68 ideas
| 4642 | No fact can be real and no proposition true unless there is a Sufficient Reason (even if we can't know it) [Leibniz] |
| Full Idea: The principle of sufficient reason says no fact can be real or existing and no proposition can be true unless there is a sufficient reason why it should be thus and not otherwise, even though in most cases these reasons cannot be known to us. | |
| From: Gottfried Leibniz (Monadology [1716], §32) | |
| A reaction: I think of this as my earliest philosophical perception, a childish rebellion against being told that there was 'no reason' for something. My intuition tells me that it is correct, and the foundation of ontology and truth. Don't ask me to justify it! |
| 2115 | Everything in the universe is interconnected, so potentially a mind could know everything [Leibniz] |
| Full Idea: Every body is sensitive to everything in the universe, so that one who saw everything could read in each body what is happening everywhere, and even what has happened and will happen. | |
| From: Gottfried Leibniz (Monadology [1716], §61) |
| 9449 | The plausible Barcan formula implies modality in the actual world [Bird] |
| Full Idea: Modality in the actual world is the import of the Barcan formula, and there are good reasons for accepting the Barcan formula. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 1.2) | |
| A reaction: If you thought logic was irrelevant to metaphysics, this should make you think twice. |
| 8729 | 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. |
| 2111 | Falsehood involves a contradiction, and truth is contradictory of falsehood [Leibniz] |
| Full Idea: We judge to be false that which involves a contradiction, and true that which is opposed or contradictory to the false. | |
| From: Gottfried Leibniz (Monadology [1716], §31) |
| 8763 | 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. |
| 18249 | 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. |
| 8764 | 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. |
| 8762 | 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. |
| 8760 | 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. |
| 8761 | 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. |
| 8744 | 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. |
| 8749 | 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. |
| 8750 | 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. |
| 8752 | 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. |
| 8753 | 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. |
| 8731 | 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. |
| 8730 | '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. |
| 9501 | If all existents are causally active, that excludes abstracta and causally isolated objects [Bird] |
| Full Idea: If one says that 'everything that exists is causally active', that rules out abstracta (notably sets and numbers), and it rules out objects that are causally isolated. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 5.5) | |
| A reaction: I like the principle. I take abstracta to be brain events, so they are causally active, within highly refined and focused brains, and if your physics is built on the notion of fields then I would think a 'causally isolated' object incoherent. |
| 9500 | If naturalism refers to supervenience, that leaves necessary entities untouched [Bird] |
| Full Idea: If one's naturalistic principles are formulated in terms of supervenience, then necessary entities are left untouched. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 5.5) | |
| A reaction: I take this to be part of the reason why some people like supervenience - that it leaves a pure 'space of reasons' which is unreachable from the flesh and blood inside a cranium. Personall I like the space of reasons, but I drop the 'pure'. |
| 7644 | The monad idea incomprehensibly spiritualises matter, instead of materialising soul [La Mettrie on Leibniz] |
| Full Idea: The Leibnizians with their monads have constructed an incomprehensible hypothesis. They have spiritualized matter rather than materialising the soul. | |
| From: comment on Gottfried Leibniz (Monadology [1716]) by Julien Offray de La Mettrie - Machine Man p.3 | |
| A reaction: I agree with La Mettrie. This disagreement shows, I think, how important the problem of interaction between mind and body was in the century after Descartes. Drastic action seemed needed to bridge the gap, one way or the other. |
| 11857 | He replaced Aristotelian continuants with monads [Leibniz, by Wiggins] |
| Full Idea: In the end Leibniz dethroned Aristotelian continuants, seen as imperfect from his point of view, in favour of monads. | |
| From: report of Gottfried Leibniz (Monadology [1716]) by David Wiggins - Sameness and Substance Renewed 3.1 | |
| A reaction: I take the 'continuants' to be either the 'ultimate subject of predication' (in 'Categories'), or 'essences' (in 'Metaphysics'). Since monads seem to be mental (presumably to explain the powers of things), this strikes me as a bit mad. |
| 7843 | Is a drop of urine really an infinity of thinking monads? [Voltaire on Leibniz] |
| Full Idea: Can you really maintain that a drop of urine is an infinity of monads, and that each one of these has ideas, however obscure, of the entire universe? | |
