161 ideas
| 12997 | Analysis is the art of finding the middle term [Leibniz] |
| 16325 | Analysis rests on natural language, but its ideal is a framework which revises language [Halbach] |
| 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] |
| 16292 | An explicit definition enables the elimination of what is defined [Halbach] |
| 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] |
| 16307 | Don't trust analogies; they are no more than a guideline [Halbach] |
| 16330 | Truth-value 'gluts' allow two truth values together; 'gaps' give a partial conception of truth [Halbach] |
| 16339 | Truth axioms prove objects exist, so truth doesn't seem to be a logical notion [Halbach] |
| 16324 | Any definition of truth requires a metalanguage [Halbach] |
| 16293 | Traditional definitions of truth often make it more obscure, rather than less [Halbach] |
| 16301 | If people have big doubts about truth, a definition might give it more credibility [Halbach] |
| 13000 | Truth is correspondence between mental propositions and what they are about [Leibniz] |
| 16297 | Semantic theories avoid Tarski's Theorem by sticking to a sublanguage [Halbach] |
| 16337 | Disquotational truth theories are short of deductive power [Halbach] |
| 16294 | Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage [Halbach] |
| 16326 | The main semantic theories of truth are Kripke's theory, and revisions semantics [Halbach] |
| 16311 | To axiomatise Tarski's truth definition, we need a binary predicate for his 'satisfaction' [Halbach] |
| 16318 | Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents [Halbach] |
| 16299 | Gödel numbering means a theory of truth can use Peano Arithmetic as its base theory [Halbach] |
| 16340 | Truth axioms need a base theory, because that is where truth issues arise [Halbach] |
| 16305 | We know a complete axiomatisation of truth is not feasible [Halbach] |
| 16313 | A theory is 'conservative' if it adds no new theorems to its base theory [Halbach, by PG] |
| 16315 | The Tarski Biconditional theory TB is Peano Arithmetic, plus truth, plus all Tarski bi-conditionals [Halbach] |
| 16314 | Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free' [Halbach] |
| 16322 | CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [Halbach] |
| 16327 | Friedman-Sheard is type-free Compositional Truth, with two inference rules for truth [Halbach] |
| 16329 | Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts [Halbach] |
| 16331 | The KF is much stronger deductively than FS, which relies on classical truth [Halbach] |
| 16332 | The KF theory is useful, but it is not a theory containing its own truth predicate [Halbach] |
| 16320 | Some say deflationism is axioms which are conservative over the base theory [Halbach] |
| 16338 | Deflationism says truth is a disquotation device to express generalisations, adding no new knowledge [Halbach] |
| 16317 | The main problem for deflationists is they can express generalisations, but not prove them [Halbach] |
| 16316 | Deflationists say truth is just for expressing infinite conjunctions or generalisations [Halbach] |
| 16319 | Compositional Truth CT proves generalisations, so is preferred in discussions of deflationism [Halbach] |
| 16335 | In Strong Kleene logic a disjunction just needs one disjunct to be true [Halbach] |
| 16334 | In Weak Kleene logic there are 'gaps', neither true nor false if one component lacks a truth value [Halbach] |
| 16309 | Every attempt at formal rigour uses some set theory [Halbach] |
| 12992 | Logic teaches us how to order and connect our thoughts [Leibniz] |
| 16333 | The underestimated costs of giving up classical logic are found in mathematical reasoning [Halbach] |
| 10056 | At bottom eternal truths are all conditional [Leibniz] |
| 16310 | A theory is some formulae and all of their consequences [Halbach] |
| 12974 | People who can't apply names usually don't understand the thing to which it applies [Leibniz] |
| 7760 | Russell only uses descriptions attributively, and Strawson only referentially [Donnellan, by Lycan] |
| 5811 | A definite description can have a non-referential use [Donnellan] |
| 5812 | Definite descriptions are 'attributive' if they say something about x, and 'referential' if they pick x out [Donnellan] |
| 5814 | 'The x is F' only presumes that x exists; it does not actually entail the existence [Donnellan] |
| 13002 | It is always good to reduce the number of axioms [Leibniz] |
| 16342 | You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system [Halbach] |
| 16341 | Normally we only endorse a theory if we believe it to be sound [Halbach] |
| 16344 | Soundness must involve truth; the soundness of PA certainly needs it [Halbach] |
| 16347 | Many new paradoxes may await us when we study interactions between frameworks [Halbach] |
| 16336 | The liar paradox applies truth to a negated truth (but the conditional will serve equally) [Halbach] |
| 13008 | Geometry, unlike sensation, lets us glimpse eternal truths and their necessity [Leibniz] |
| 12956 | Only whole numbers are multitudes of units [Leibniz] |
| 12937 | We shouldn't just accept Euclid's axioms, but try to demonstrate them [Leibniz] |
| 16321 | The compactness theorem can prove nonstandard models of PA [Halbach] |
| 16343 | The global reflection principle seems to express the soundness of Peano Arithmetic [Halbach] |
| 16312 | To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals [Halbach] |
| 16308 | Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach] |
| 12932 | The idea of being must come from our own existence [Leibniz] |
| 16345 | That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction [Halbach] |
| 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] |
| 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] |
| 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] |
| 16346 | Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach] |
| 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] |
| 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] |
| 4302 | You may experience a universal truth, but only reason can tell you that it is always true [Leibniz] |
| 12947 | We only believe in sensible things when reason helps the senses [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] |
| 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] |
| 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] |
| 12938 | An idea is an independent inner object, which expresses the qualities of things [Leibniz] |
| 12950 | We must distinguish images from exact defined ideas [Leibniz] |
| 12945 | Thoughts correspond to sensations, but ideas are independent of thoughts [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] |
| 10435 | A definite description 'the F' is referential if the speaker could thereby be referring to something not-F [Donnellan, by Sainsbury] |
| 10451 | Donnellan is unclear whether the referential-attributive distinction is semantic or pragmatic [Bach on Donnellan] |
| 5813 | A description can successfully refer, even if its application to the subject is not believed [Donnellan] |
| 5815 | Whether a definite description is referential or attributive depends on the speaker's intention [Donnellan] |
| 16298 | We need propositions to ascribe the same beliefs to people with different languages [Halbach] |
| 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] |
| 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] |