of all thisnesses, and to primitiveness of individual identity. He regards thisnesses as conjunctions of simpler, logically independent suchnesses. | |
| From: report of Gottfried Leibniz (works [1690]) by Robert Merrihew Adams - Primitive Thisness and Primitive Identity 5 | |
| A reaction: Hence Leibniz is held to say that all of the qualitative properties are 'essential' to the object, since all of them are needed to constitute its identity. Hence absolutely nothing about an object, even an electron, could be different, which is daft. |
| 13091 | Leibnizian substances add concept, law, force, form and soul [Leibniz, by Cover/O'Leary-Hawthorne] |
| Full Idea: To the traditional idea of substance (independent, subjects of predication, active, persistent) Leibniz adds, distinctively, complete individual concept, law-of-the-series, active force, form and soul or entelechy. | |
| From: report of Gottfried Leibniz (works [1690]) by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 6.1.1 | |
| A reaction: 'Form' seems to be Aristotelian, and 'soul' seems ridiculous. I don't think the 'complete concept' is much help. However, the 'law-in-the-series' is very interesting (Idea 13079), if employed sensibly, and 'active force' is spot-on. Powers define reality. |
| 7561 | Substances are essentially active [Leibniz, by Jolley] |
| Full Idea: For Leibniz, it is the very essence of substances to be sources of activity. | |
| From: report of Gottfried Leibniz (works [1690]) by Nicholas Jolley - Leibniz Ch.2 | |
| A reaction: This makes the views of Leibniz sympathetic to modern essentialism (of which I am a fan), because it places active power at the centre of what it is to exist, rather than action being imposed on matter which is otherwise passive. |
| 12715 | Leibniz strengthened hylomorphism by connecting it to force in physics [Leibniz, by Garber] |
| Full Idea: A standard criticism of the scholastic notions of matter and form is that they are obscure and unintelligible. But in Leibniz's system they are connected directly with notions of active and passive force that play an intelligible roles in his physics. | |
| From: report of Gottfried Leibniz (works [1690]) by Daniel Garber - Leibniz:Body,Substance,Monad 4 | |
| A reaction: This seems to me to be very appealing. Aristotle was clearly on the right lines, but just ran out of things to say, once he had pointed in the right direction. Maybe 'fields' and 'strings' can fill out the Aristotelian conception of form. |
| 11878 | Leibniz's view (that all properties are essential) is extreme essentialism, not its denial [Leibniz, by Mackie,P] |
| Full Idea: The view standardly attributed to Leibniz, that makes all an individual's properties essential to it should be regarded as an extreme version of essentialism, not a denial of essentialism. | |
| From: report of Gottfried Leibniz (works [1690]) by Penelope Mackie - How Things Might Have Been 1.1 | |
| A reaction: Wiggins disagrees, saying that Leibniz was not an essentialist, which is an interesting topic of research for those who are interested. I would take Leibniz to be not an essentialist, on that basis, as essentialism makes a distinction. See Quine on that. |
| 11862 | Leibniz was not an essentialist [Leibniz, by Wiggins] |
| Full Idea: Leibniz was not an essentialist. | |
| From: report of Gottfried Leibniz (works [1690]) by David Wiggins - Sameness and Substance Renewed 4.2 n4 | |
| A reaction: Assuming this is right, it is rather helpful, because you can read mountains of Leibniz without ever being quite sure. Mackie says he IS an extreme essentialist, treating all properties as essential. Wiggins makes more sense there. |
| 9848 | Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett] |
| Full Idea: Husserl says the only ground for assuming the replaceability of one content by another is their identity; we are therefore not entitled to define their identity as consisting in their replaceability. | |
| From: report of Michael Dummett (Frege philosophy of mathematics [1991]) by Michael Dummett - Frege philosophy of mathematics Ch.12 | |
| A reaction: This is a direct challenge to Frege. Tricky to arbitrate, as it is an issue of conceptual priority. My intuition is with Husserl, but maybe the two are just benignly inerdefinable. |
| 9842 | Frege introduced criteria for identity, but thought defining identity was circular [Dummett] |
| Full Idea: In his middle period Frege rated identity indefinable, on the ground that every definition must take the form of an identity-statement. Frege introduced the notion of criterion of identity, which has been widely used by analytical philosophers. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.10) | |
| A reaction: The objection that attempts to define identity would be circular sounds quite plausible. It sounds right to seek a criterion for type-identity (in shared properties or predicates), but token-identity looks too fundamental to give clear criteria. |