| From: comment on Gottfried Leibniz (Monadology [1716]) by Francois-Marie Voltaire - works Vol 22:434 | |
| A reaction: Monads are a bit like Christian theology - if you meet them cold they seem totally ridiculous, but if you meet them after ten years of careful preliminary study they make (apparently) complete sense. Defenders of panpsychism presumably like them. |
| 12751 | It is unclear in 'Monadology' how extended bodies relate to mind-like monads. [Garber on Leibniz] |
| Full Idea: It is never clear in the 'Monadologie' how exactly the world of extended bodies is related to the world of simple substances, the world of non-extended and mind-like monads. | |
| From: comment on Gottfried Leibniz (Monadology [1716]) by Daniel Garber - Leibniz:Body,Substance,Monad 9 | |
| A reaction: Leibniz was always going to hit the interaction problem, as soon as he started giving an increasingly spiritual account of what a substance, and hence marginalising the 'force' which had held centre-stage earlier on. Presumably they are 'parallel'. |
| 19363 | Changes in a monad come from an internal principle, and the diversity within its substance [Leibniz] |
| Full Idea: A monad's natural changes come from an internal principle, ...but there must be diversity in that which changes, which produces the specification and variety of substances. | |
| From: Gottfried Leibniz (Monadology [1716], §11-12) | |
| A reaction: You don't have to like monads to like this generalisation (and Perkins says Leibniz had a genius for generalisations). Metaphysics must give an account of change. Succeeding time-slices etc explain nothing. Principle and substance must meet. |
| 19352 | A 'monad' has basic perception and appetite; a 'soul' has distinct perception and memory [Leibniz] |
| Full Idea: The general name 'monad' or 'entelechy' may suffice for those substances which have nothing but perception and appetition; the name 'souls' may be reserved for those having perception that is more distinct and accompanied by memory. | |
| From: Gottfried Leibniz (Monadology [1716], §19) | |
| A reaction: It is basic to the study of Leibniz that you don't think monads are full-blown consciousnesses. He isn't really a panpsychist, because the level of mental activity is so minimal. There seem to be degrees of monadhood. |
| 9502 | There might be just one fundamental natural property [Bird] |
| Full Idea: The thought that there might be just one fundamental natural property is not that strange. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 6.3) | |
| A reaction: A nice variation on the Parmenides idea that only the One exists. Bird's point would refer to a possible unification of modern physics. We see, for example, the forces of electricity and of magnetism turning out to be the same force. |
| 9477 | Categorical properties are not modally fixed, but change across possible worlds [Bird] |
| Full Idea: Categorical properties do not have their dispositional characters modally fixed, but may change their dispositional characters (and their causal and nomic behaviour more generally) across different worlds. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.1) | |
| A reaction: This is the key ground for Bird's praiseworth opposition to categorical propertie. I take it to be a nonsense to call the category in which we place something a 'property' of that thing. A confusion of thought with reality. |
| 9490 | The categoricalist idea is that a property is only individuated by being itself [Bird] |
| Full Idea: In the categoricalist view, the essential properties of a natural property are limited to its essentially being itself and not some distinct property. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 4.1) | |
| A reaction: He associates this view with Lewis (modern regularity view) and Armstrong (nomic necessitation), and launches a splendid attack against it. I have always laughed at the idea that 'being Socrates' was one of the properties of Socrates. |
| 9495 | If we abstractly define a property, that doesn't mean some object could possess it [Bird] |
| Full Idea: The possibility of abstract definition does not show that we have defined a property that we can know, independently of any theory, that it is physically possible for some object to possess. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 4.2.3.1) | |
| A reaction: This is a naturalist resisting the idea that there is no more to a property than set-membership. I strongly agree. We need a firm notion of properties as features of the actual world; anything else should be called something like 'categorisations'. |
| 9492 | Categoricalists take properties to be quiddities, with no essential difference between them [Bird] |
| Full Idea: The categoricalist conception of properties takes them to be quiddities, which are primitive identities between fundamental qualities, having no difference with regard to their essence. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 4.5) | |
| A reaction: Compare 'haecceitism' about indentity of objects, though 'quidditism' sounds even less plausible. Bird attributes this view to Lewis and Armstrong, and makes it sound well daft. |
| 9503 | To name an abundant property is either a Fregean concept, or a simple predicate [Bird] |
