128 ideas
12997 | Analysis is the art of finding the middle term [Leibniz] |
13009 | A reason is a known truth which leads to assent to some further truth [Leibniz] |
12963 | Opposing reason is opposing truth, since reason is a chain of truths [Leibniz] |
19360 | General principles, even if unconscious, are indispensable for thinking [Leibniz] |
12983 | A nominal definition is of the qualities, but the real definition is of the essential inner structure [Leibniz] |
12982 | One essence can be expressed by several definitions [Leibniz] |
12976 | If our ideas of a thing are imperfect, the thing can have several unconnected definitions [Leibniz] |
12984 | Real definitions, unlike nominal definitions, display possibilities [Leibniz] |
12980 | Genus and differentia might be swapped, and 'rational animal' become 'animable rational' [Leibniz] |
13000 | Truth is correspondence between mental propositions and what they are about [Leibniz] |
12992 | Logic teaches us how to order and connect our thoughts [Leibniz] |
10056 | At bottom eternal truths are all conditional [Leibniz] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
12974 | People who can't apply names usually don't understand the thing to which it applies [Leibniz] |
13002 | It is always good to reduce the number of axioms [Leibniz] |
13008 | Geometry, unlike sensation, lets us glimpse eternal truths and their necessity [Leibniz] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
12956 | Only whole numbers are multitudes of units [Leibniz] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
12937 | We shouldn't just accept Euclid's axioms, but try to demonstrate them [Leibniz] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
12932 | The idea of being must come from our own existence [Leibniz] |
12966 | Objects of ideas can be divided into abstract and concrete, and then further subdivided [Leibniz] |
12993 | Have five categories - substance, quantity, quality, action/passion, relation - and their combinations [Leibniz] |
12989 | Our true divisions of nature match reality, but are probably incomplete [Leibniz] |
12959 | We discern active power from our minds, so mind must be involved in all active powers [Leibniz] |
12967 | I use the word 'entelechy' for a power, to include endeavour, as well as mere aptitude [Leibniz] |
12965 | All occurrence in the depth of a substance is spontaneous 'action' [Leibniz] |
12999 | Substances are primary powers; their ways of being are the derivative powers [Leibniz] |
5056 | Material or immaterial substances cannot be conceived without their essential activity [Leibniz] |
12969 | The active powers which are not essential to the substance are the 'real qualities' [Leibniz] |
12941 | There cannot be power without action; the power is a disposition to act [Leibniz] |
7720 | Two things can only resemble one another in some respect, and that may reintroduce a universal [Lowe] |
12990 | Real (non-logical) abstract terms are either essences or accidents [Leibniz] |
12939 | Wholly uniform things like space and numbers are mere abstractions [Leibniz] |
12979 | The only way we can determine individuals is by keeping hold of them [Leibniz] |
12971 | If two individuals could be indistinguishable, there could be no principle of individuation [Leibniz] |
13098 | We use things to distinguish places and times, not vice versa [Leibniz] |
13075 | No two things are quite the same, so there must be an internal principle of distinction [Leibniz] |
12953 | Fluidity is basic, and we divide into bodies according to our needs [Leibniz] |
12943 | Individuality is in the bond substance gives between past and future [Leibniz] |
11855 | Substances cannot be bare, but have activity as their essence [Leibniz] |
7712 | On substances, Leibniz emphasises unity, Spinoza independence, Locke relations to qualities [Lowe] |
12970 | We can imagine two bodies interpenetrating, as two rays of light seem to [Leibniz] |
12986 | The essence of baldness is vague and imperfect [Leibniz] |
12968 | A 'substratum' is just a metaphor for whatever supports several predicates [Leibniz] |
12931 | Particular truths are just instances of general truths [Leibniz] |
12811 | We can't know individuals, or determine their exact individuality [Leibniz] |
12981 | Essence is just the possibility of a thing [Leibniz] |
5057 | If you fully understand a subject and its qualities, you see how the second derive from the first [Leibniz] |
12987 | For some sorts, a member of it is necessarily a member [Leibniz] |
12884 | The same whole ceases to exist if a part is lost [Leibniz] |
12975 | We have a distinct idea of gold, to define it, but not a perfect idea, to understand it [Leibniz] |
12805 | If two people apply a single term to different resemblances, they refer to two different things [Leibniz] |
12806 | Locke needs many instances to show a natural kind, but why not a single instance? [Leibniz, by Jolley] |
12972 | Bodies, like Theseus's ship, are only the same in appearance, and never strictly the same [Leibniz] |
5055 | No two things are totally identical [Leibniz] |
12978 | A perfect idea of an object shows that the object is possible [Leibniz] |
17079 | Proofs of necessity come from the understanding, where they have their source [Leibniz] |
12998 | Understanding grasps the agreements and disagreements of ideas [Leibniz] |
12960 | We understand things when they are distinct, and we can derive necessities from them [Leibniz] |