| 16504 | Two eggs can't be identical, because the same truths can't apply to both of them [Leibniz] |
| Full Idea: It isn't possible to have two particulars that are similar in all respects - for example two eggs - for it is necessary that some things can be said about one of them that cannot be said about the other, else they could be substituted for one another. | |
| From: Gottfried Leibniz (works [1690]), quoted by David Wiggins - Sameness and Substance 2.2 | |
| A reaction: [from a 'fragment' for which Wiggins gives a reference] This quotation doesn't rest the distinctness of the eggs on some intrinsic difference, but on the fact that we can say different things about the two eggs. |
| 8650 | Things are the same if one can be substituted for the other without loss of truth [Leibniz] |
| Full Idea: Leibniz's definition is as follows: Things are the same as each other, of which one can be substituted for the other without loss of truth ('salva veritate'). | |
| From: Gottfried Leibniz (works [1690]), quoted by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §65 | |
| A reaction: Frege doesn't give a reference. (Anyone know it?). This famous definition is impressive, but has problems when the items being substituted appear in contexts of belief. 'Oedipus believes Jocasta (his mother!) would make a good wife'. |
| 13828 | Necessary truths are those provable from identities by pure logic in finite steps [Leibniz, by Hacking] |
| Full Idea: Leibniz argued that the necessary truths are just those which can be proved from identities by pure logic in a finite number of steps. ...[232] this claim is vindicated by Gentzen's sequent calculus. | |
| From: report of Gottfried Leibniz (works [1690]) by Ian Hacking - What is Logic? §01 | |
| A reaction: This seems an odd idea, as if there were no necessary truths other than those for which a proof could be constructed. Sounds like intuitionism. |
| 13084 | How can things be incompatible, if all positive terms seem to be compatible? [Leibniz] |
| Full Idea: It is yet unknown to me what is the reason of the incompossibility of things, or how it is that different essences can be opposed to each other, seeing that all purely positive terms seem to be compatible. | |
| From: Gottfried Leibniz (works [1690], G VII:194), quoted by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 3.4.4 | |
| A reaction: Since 'heavy' seems straightforwardly opposed to 'light', we would have to ask what he means by 'positive'. The suspicion is that all things are compossible by definition, so it is not surprising that impossibilities are a bit puzzling. |
| 4307 | A reason must be given why contingent beings should exist rather than not exist [Leibniz] |
| Full Idea: A reason must be given why contingent beings should exist rather than not exist. | |
| From: Gottfried Leibniz (works [1690]) | |
| A reaction: Spinoza rejects all contingency, but this seems an interesting support for it, even though we may need a reason for something where God does not because it is self-evident. |
| 15883 | Leibniz narrows down God's options to one, by non-contradiction, sufficient reason, indiscernibles, compossibility [Leibniz, by Harré] |
| Full Idea: Leibniz sets up increasingly stringent conditions possible worlds must meet. The weakest is non-contradiction, for truths of reason; then sufficient reason, for rational worlds; then identity of indiscernibles, for duplicates; then compossibility. | |
| From: report of Gottfried Leibniz (works [1690]) by Rom Harré - Laws of Nature 4 | |
| A reaction: [my summary of a very nice two pages by Harré] God is the source of the principles which do the narrowing down. |
| 18822 | Each monad expresses all its compatible monads; a possible world is the resulting equivalence class [Leibniz, by Rumfitt] |
| Full Idea: Leibniz argued that each monad mirrors or expresses every monad with which it is compossible. Hence compossibility is an equivalence relation among monads; possible worlds may then be identified as the corresponding equivalence classes. | |
| From: report of Gottfried Leibniz (works [1690]) by Ian Rumfitt - The Boundary Stones of Thought 6.1 | |
| A reaction: [Rumfitt cites Benson Mates 1986:IV.1 for this claim] There is an analogous world of all the human minds that are in communication with one another - something like a 'culture'. |
| 7837 | Leibniz proposed possible worlds, because they might be evil, where God would not create evil things [Leibniz, by Stewart,M] |
| Full Idea: In his early writings the principle of sufficient reason made it difficult for Leibniz to conceive of possible things;...raising this to possible worlds means God does not choose things that are evil, but chooses a world which must have evil in it. | |
| From: report of Gottfried Leibniz (works [1690]) by Matthew Stewart - The Courtier and the Heretic Ch.14 | |