| Full Idea: It isn't clear what it is to name an abundant property. One might reify them, as akin to Fregean concepts, or it might be equivalent to a simple predication. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 7.1.2) | |
| A reaction: 'Fregean concepts' would make them functions that purely link things (hence relational?). One suspects that people who actually treat abundant properties as part of their ontology (Lewis) are confusing natural properties with predicates. |
| 14540 | Only real powers are fundamental [Bird, by Mumford/Anjum] |
| Full Idea: Bird says only real powers are fundamental. | |
| From: report of Alexander Bird (Nature's Metaphysics [2007]) by S.Mumford/R.Lill Anjum - Getting Causes from Powers 1.5 | |
| A reaction: They disagree, and want higher-level properties in their ontology. I'm with Bird, except that something must exist to have the powers. Powers are fundamental to all the activity of nature, and are intrinsic to the stuff which constitutes nature. |
| 9450 | If all properties are potencies, and stimuli and manifestation characterise them, there is a regress [Bird] |
| Full Idea: Potencies are characterized in terms of their stimulus and manifestation properties, then if potencies are the only properties then these properties are also potencies, and must be characterized by yet further properties, leading to a vicious regress. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 1.2) | |
| A reaction: This is cited as the most popular objection to the dispositional account of properties. |
| 9498 | The essence of a potency involves relations, e.g. mass, to impressed force and acceleration [Bird] |
| Full Idea: The essence of a potency involves a relation to something else; if inertial mass is a potency then its essence involves a relation to a stimulus property (impressed force) and a manifestation property (acceleration). | |
| From: Alexander Bird (Nature's Metaphysics [2007], 5.3.3) | |
| A reaction: It doesn't seem quite right to say that the relations are part of the essence, if they might not occur, but some other relations might happen in their place. An essence is what makes a relation possible (like being good-looking). |
| 9474 | A disposition is finkish if a time delay might mean the manifestation fizzles out [Bird] |
| Full Idea: Finkish dispositions arise because the time delay between stimulus and manifestation provides an opportunity for the disposition to go out of existence and so halt the process that would bring about the manifestation. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 2.2.3) | |
| A reaction: This is a problem for the conditional analysis of dispositions; there may be a disposition, but it never reaches manifestation. Bird rightly points us towards actual powers rather than dispositions that need manifestation. |
| 9475 | A robust pot attached to a sensitive bomb is not fragile, but if struck it will easily break [Bird] |
| Full Idea: If a robust iron pot is attached to a bomb with a sensitive detonator. If the pot is struck, the bomb will go off, so they counterfactual 'if the pot were struck it would break' is true, but it is not a fragile pot. This is a 'mimic' of the disposition. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 2.2.5.1) | |
| A reaction: A very nice example, showing that a true disposition would have to be an internal feature (a power) of the pot itself, not a mere disposition to behave. The problem is these pesky empiricists, who want to reduce it all to what is observable. |
| 9499 | Megarian actualists deny unmanifested dispositions [Bird] |
| Full Idea: The Megarian actualist denies that a disposition can exist without being manifested. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 5.4) | |
| A reaction: I agree with Bird that this extreme realism seems wrong. As he puts it (p.109), "unrealized possibilities must be part of the actual world". This commitment is beginning to change my understanding of the world I am looking at. |
| 9486 | Why should a universal's existence depend on instantiation in an existing particular? [Bird] |
| Full Idea: An instantiation condition seems to be a failure of nerve as regards realism about universals. If universals really are entities in their own right, why should their existence depend upon a relationship with existing particulars? | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.2.2) | |
| A reaction: I like this challenge, which seems to leave fans of universals no option but full-blown Platonism, which most of them recognise as being deeply implausible. |
| 9472 | Resemblance itself needs explanation, presumably in terms of something held in common [Bird] |
| Full Idea: The realist view of resemblance nominalism is that it is resemblance that needs explaining. When there is resemblance it is natural to want to explain it, in terms of something held in common. Explanations end somewhere, but not with resemblance. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 2.1.2) | |
| A reaction: I smell a regress. If a knife and a razor resemble because they share sharpness, you have to see that the sharp phenomenon falls within the category of 'sharpness' before you can make the connection, which is spotting its similarity. |
