38 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) |
| 9065 | S5 collapses iterated modalities (◊□P→□P, and ◊◊P→◊P) [Keefe/Smith] |
| Full Idea: S5 collapses iterated modalities (so ◊□P → □P, and ◊◊P → ◊P). | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §5) | |
| A reaction: It is obvious why this might be controversial, and there seems to be a general preference for S4. There may be confusions of epistemic and ontic (and even semantic?) possibilities within a single string of modalities. |
| 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) |
| 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. |
| 9064 | Objects such as a cloud or Mount Everest seem to have fuzzy boundaries in nature [Keefe/Smith] |
| Full Idea: A common intuition is that a vague object has indeterminate or fuzzy spatio-temporal boundaries, such as a cloud. Mount Everest can only have arbitrary boundaries placed around it, so in nature it must have fuzzy boundaries. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §5) | |
| A reaction: We would have to respond by questioning whether Everest counts precisely as an 'object'. At the microscopic or subatomic level it seems that virtually everything has fuzzy boundaries. Maybe boundaries don't really exist. |
| 9044 | If someone is borderline tall, no further information is likely to resolve the question [Keefe/Smith] |
| Full Idea: If Tek is borderline tall, the unclarity does not seem to be epistemic, because no amount of further information about his exact height (or the heights of others) could help us decide whether he is tall. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
| A reaction: One should add also that information about social conventions or conventions about the usage of the word 'tall' will not help either. It seems fairly obvious that God would not know whether Tek is tall, so the epistemic view is certainly counterintuitive. |
| 9048 | The simplest approach, that vagueness is just ignorance, retains classical logic and semantics [Keefe/Smith] |
| Full Idea: The simplest approach to vagueness is to retain classical logic and semantics. Borderline cases are either true or false, but we don't know which, and, despite appearances, vague predicates have well-defined extensions. Vagueness is ignorance. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
| A reaction: It seems to me that you must have a rather unhealthy attachment to the logicians' view of the world to take this line. It is the passion of the stamp collector, to want everything in sets, with neatly labelled properties, and inference lines marked out. |
| 9055 | The epistemic view of vagueness must explain why we don't know the predicate boundary [Keefe/Smith] |
| Full Idea: A key question for the epistemic view of vagueness is: why are we ignorant of the facts about where the boundaries of vague predicates lie? | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §2) | |
| A reaction: Presumably there is a range of answers, from laziness, to inability to afford the instruments, to limitations on human perception. At the limit, with physical objects, how do we tell whether it is us or the object which is afflicted with vagueness? |
| 9049 | Supervaluationism keeps true-or-false where precision can be produced, but not otherwise [Keefe/Smith] |
| Full Idea: The supervaluationist view of vagueness is that 'tall' comes out true or false on all the ways in which we can make 'tall' precise. There is a gap for borderline cases, but 'tall or not-tall' is still true wherever you draw a boundary. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
| A reaction: [Kit Fine is the spokesperson for this; it preserves classical logic, but not semantics] This doesn't seem to solve the problem of vagueness, but it does (sort of) save the principle of excluded middle. |
| 9056 | Vague statements lack truth value if attempts to make them precise fail [Keefe/Smith] |
| Full Idea: The supervaluationist view of vagueness proposes that a sentence is true iff it is true on all precisifications, false iff false on all precisifications, and neither true nor false otherwise. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §3) | |
| A reaction: This seems to be just a footnote to the Russell/Unger view, that logic works if the proposition is precise, but otherwise it is either just the mess of ordinary life, or the predicate doesn't apply at all. |
| 9058 | Some of the principles of classical logic still fail with supervaluationism [Keefe/Smith] |
| Full Idea: Supervaluationist logic (now with a 'definite' operator D) fails to preserve certain classical principles about consequence and rules of inference. For example, reduction ad absurdum, contraposition, the deduction theorem and argument by cases. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §3) | |
| A reaction: The aim of supervaluationism was to try to preserve some classical logic, especially the law of excluded middle, in the face of problems of vagueness. More drastic views, like treating vagueness as irrelevant to logic, or the epistemic view, do better. |
| 9059 | The semantics of supervaluation (e.g. disjunction and quantification) is not classical [Keefe/Smith] |
| Full Idea: The semantics of supervaluational views is not classical. A disjunction can be true without either of its disjuncts being true, and an existential quantification can be true without any of its substitution instances being true. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §3) | |
| A reaction: There is a vaguely plausible story here (either red or orange, but not definitely one nor tother; there exists an x, but which x it is is undecidable), but I think I will vote for this all being very very wrong. |