| A reaction: Where we think of possible worlds as explanations for conditional and counterfactual truths (I take it), Leibniz developed the original idea as part of his huge effort to achieve a consistent theodicy. |
| 13080 | Leibniz has a counterpart view of de re counterfactuals [Leibniz, by Cover/O'Leary-Hawthorne] |
| Full Idea: When Leibniz has the grounds of de re counterfactuals in mind, a counterpart picture, we have argued, is at work. | |
| From: report of Gottfried Leibniz (works [1690]) by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 3.2.2 | |
| A reaction: If Leibniz were a 'superessentialist', then individuals would be totally worldbound (because their relations would be essential). Cover/Hawthorne argue that he is just a 'strong' essentialist, allowing possible counterparts. Quite persuasive. |
| 19332 | For Leibniz, divine understanding grasps every conceivable possibility [Leibniz, by Perkins] |
| Full Idea: For Leibniz, what is this understanding which God has? What does it contain? All possibilities in all possible combinations, that is, everything which can be conceived. | |
| From: report of Gottfried Leibniz (works [1690]) by Franklin Perkins - Leibniz: Guide for the Perplexed 2.III | |
| A reaction: I like this, because it strikes me as essential that understanding should embrace possibilities as well as actualities. Perkins points out that the possibilities are restricted by an awareness of the limitations imposed by combination. |
| 5509 | Leibniz said dualism of mind and body is illusion, and there is only mind [Leibniz, by Martin/Barresi] |
| Full Idea: Leibniz held that dualism of mind and body is an illusion and that both are really the same thing, and that this thing is mind. | |
| From: report of Gottfried Leibniz (works [1690]) by R Martin / J Barresi - Introduction to 'Personal Identity' p.22 | |
| A reaction: I am puzzled by this, as Leibniz is famous for the view that mind and body are parallel. See idea 5038, and also 2109 and 2596. Monads are, of course, entirely mental, and are the building blocks of reality. Clearly I (and you) must read more Leibniz. |
| 7568 | Leibniz is an idealist insofar as the basic components of his universe are all mental [Leibniz, by Jolley] |
| Full Idea: To say that Leibniz is an idealist is to say that simple substances, the basic building-blocks of the universe, are all mental or at least quasi-mental in nature | |
| From: report of Gottfried Leibniz (works [1690]) by Nicholas Jolley - Leibniz Ch.3 | |
| A reaction: This is a bit different from the Berkelian type of idealism, which says that reality consists entirely of events within thinking minds. Is a monad the thinker or the thought? |
| 13092 | The essence of substance is the law of its changes, as in the series of numbers [Leibniz] |
| Full Idea: The essence of substance consists in ...the law of the sequence of changes, as in the nature of the series in numbers. | |
| From: Gottfried Leibniz (works [1690], A 6.3.326), quoted by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 6.1.2 | |
| A reaction: Thus we might say, in this spirit, that the essence of number is the successor operation, as defined by Dedekind and Peano (and perhaps their amenability to inductive proof). I like this. Metaphysicians rule - they penetrate the heart of nature. |
| 19354 | Leibniz introduced the idea of degrees of consciousness, essential for his monads [Leibniz, by Perkins] |
| Full Idea: The designation of degrees of conscious awareness is one of Leibniz's most significant innovations, and it is fundamental to almost every aspect of his account of monads. | |
| From: report of Gottfried Leibniz (works [1690]) by Franklin Perkins - Leibniz: Guide for the Perplexed 4.I | |
| A reaction: A very important development, which seems to have been ignored by philosophers for three hundred years, since they usually treat consciousness as all-or-nothing. Introspection makes degrees obvious, and I suspect sparrows are down the scale. |
| 7841 | We think we are free because the causes of the will are unknown; determinism is a false problem [Leibniz] |
| Full Idea: The will has its causes, but since we are ignorant of them, we believe ourselves independent. It is this chimera of imaginary independence which revolts us against determinism, and which brings us to believe there are difficulties where there are none. | |
| From: Gottfried Leibniz (works [1690]), quoted by Matthew Stewart - The Courtier and the Heretic Ch.16 | |
| A reaction: It seems that in his notebooks Leibniz was actually a (Spinozan) determinist. So he should have been, given his view that we live in the best of all possible worlds, and his claim that mind and brain run like two clocks. (Ideas 2114 and 2596) |
| 5510 | Leibniz has a panpsychist view that physical points are spiritual [Leibniz, by Martin/Barresi] |