| 7931 | If a substance is just a thing that has properties, it seems to be a characterless non-entity [Leibniz, by Macdonald,C] |
| Full Idea: For Leibniz, to distinguish between a substance and its properties in order to provide a thing or entity in which properties can inhere leads necessarily to the absurd conclusion that the substance itself must be a truly characterless non-entity. | |
| From: report of Gottfried Leibniz (Monadology [1716]) by Cynthia Macdonald - Varieties of Things Ch.3 | |
| A reaction: This is obviously one of the basic thoughts in any discussion of substances. It is why physicists ignore them, and Leibniz opted for a 'bundle' theory. But the alternative seems daft too - free-floating properties, hooked onto one another. |
| 17554 | There must be some internal difference between any two beings in nature [Leibniz] |
| Full Idea: There are never two beings in nature that are perfectly alike, two beings in which it is not possible to discover an internal difference, that is, one founded on an intrinsic denomination. | |
| From: Gottfried Leibniz (Monadology [1716], §09) | |
| A reaction: From this it follows that if two things really are indiscernible, then we must say that they are one thing. He says monads all differ from one another. People certainly do. Leibniz must say this of electrons. How can he know this? |
| 9482 | If the laws necessarily imply p, that doesn't give a new 'nomological' necessity [Bird] |
| Full Idea: It does not add to the kinds of necessity to say that p is 'nomologically necessary' iff (the laws of nature → p) is metaphysically necessary. That trick of construction could be pulled for 'feline necessity' (true in all worlds that contain cats). | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.1.2) | |
| A reaction: I love it! Bird seems to think that the only necessity is 'metaphysical' necessity, true in all possible worlds, and he is right. The question arises in modal logic, though, of the accessibility between worlds (which might give degrees of necessity?). |
| 9481 | Logical necessitation is not a kind of necessity; George Orwell not being Eric Blair is not a real possibility [Bird] |
| Full Idea: I do not regard logical necessitation as a kind of necessity. It is logically possible that George Orwell is not Eric Blair, but in what sense is this any kind of possibility? It arises from having two names, but that confers no genuine possibility. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.1.2) | |
| A reaction: How refreshing. All kinds of concepts like this are just accepted by philosophers as obvious, until someone challenges them. The whole undergrowth of modal thinking needs a good flamethrower taken to it. |
| 2112 | Truths of reason are known by analysis, and are necessary; facts are contingent, and their opposites possible [Leibniz] |
| Full Idea: There are two kinds of truths: of reasoning and of facts. Truths of reasoning are necessary and their opposites impossible. Facts are contingent and their opposites possible. A necessary truth is known by analysis. | |
| From: Gottfried Leibniz (Monadology [1716], §33) |
| 9505 | Empiricist saw imaginability and possibility as close, but now they seem remote [Bird] |
| Full Idea: Whereas the link between imaginability and possibility was once held, under the influence of empiricism, to be close, it is now widely held to be very remote. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 8) | |
| A reaction: Tim Williamson nicely argues the opposite - that assessment of possibility is an adjunct of our ability to think counterfactually, which is precisely an operation of the imagination. Big error is possible, but how else could we do it? |
| 9491 | Haecceitism says identity is independent of qualities and without essence [Bird] |
| Full Idea: The core of haecceitism is the view that the transworld identity of particulars does not supervene on their qualitative features. ...The simplest expression of it is that particulars lack essential properties. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 4.2.1) | |
| A reaction: This seems to be something the 'bare substratum' account of substance (associated with Locke). You are left with the difficulty of how to individuate an instance of the haecceity, as opposed to the bundle of properties attached to it. |
| 9344 | Mathematical analysis ends in primitive principles, which cannot be and need not be demonstrated [Leibniz] |
| Full Idea: At the end of the analytical method in mathematics there are simple ideas of which no definition can be given. Moreover there are axioms and postulates, in short, primitive principles, which cannot be demonstrated and do not need demonstration. | |
| From: Gottfried Leibniz (Monadology [1716], §35) | |
| A reaction: My view is that we do not know such principles when we apprehend them in isolation. I would call them 'intuitions'. They only ascend to the status of knowledge when the mathematics is extended and derived from them, and found to work. |
| 8725 | 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. |
| 2110 | We all expect the sun to rise tomorrow by experience, but astronomers expect it by reason [Leibniz] |