| 9060 | Supervaluation misunderstands vagueness, treating it as a failure to make things precise [Keefe/Smith] |
| Full Idea: Why should we think vague language is explained away by how things would be if it were made precise? Supervaluationism misrepresents vague expressions, as vague only because we have not bothered to make them precise. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §3) | |
| A reaction: The theory still leaves a gap where vagueness is ineradicable, so the charge doesn't seem quite fair. Logicians always yearn for precision, but common speech enjoys wallowing in a sea of easy-going vagueness, which works fine. |
| 9050 | A third truth-value at borderlines might be 'indeterminate', or a value somewhere between 0 and 1 [Keefe/Smith] |
| Full Idea: One approach to predications in borderline cases is to say that they have a third truth value - 'neutral', 'indeterminate' or 'indefinite', leading to a three-valued logic. Or a degree theory, such as fuzzy logic, with infinite values between 0 and 1. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
| A reaction: This looks more like a strategy for computer programmers than for metaphysicians, as it doesn't seem to solve the difficulty of things to which no one can quite assign any value at all. Sometimes you can't be sure if an entity is vague. |
| 9061 | People can't be placed in a precise order according to how 'nice' they are [Keefe/Smith] |
| Full Idea: There is no complete ordering of people by niceness, and two people could be both fairly nice, nice to intermediate degrees, while there is no fact of the matter about who is the nicer. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §4) | |
| A reaction: This is a difficulty if you are trying to decide vague predicates by awarding them degrees of truth. Attempts to place a precise value on 'nice' seem to miss the point, even more than utilitarian attempts to score happiness. |
| 9062 | If truth-values for vagueness range from 0 to 1, there must be someone who is 'completely tall' [Keefe/Smith] |
| Full Idea: Many-valued theories still seem to have a sharp boundary between sentences taking truth-value 1 and those taking value less than 1. So there is a last man in our sorites series who counts as 'completely tall'. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §4) | |
| A reaction: Lovely. Completely nice, totally red, perfectly childlike, an utter mountain, one hundred per cent amused. The enterprise seems to have the same implausibility found in Bayesian approaches to assessing evidence. |
| 9063 | How do we decide if my coat is red to degree 0.322 or 0.321? [Keefe/Smith] |
| Full Idea: What could determine which is the correct function, settling that my coat is red to degree 0.322 rather than 0.321? | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §4) | |
| A reaction: It is not just the uncertainty of placing the coat on the scale. The two ends of the scale have all the indeterminacy of being red rather than orange (or, indeed, pink). You are struggling to find a spot on the ruler, when the ruler is placed vaguely. |
| 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. |
| 9045 | Vague predicates involve uncertain properties, uncertain objects, and paradoxes of gradual change [Keefe/Smith] |
| Full Idea: Three interrelated features of vague predicates such as 'tall', 'red', 'heap', 'child' are that they have borderline cases (application is uncertain), they lack well-defined extensions (objects are uncertain), and they're susceptible to sorites paradoxes. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
| A reaction: The issue will partly depend on what you think an object is: choose from bundles of properties, total denial, essential substance, or featureless substance with properties. The fungal infection of vagueness could creep in at any point, even the words. |
| 9047 | Many vague predicates are multi-dimensional; 'big' involves height and volume; heaps include arrangement [Keefe/Smith] |
| Full Idea: Many vague predicates are multi-dimensional. 'Big' of people depends on both height and volume; 'nice' does not even have clear dimensions; whether something is a 'heap' depends both the number of grains and their arrangement. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
| A reaction: Anyone who was hoping for a nice tidy theory for this problem should abandon hope at this point. Huge numbers of philosophical problems can be simplified by asking 'what exactly do you mean here?' (e.g. tall or bulky?). |
| 9053 | If there is a precise borderline area, that is not a case of vagueness [Keefe/Smith] |
| Full Idea: If a predicate G has a sharply-bounded set of cases falling in between the positive and negative, this shows that merely having borderline cases is not sufficient for vagueness. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
| A reaction: Thus you might have 'pass', 'fail' and 'take the test again'. But there seem to be two cases in the border area: will decide later, and decision seems impossible. And the sharp boundaries may be quite arbitrary. |
| 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? |
| 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) |
| 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. |
| 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) |
| 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. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 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. |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |
| 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) |