| Full Idea: In Leibniz's panpsychism, the so-called 'physical' points are souls or spiritual 'monads'. | |
| From: report of Gottfried Leibniz (works [1690]) by R Martin / J Barresi - Introduction to 'Personal Identity' p.23 | |
| A reaction: I'm not convinced that 'panpsychism' is the right description for Leibniz's theory of monads. I take panpsychism to be either a dualist or a dual aspect (or property dualism) view. Leibniz seems to believe there is strictly one substance. |
| 7564 | Occasionalism give a false view of natural laws, miracles, and substances [Leibniz, by Jolley] |
| Full Idea: Leibniz's three objections to occasionalism are: it disturbs the concept of laws of nature used in physics; it introduces perpetual miracles; and it doesn't recognise activity of substances (leading to the Spinozan heresy that God is the only substance). | |
| From: report of Gottfried Leibniz (works [1690]) by Nicholas Jolley - Leibniz Ch.2 | |
| A reaction: I wonder what would happen if, within the viewpoint of occasionalism, God suddenly packed up and abandoned his job? Presumably the world wouldn't disappear, so there would still be substances, but passive ones, in chaos. |
| 19372 | Concepts are ordered, and show eternal possibilities, deriving from God [Leibniz, by Arthur,R] |
| Full Idea: Leibniz understood concepts as corresponding to eternal possibilities, with both concepts and their ordering having their foundation in the divine mind. | |
| From: report of Gottfried Leibniz (works [1690]) by Richard T.W. Arthur - Leibniz 2 'Nominalism' | |
| A reaction: It is is no longer the fashion to think of concepts as 'ordered', and yet there is a multitude of dependence relations between them. |
| 9849 | Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett] |
| Full Idea: One powerful argument for a thesis that one notion is conceptually prior to another is the possibility of defining the first without reference to the second. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12) | |
| A reaction: You'd better check whether you can't also define the second without reference to the first before you rank their priority. And maybe 'conceptual priority' is conceptually prior to 'definition' (i.e. definition needs a knowledge of priority). Help! |
| 9850 | An argument for conceptual priority is greater simplicity in explanation [Dummett] |
| Full Idea: An argument for conceptual priority is greater simplicity in explanation. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12) | |
| A reaction: One might still have to decide priority between two equally simple (or complex) concepts. I begin to wonder whether 'priority' has any other than an instrumental meaning (according to which direction you wish to travel - is London before Edinburgh?). |
| 9873 | Abstract terms are acceptable as long as we know how they function linguistically [Dummett] |
| Full Idea: To recognise abstract terms as perfectly proper items of a vocabulary depends upon allowing that all that is necessary for the lawful introduction of a range of expressions into the language is a coherent account of how they are to function in sentences. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.16) | |
| A reaction: Why can't the 'coherent account' of the sentences include the fact that there must be something there for the terms to refer to? How else are we to eliminate nonsense words which obey good syntactical rules? Cf. Idea 9872. |
| 9993 | There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait] |
| Full Idea: Dummett uses the term 'logical abstraction' for the construction of the abstract objects as equivalence classes, but it is not clear why we should call this construction 'logical'. | |
| From: report of Michael Dummett (Frege philosophy of mathematics [1991]) by William W. Tait - Frege versus Cantor and Dedekind n 14 | |
| A reaction: This is a good objection, and Tait offers a much better notion of 'logical abstraction' (as involving preconditions for successful inference), in Idea 9981. |
| 9857 | We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett] |
| Full Idea: We arrive at the concept of suicide by considering both occurrences in the sentence 'Cato killed Cato' of the proper name 'Cato' as simultaneously replaceable by another name, say 'Brutus', and so apprehending the pattern common to both sentences. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.14) | |
| A reaction: This is intended to illustrate Frege's 'logical abstraction' technique, as opposed to wicked psychological abstraction. The concept of suicide is the pattern 'x killed x'. This is a crucial example if we are to understand abstraction... |
| 9833 | To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett] |