| Full Idea: When we expect it to be day tomorrow, we all behave as empiricists, because until now it has always happened thus. The astronomer alone knows this by reason. | |
| From: Gottfried Leibniz (Monadology [1716], §28) |
| 9487 | We can't reject all explanations because of a regress; inexplicable A can still explain B [Bird] |
| Full Idea: Some regard the potential regress of explanations as a reason to think that the very idea of explanation is illusory. This is a fallacy; it is not a necessary condition on A's explaining B that we have an explanation for A also. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.2.4) | |
| A reaction: True, though to say 'B is explained by A, but A is totally baffling' is not the account we are dreaming of. And the explanation would certainly fail if we could say nothing at all about A, apart from naming it. |
| 2109 | Increase a conscious machine to the size of a mill - you still won't see perceptions in it [Leibniz] |
| Full Idea: If a conscious machine were increased in size, one might enter it like a mill, but we should only see the parts impinging on one another; we should not see anything which would explain a perception. | |
| From: Gottfried Leibniz (Monadology [1716], §17) | |
| A reaction: A wonderful image for capturing a widely held intuition. It seems to motivate Colin McGinn's 'Mysterianism'. The trouble is Leibniz didn't think big/small enough. Down at the level of molecules it might become obvious what a perception is. 'Might'. |
| 19362 | We know the 'I' and its contents by abstraction from awareness of necessary truths [Leibniz] |
| Full Idea: It is through the knowledge of necessary truths and through their abstraction that we rise to reflective acts, which enable us to think of that which is called "I" and enable us to consider that this or that is in us. | |
| From: Gottfried Leibniz (Monadology [1716], §30) | |
| A reaction: For Leibniz, necessary truth can only be known a priori. Sense experience won't reveal the self, as Hume observed. We evidently 'abstract' the idea of 'I' from the nature of a priori thought. Animals have no self (or morals) for this reason. |
| 12707 | The true elements are atomic monads [Leibniz] |
| Full Idea: Monads are the true atoms of nature and, in brief, the elements of things. | |
| From: Gottfried Leibniz (Monadology [1716], (opening)), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 2 | |
| A reaction: Thus in one sentence Leibniz gives us a theory of natural elements, and an account of atoms. This kind of speculation got metaphysics a bad name when science unravelled a more accurate picture. The bones must be picked out of Leibniz. |
| 9493 | We should explain causation by powers, not powers by causation [Bird] |
| Full Idea: The notion of 'causal power' is not to be analysed in terms of causation; if anything, the relationship is the reverse. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 4.2.1 n71) | |
| A reaction: It is a popular view these days to take causation as basic (as opposed to the counterfactual account), but I prefer this view. If anything is basic in nature, it is the dynamic force in the engine room, which is the active powers of substances. |
| 9494 | Singularism about causes is wrong, as the universals involved imply laws [Bird] |
| Full Idea: While singularists about causation might think that a particular has its causal powers independently of law, it is difficult to see how a universal could have or confer causal powers without generating what we would naturally think of as a law. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 4.2.1 n71) | |
| A reaction: This is a middle road between the purely singularist account (Anscombe) and the fully nomological account. We might say that a caused event will be 'involved in law-like behaviour', without attributing the cause to a law. |
| 9507 | Laws are explanatory relationships of things, which supervene on their essences [Bird] |
| Full Idea: The laws of a domain are the fundamental, general explanatory relationships between kinds, quantities, and qualities of that domain, that supervene upon the essential natures of those things. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 10.1) | |
| A reaction: This is the scientific essentialist view of laws [see entries there, in 'Laws of Nature']. There seems uncertainty between 'kinds' and 'qualities' (with 'quantities' looking like a category mistake). I vote, with Ellis, for natural kinds as the basis. |
| 9488 | Laws are either disposition regularities, or relations between properties [Bird] |
| Full Idea: Instead of viewing laws as regular relationships between dispositional properties and stimulus-manifestation, they can be conceived of as a relation between properties. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.4) | |
| A reaction: Bird offers these as the two main views, with the first coming from scientific essentialism, and the second from Armstrong's account of universals. Personally I favour the first, but Bird suggests that powers give the best support for both views. |
| 9496 | That other diamonds are hard does not explain why this one is [Bird] |
| Full Idea: The fact that some other diamonds are hard does not explain why this diamond is hard. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 4.3.2) | |
