179 ideas
| 12997 | Analysis is the art of finding the middle term [Leibniz] |
| 7001 | If you begin philosophy with language, you find yourself trapped in it [Heil] |
| 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] |
| 7037 | Parsimony does not imply the world is simple, but that our theories should try to be [Heil] |
| 7038 | A theory with few fundamental principles might still posit a lot of entities [Heil] |
| 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] |
| 7004 | The view that truth making is entailment is misguided and misleading [Heil] |
| 13000 | Truth is correspondence between mental propositions and what they are about [Leibniz] |
| 13520 | A 'tautology' must include connectives [Wolf,RS] |
| 13524 | Deduction Theorem: T∪{P}|-Q, then T|-(P→Q), which justifies Conditional Proof [Wolf,RS] |
| 13521 | Universal Specification: ∀xP(x) implies P(t). True for all? Then true for an instance [Wolf,RS] |
| 13522 | Universal Generalization: If we prove P(x) with no special assumptions, we can conclude ∀xP(x) [Wolf,RS] |
| 13523 | Existential Generalization (or 'proof by example'): if we can say P(t), then we can say something is P [Wolf,RS] |
| 13529 | Empty Set: ∃x∀y ¬(y∈x). The unique empty set exists [Wolf,RS] |
| 13526 | Comprehension Axiom: if a collection is clearly specified, it is a set [Wolf,RS] |
| 7035 | God does not create the world, and then add the classes [Heil] |
| 12992 | Logic teaches us how to order and connect our thoughts [Leibniz] |
| 13534 | In first-order logic syntactic and semantic consequence (|- and |=) nicely coincide [Wolf,RS] |
| 13535 | First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation [Wolf,RS] |
| 10056 | At bottom eternal truths are all conditional [Leibniz] |
| 12974 | People who can't apply names usually don't understand the thing to which it applies [Leibniz] |
| 13519 | Model theory uses sets to show that mathematical deduction fits mathematical truth [Wolf,RS] |
| 13531 | Model theory reveals the structures of mathematics [Wolf,RS] |
| 13532 | Model theory 'structures' have a 'universe', some 'relations', some 'functions', and some 'constants' [Wolf,RS] |
| 13533 | First-order model theory rests on completeness, compactness, and the Löwenheim-Skolem-Tarski theorem [Wolf,RS] |
| 13537 | An 'isomorphism' is a bijection that preserves all structural components [Wolf,RS] |
| 13539 | The LST Theorem is a serious limitation of first-order logic [Wolf,RS] |
| 13002 | It is always good to reduce the number of axioms [Leibniz] |
| 13538 | If a theory is complete, only a more powerful language can strengthen it [Wolf,RS] |
| 13525 | Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS] |
| 13008 | Geometry, unlike sensation, lets us glimpse eternal truths and their necessity [Leibniz] |
| 13530 | An ordinal is an equivalence class of well-orderings, or a transitive set whose members are transitive [Wolf,RS] |
| 12956 | Only whole numbers are multitudes of units [Leibniz] |
| 12937 | We shouldn't just accept Euclid's axioms, but try to demonstrate them [Leibniz] |
| 13518 | Modern mathematics has unified all of its objects within set theory [Wolf,RS] |
| 12932 | The idea of being must come from our own existence [Leibniz] |
| 7017 | The reductionist programme dispenses with levels of reality [Heil] |
| 7003 | There are levels of organisation, complexity, description and explanation, but not of reality [Heil] |
| 12966 | Objects of ideas can be divided into abstract and concrete, and then further subdivided [Leibniz] |
| 7045 | Realism says some of our concepts 'cut nature at the joints' [Heil] |
| 7065 | Anti-realists who reduce reality to language must explain the existence of language [Heil] |
| 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] |
| 7020 | Concepts don't carve up the world, which has endless overlooked or ignored divisions [Heil] |
| 7007 | I think of properties as simultaneously dispositional and qualitative [Heil] |
| 7015 | A predicate applies truly if it picks out a real property of objects [Heil] |
| 7042 | A theory of universals says similarity is identity of parts; for modes, similarity is primitive [Heil] |
| 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] |
| 7023 | Powers or dispositions are usually seen as caused by lower-level qualities [Heil] |
| 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] |
| 7025 | Are a property's dispositions built in, or contingently added? [Heil] |
| 12941 | There cannot be power without action; the power is a disposition to act [Leibniz] |
| 7034 | Universals explain one-over-many relations, and similar qualities, and similar behaviour [Heil] |
| 7039 | How could you tell if the universals were missing from a world of instances? [Heil] |
| 7009 | Similarity among modes will explain everthing universals were for [Heil] |
| 7041 | Similar objects have similar properties; properties are directly similar [Heil] |
| 7032 | Objects join sets because of properties; the property is not bestowed by set membership [Heil] |
| 7008 | Trope theorists usually see objects as 'bundles' of tropes [Heil] |