| Full Idea: To get units by abstraction, units arrived at by abstraction from forks must the identical to that abstracted from spoons, with no trace of individuality. But if spoons can no longer be differentiated from forks, they can't differ from one another either. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 8) | |
| A reaction: [compressed] Dummett makes the point better than Frege did. Can we 'think of a fork insofar as it is countable, ignoring its other features'? What are we left thinking of? Frege says it must still be the whole fork. 'Nice fork, apart from the colour'. |
| 13467 | Leibniz was the first modern to focus on sentence-sized units (where empiricists preferred word-size) [Leibniz, by Hart,WD] |
| Full Idea: Leibniz seems to be the first modern philosopher to focus on sentence-sized units that he called propositions. The Empiricists among the moderns focused on word-sized units like ideas. | |
| From: report of Gottfried Leibniz (works [1690]) by William D. Hart - The Evolution of Logic 2 | |
| A reaction: Historically, the sentential logic of the Stoics has a claim to have started this one. I find my initial sympathies to be with the empiricists. |
| 9836 | Fregean semantics assumes a domain articulated into individual objects [Dummett] |
| Full Idea: A Fregean semantics assumes a domain already determinately articulated into individual objects. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 8) | |
| A reaction: A more interesting criticism than most of Dummett's other challenges to the Frege/Davidson view. I am beginning to doubt whether the semantics and the ontology can ever be divorced from the psychology, of thought, interests, focus etc. |
| 19365 | Limited awareness leads to bad choices, and unconscious awareness makes us choose the bad [Leibniz, by Perkins] |
| Full Idea: For Leibniz, while the limits of our knowledge explain why we sometimes choose things we think are good but which turn out to be bad, the force of minute perceptions explains why we sometimes choose things that we know are bad. | |
| From: report of Gottfried Leibniz (works [1690]) by Franklin Perkins - Leibniz: Guide for the Perplexed 4.IV | |
| A reaction: To be overwhelmed by selfish greed doesn't sound like a 'minute perception'. Leibniz thinks all desires are reactions to perceptions. Observing our degrees of knowledge is an interesting response to the intellectualist view of weakness of will. |
| 8110 | Leibniz identified beauty with intellectual perfection [Leibniz, by Gardner] |
| Full Idea: Leibniz identified beauty with intellectual perfection. | |
| From: report of Gottfried Leibniz (works [1690]) by Sebastian Gardner - Aesthetics 1.2.1 | |
| A reaction: Well he would, wouldn't he? Swots like Leibniz are inclined to value things which only they can fully appreciate. There may be intellectual subject matter in the study of a rose, but I do not believe that it is needed to appreciate the beauty. |
| 7569 | Humans are moral, and capable of reward and punishment, because of memory and self-consciousness [Leibniz, by Jolley] |
| Full Idea: For Leibniz, it is by virtue of possessing memory and self-consciousness that human minds are moral beings, capable of reward and punishment. | |
| From: report of Gottfried Leibniz (works [1690]) by Nicholas Jolley - Leibniz Ch.4 | |
| A reaction: I like this because it makes no mention of free will (though Leibniz struggled to defend free will). I would add meta-thought (the ability to ponder and evaluate our own thinking), which makes a change of mind possible. |
| 7574 | Natural law theory is found in Aquinas, in Leibniz, and at the Nuremberg trials [Leibniz, by Jolley] |
| Full Idea: Leibniz rejects Hobbes's legal positivism in favour of the older natural law theory associated with Aquinas (which says nothing can be a law unless it derives from natural justice). The older view was revived at Nuremberg, to prosecute Nazis. | |
| From: report of Gottfried Leibniz (works [1690]) by Nicholas Jolley - Leibniz Ch.7 | |
| A reaction: This seems to suggest that Hobbes and co were using Ockham's Razor to eliminate morality from the law, but that the Nuremberg situation (and modern trials in The Hague) show that there is a necessity for natural law in international situations. |
| 12728 | Leibniz rejected atoms, because they must be elastic, and hence have parts [Leibniz, by Garber] |
| Full Idea: Leibniz held that there can be no atoms in nature, nothing perfectly solid and hard, since elasticity entails the existence of smaller parts that can move with respect to one another. | |
| From: report of Gottfried Leibniz (works [1690]) by Daniel Garber - Leibniz:Body,Substance,Monad 5 | |
| A reaction: Thus, I suppose, we discover that atoms have mercurial electron shells. Are quarks or electrons elastic? The debate about true atoms is not over, and probably never will be. Leibniz's point is a good one. |
| 19374 | Microscopes and the continuum suggest that matter is endlessly divisible [Leibniz] |