| A reaction: A very nice aphorism! It pinpoints the whole error of trying to explain the behaviour of the world by citing laws. Why should this item obey that law? Bird prefers 'powers', and so do I. |
| 9479 | Dispositional essentialism says laws (and laws about laws) are guaranteed regularities [Bird] |
| Full Idea: For the regularity version of dispositional essentialism about laws, laws are those regularities whose truth is guaranteed by the essential dispositional nature of one or more of the constituents. Regularities that supervene on such laws are also laws. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.1.2) | |
| A reaction: Even if you accept necessary behaviour resulting from essential dispositions, you still need to distinguish the important regularities from the accidental ones, so the word 'guarantee' is helpful, even if it raises lots of difficulties. |
| 9473 | Laws cannot offer unified explanations if they don't involve universals [Bird] |
| Full Idea: Laws, or what flow from them, are supposed to provide a unified explanation of the behaviours of particulars. Without universals the explanation of the behaviours of things lacks the required unity. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 2.1.2) | |
| A reaction: Sounds a bit question-begging? Gravity seems fairly unified, whereas the frequency of London buses doesn't. Maybe I could unify bus-behaviour by positing a few new universals? The unity should first be in the phenomena, not in the explanation. |
| 9484 | If the universals for laws must be instantiated, a vanishing particular could destroy a law [Bird] |
| Full Idea: If universals exist only where and when they are instantiated, this make serious trouble for the universals view of laws. It would be most odd if a particular, merely by changing its properties, could cause a law to go out of existence. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.2.2) | |
| A reaction: This sounds conclusive. He notes that this is probably why Armstrong does not adopt this view (though Lowe seems to favour it). Could there be a possible property (and concomitant law) which was never ever instantiated? |
| 9506 | Salt necessarily dissolves in water, because of the law which makes the existence of salt possible [Bird] |
| Full Idea: We cannot have a world where it is true both that salt exists (which requires Coulomb's Law to be true), and that it fails to dissolve in water (which requires Coulomb's Law to be false). So the dissolving is necessary even if the Law is contingent. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 8.2) | |
| A reaction: Excellent. It is just like the bonfire on the Moon (imaginable through ignorance, but impossible). People who assert that the solubility of salt is contingent tend not to know much about chemistry. |
| 23713 | Most laws supervene on fundamental laws, which are explained by basic powers [Bird, by Friend/Kimpton-Nye] |
| Full Idea: According to Bird, non-fundamental laws supervene on fundamental laws, and so are ultimately explained by fundamental powers. | |
| From: report of Alexander Bird (Nature's Metaphysics [2007]) by Friend/Kimpton-Nye - Dispositions and Powers 3.6.1 | |
| A reaction: This looks like the picture I subscribe to. Roughly, fundamental laws are explained by powers, and non-fundamental laws are explained by properties, which are complexes of powers. 'Fundamental' may not be a precise term! |
| 9489 | Essentialism can't use conditionals to explain regularities, because of possible interventions [Bird] |
| Full Idea: The straightforward dispositional essentialist account of laws by subjunctive conditionals is false because dispositions typically suffer from finks and antidotes. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.4) | |
| A reaction: [Finks and antidotes intervene before a disposition can take effect] This seems very persuasive to me, and shows why you can't just explain laws as counterfactual or conditional claims. Explanation demands what underlies them. |
| 9504 | The relational view of space-time doesn't cover times and places where things could be [Bird] |
| Full Idea: The obvious problem with the simple relational view of space and time is that it fails to account for the full range of spatio-temporal possibility. There seem to be times and places where objects and events could be, but are not. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 7.3.2) | |
| A reaction: This view seems strongly supported by intuition. I certainly don't accept the views of physicists and cosmologists on the subject, because they seem to approach the whole thing too instrumentally. |
| 2114 | This is the most perfect possible universe, in its combination of variety with order [Leibniz] |
| Full Idea: From all the possible universes God chooses this one to obtain as much variety as possible, but with the greatest order possible; that is, it is the means of obtaining the greatest perfection possible. | |
| From: Gottfried Leibniz (Monadology [1716], §58) |
| 2113 | God alone (the Necessary Being) has the privilege that He must exist if He is possible [Leibniz] |
| Full Idea: God alone (or the Necessary Being) has the privilege that He must exist if He is possible. | |
| From: Gottfried Leibniz (Monadology [1716], §45) |