| 7018 | Objects are substances, which are objects considered as the bearer of properties [Heil] |
| 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] |
| 7019 | Maybe there is only one substance, space-time or a quantum field [Heil] |
| 11855 | Substances cannot be bare, but have activity as their essence [Leibniz] |
| 7046 | Rather than 'substance' I use 'objects', which have properties [Heil] |
| 7047 | Statues and bronze lumps have discernible differences, so can't be identical [Heil] |
| 7048 | Do we reduce statues to bronze, or eliminate statues, or allow statues and bronze? [Heil] |
| 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] |
| 12933 | Arithmetic and geometry are implicitly innate, awaiting revelation [Leibniz] |
| 12991 | Children learn language fast, with little instruction and few definitions [Leibniz] |
| 12929 | All of our thoughts come from within the soul, and not from the senses [Leibniz] |
| 12940 | What is left of the 'blank page' if you remove the ideas? [Leibniz] |
| 7028 | If properties were qualities without dispositions, they would be undetectable [Heil] |
| 7029 | Can we distinguish the way a property is from the property? [Heil] |
| 7030 | Properties don't possess ways they are, because that just is the property [Heil] |
| 7051 | Objects only have secondary qualities because they have primary qualities [Heil] |
| 7044 | Secondary qualities are just primary qualities considered in the light of their effect on us [Heil] |
| 7052 | Colours aren't surface properties, because of radiant sources and the colour of the sky [Heil] |
| 19358 | Colour and pain must express the nature of their stimuli, without exact resemblance [Leibniz] |
| 7053 | Treating colour as light radiation has the implausible result that tomatoes are not red [Heil] |
| 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] |
| 12947 | We only believe in sensible things when reason helps the senses [Leibniz] |
| 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] |
| 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] |
| 7066 | If the world is just texts or social constructs, what are texts and social constructs? [Heil] |
| 7021 | If the world is theory-dependent, the theories themselves can't be theory-dependent [Heil] |
| 7026 | Science is sometimes said to classify powers, neglecting qualities [Heil] |
| 5053 | The instances confirming a general truth are never enough to establish its necessity [Leibniz] |
| 7060 | One form of explanation is by decomposition [Heil] |
| 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] |
| 7010 | Dispositionality provides the grounding for intentionality [Heil] |
| 7054 | Intentionality now has internalist (intrinsic to thinkers) and externalist (environment or community) views [Heil] |
| 7011 | Qualia are not extra appendages, but intrinsic ingredients of material states and processes [Heil] |
| 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] |
| 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] |
| 7061 | Philosophers' zombies aim to show consciousness is over and above the physical world [Heil] |
| 7063 | Zombies are based on the idea that consciousness relates contingently to the physical [Heil] |
| 7064 | Functionalists deny zombies, since identity of functional state means identity of mental state [Heil] |
| 7027 | Functionalists say objects can be the same in disposition but differ in quality [Heil] |
| 7062 | Functionalism cannot explain consciousness just by functional organisation [Heil] |
| 7059 | The 'explanatory gap' is used to say consciousness is inexplicable, at least with current concepts [Heil] |
| 7012 | If a car is a higher-level entity, distinct from its parts, how could it ever do anything? [Heil] |
| 7043 | Multiple realisability is actually one predicate applying to a diverse range of properties [Heil] |
| 12935 | Every feeling is the perception of a truth [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] |
| 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] |
| 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] |
| 7058 | Externalism is causal-historical, or social, or biological [Heil] |
| 7057 | Intentionality is based in dispositions, which are intrinsic to agents, suggesting internalism [Heil] |
| 7013 | The Picture Theory claims we can read reality from our ways of speaking about it [Heil] |
| 7002 | If propositions are states of affairs or sets of possible worlds, these lack truth values [Heil] |
| 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] |
| 7016 | The standard view is that causal sequences are backed by laws, and between particular events [Heil] |
| 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] |
| 7036 | The real natural properties are sparse, but there are many complex properties [Heil] |
| 12954 | God's essence is the source of possibilities, and his will the source of existents [Leibniz] |
| 12988 | The universe contains everything possible for its perfect harmony [Leibniz] |
| 1414 | A perfection is a simple quality, which is positive and absolute, and has no limit [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] |