| Full Idea: Micrographers observe qualities of larger things found in smaller things. And if this proceeds to infinity - which is possible since the continuum is divisible to infinity - any atom will be an infinite species, and there will be worlds within worlds. | |
| From: Gottfried Leibniz (works [1690], A VI ii 241) | |
| A reaction: [a work of the 1670s] The microscope had a huge impact on Leibniz, much more than the telescope. |
| 7560 | Leibniz struggled to reconcile bodies with a reality of purely soul-like entities [Jolley on Leibniz] |
| Full Idea: Leibniz seems never to have made up his mind completely on how to accommodate bodies within a metaphysic which recognises only soul-like entities as fully real. | |
| From: comment on Gottfried Leibniz (works [1690]) by Nicholas Jolley - Leibniz Intro | |
| A reaction: [The soul-like entities are his 'monads']. His choice must be to either say they are unreal, or that they are real and separate from the monads, or that they are a manifestation of the monads. His problem, not mine. |
| 16683 | Leibniz eventually said resistance, rather than extension, was the essence of body [Leibniz, by Pasnau] |
| Full Idea: Leibniz eventually rejected extension altogether as part of the essence of body, and replaced it with resistance. | |
| From: report of Gottfried Leibniz (works [1690]) by Robert Pasnau - Metaphysical Themes 1274-1671 15.5 | |
| A reaction: This makes body consist of active force, rather than mere geometry. Much better. |
| 12725 | Leibniz wanted to explain motion and its laws by the nature of body [Leibniz, by Garber] |
| Full Idea: Leibniz seeks the big picture: the nature of body as a grounding for an account of motion and its laws. | |
| From: report of Gottfried Leibniz (works [1690]) by Daniel Garber - Leibniz:Body,Substance,Monad 4 | |
| A reaction: Garber is contrasting this with Newton's approaches, who just pleads ignorance of the bigger picture. Essentialists must beware of inventing a bigger picture simply because they desperately want a bigger picture. |
| 16507 | The law within something fixes its persistence, and accords with general laws of nature [Leibniz] |
| Full Idea: Nothing is permanent in a substance except the law itself which determines the continuous succession of its states and accords within the individual substance with the laws of nature that govern the whole world. | |
| From: Gottfried Leibniz (works [1690], G II:263), quoted by David Wiggins - Sameness and Substance 3 epig | |
| A reaction: An interesting link between the law-of-series within a substance, and the broader concept of laws outside it. |
| 7859 | Leibniz had an unusual commitment to the causal completeness of physics [Leibniz, by Papineau] |
| Full Idea: Unlike most philosophers prior to the twentieth century, Leibniz was committed to the causal completeness of physics. | |
| From: report of Gottfried Leibniz (works [1690]) by David Papineau - Thinking about Consciousness 1.4 | |
| A reaction: It has been suggested that Leibniz was actually, in private, a determinist (see Idea 7841), which would fit. Leibniz is enigmatic, but he may have proposed the closure of physics to glorify God, only to find that God was beginning to look irrelevant. |
| 15307 | Leibniz uses 'force' to mean both activity and potential [Leibniz] |
| Full Idea: At this early period exegetical problems abound, since Leibniz uses 'force' both for actually acting forces and for potentials or powers. | |
| From: Gottfried Leibniz (works [1690], 9.II), quoted by Harré,R./Madden,E.H. - Causal Powers 9.II.B | |
| A reaction: I take Leibniz to be a key figure in the development of the Aristotelian approach, because he connected Aristotelian potential and essence with 'force' in the new physics. This is helpful in reading him correctly. |
| 18257 | Why should the limit of measurement be points, not intervals? [Dummett] |
| Full Idea: By what right do we assume that the limit of measurement is a point, and not an interval? | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 22 'Quantit') |
| 3889 | God's existence is either necessary or impossible [Leibniz, by Scruton] |
| Full Idea: Leibniz said that the ontological argument does not prove God's existence, but only the God's existence is either necessary or impossible. | |
| From: report of Gottfried Leibniz (works [1690]) by Roger Scruton - Modern Philosophy:introduction and survey 13.5 |
| 7842 | Leibniz was closer than Spinoza to atheism [Leibniz, by Stewart,M] |
| Full Idea: Leibniz sailed closer to the winds of unbelief than Spinoza did. | |
| From: report of Gottfried Leibniz (works [1690]) by Matthew Stewart - The Courtier and the Heretic Ch.16 | |
| A reaction: This is an unusual view, but Stewart's view is that whereas Spinoza is always sincere in his writings, Leibniz is inclined to put a very conservative spin on his opinions. A key question for Leibniz is "Is God merely a monad?" |