13006 | Certainty is where practical doubt is insane, or at least blameworthy [Leibniz] |
12996 | I know more than I think, since I know I think A then B then C [Leibniz] |
13003 | The Cogito doesn't prove existence, because 'I am thinking' already includes 'I am' [Leibniz] |
21253 | Descartes needs to demonstrate how other people can attain his clear and distinct conceptions [Leibniz] |
12929 | All of our thoughts come from within the soul, and not from the senses [Leibniz] |
12933 | Arithmetic and geometry are implicitly innate, awaiting revelation [Leibniz] |
12991 | Children learn language fast, with little instruction and few definitions [Leibniz] |
12940 | What is left of the 'blank page' if you remove the ideas? [Leibniz] |
19358 | Colour and pain must express the nature of their stimuli, without exact resemblance [Leibniz] |
12948 | A pain doesn't resemble the movement of a pin, but it resembles the bodily movement pins cause [Leibniz] |
13005 | Truth arises among sensations from grounding reasons and from regularities [Leibniz] |
7710 | Perception is a mode of belief-acquisition, and does not involve sensation [Lowe] |
7711 | Science requires a causal theory - perception of an object must be an experience caused by the object [Lowe] |
4302 | You may experience a universal truth, but only reason can tell you that it is always true [Leibniz] |
12930 | The senses are confused, and necessities come from distinct intellectual ideas [Leibniz] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
12947 | We only believe in sensible things when reason helps the senses [Leibniz] |
13001 | Our sensation of green is a confused idea, like objects blurred by movement [Leibniz] |
12949 | Light takes time to reach us, so objects we see may now not exist [Leibniz] |
5053 | The instances confirming a general truth are never enough to establish its necessity [Leibniz] |
12977 | We will only connect our various definitions of gold when we understand it more deeply [Leibniz] |
5054 | Animal thought is a shadow of reasoning, connecting sequences of images by imagination [Leibniz] |
12944 | It is a serious mistake to think that we are aware of all of our perceptions [Leibniz] |
12951 | Abstraction attends to the general, not the particular, and involves universal truths [Leibniz] |
19364 | Volition automatically endeavours to move towards what it sees as good (and away from bad) [Leibniz] |
7714 | Personal identity is a problem across time (diachronic) and at an instant (synchronic) [Lowe] |
12942 | Memory doesn't make identity; a man who relearned everything would still be the same man [Leibniz] |
12973 | We know our own identity by psychological continuity, even if there are some gaps [Leibniz] |
19368 | The will determines action, by what is seen as good, but it does not necessitate it [Leibniz] |
12935 | Every feeling is the perception of a truth [Leibniz] |
7715 | Mentalese isn't a language, because it isn't conventional, or a means of public communication [Lowe] |
12950 | We must distinguish images from exact defined ideas [Leibniz] |
19357 | The idea of green seems simple, but it must be compounded of the ideas of blue and yellow [Leibniz] |
12938 | An idea is an independent inner object, which expresses the qualities of things [Leibniz] |
12945 | Thoughts correspond to sensations, but ideas are independent of thoughts [Leibniz] |
12995 | The name 'gold' means what we know of gold, and also further facts about it which only others know [Leibniz] |
12807 | The word 'gold' means a hidden constitution known to experts, and not just its appearances [Leibniz] |
7722 | If meaning is mental pictures, explain "the cat (or dog!) is NOT on the mat" [Lowe] |
12946 | The idea of the will includes the understanding [Leibniz] |
12964 | If would be absurd not to disagree with someone's taste if it was a taste for poisons [Leibniz] |
12958 | Love is pleasure in the perfection, well-being or happiness of its object [Leibniz] |
12957 | The good is the virtuous, the pleasing, or the useful [Leibniz] |
12962 | Pleasure is a sense of perfection [Leibniz] |
12934 | We can't want everyone to have more than their share, so a further standard is needed [Leibniz] |
12936 | There are natural rewards and punishments, like illness after over-indulgence [Leibniz] |
11856 | Qualities should be predictable from the nature of the subject [Leibniz] |
12994 | Gold has a real essence, unknown to us, which produces its properties [Leibniz] |
12808 | Part of our idea of gold is its real essence, which is not known to us in detail [Leibniz] |
12985 | Maybe motion is definable as 'change of place' [Leibniz] |
12952 | Space is an order among actual and possible things [Leibniz] |
12955 | If there were duration without change, we could never establish its length [Leibniz] |
12954 | God's essence is the source of possibilities, and his will the source of existents [Leibniz] |
1414 | A perfection is a simple quality, which is positive and absolute, and has no limit [Leibniz] |
12988 | The universe contains everything possible for its perfect harmony [Leibniz] |
21252 | Perfections must have overlapping parts if their incompatibility is to be proved [Leibniz] |
19328 | Without the principle of sufficient reason, God's existence could not be demonstrated [Leibniz] |
5058 | Animals have thought and sensation, and indestructible immaterial souls [Leibniz] |