108 ideas
| 2546 | Philosophy is a magnificent failure in its attempt to overstep the limits of our knowledge [McGinn] |
| 6052 | Definitions identify two concepts, so they presuppose identity [McGinn] |
| 17774 | Definitions make our intuitions mathematically useful [Mayberry] |
| 17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
| 6064 | Regresses are only vicious in the context of an explanation [McGinn] |
| 6088 | Truth is a method of deducing facts from propositions [McGinn] |
| 6084 | 'Snow does not fall' corresponds to snow does fall [McGinn] |
| 6085 | The idea of truth is built into the idea of correspondence [McGinn] |
| 6083 | The coherence theory of truth implies idealism, because facts are just coherent beliefs [McGinn] |
| 6086 | Truth is the property of propositions that makes it possible to deduce facts [McGinn] |
| 6087 | Without the disquotation device for truth, you could never form beliefs from others' testimony [McGinn] |
| 17796 | There is a semi-categorical axiomatisation of set-theory [Mayberry] |
| 17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry] |
| 17800 | The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry] |
| 17801 | The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry] |
| 17803 | Limitation of size is part of the very conception of a set [Mayberry] |
| 17786 | The mainstream of modern logic sees it as a branch of mathematics [Mayberry] |
| 17788 | First-order logic only has its main theorems because it is so weak [Mayberry] |
| 17791 | Only second-order logic can capture mathematical structure up to isomorphism [Mayberry] |
| 6051 | In 'x is F and x is G' we must assume the identity of x in the two statements [McGinn] |
| 6055 | Both non-contradiction and excluded middle need identity in their formulation [McGinn] |
| 6059 | Identity is unitary, indefinable, fundamental and a genuine relation [McGinn] |
| 2544 | Thoughts have a dual aspect: as they seem to introspection, and their underlying logical reality [McGinn] |
| 6067 | Existential quantifiers just express the quantity of things, leaving existence to the predicate 'exists' [McGinn] |
| 6042 | The quantifier is overrated as an analytical tool [McGinn] |
| 17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
| 6069 | 'Partial quantifier' would be a better name than 'existential quantifier', as no existence would be implied [McGinn] |
| 6068 | We need an Intentional Quantifier ("some of the things we talk about.."), so existence goes into the proposition [McGinn] |
| 17790 | No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry] |
| 17779 | 'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry] |
| 17778 | Axiomatiation relies on isomorphic structures being essentially the same [Mayberry] |
| 17780 | 'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry] |
| 17789 | No logic which can axiomatise arithmetic can be compact or complete [Mayberry] |
| 6007 | If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R] |
| 6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
| 6008 | Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R] |
| 17784 | Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry] |
| 17782 | Greek quantities were concrete, and ratio and proportion were their science [Mayberry] |
| 17781 | Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry] |
| 17799 | Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry] |
| 17797 | Cantor extended the finite (rather than 'taming the infinite') [Mayberry] |
| 17775 | If proof and definition are central, then mathematics needs and possesses foundations [Mayberry] |
| 17776 | The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry] |
| 17777 | Foundations need concepts, definition rules, premises, and proof rules [Mayberry] |
| 17804 | Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry] |
| 17792 | 1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry] |
| 17793 | It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry] |
| 17794 | Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry] |
| 17802 | We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry] |
| 17805 | Set theory is not just another axiomatised part of mathematics [Mayberry] |
| 6070 | Existence is a primary quality, non-existence a secondary quality [McGinn] |
| 6062 | Existence can't be analysed as instantiating a property, as instantiation requires existence [McGinn] |
| 6065 | We can't analyse the sentence 'something exists' in terms of instantiated properties [McGinn] |
| 22427 | To explain object qualities, primary qualities must be more than mere sources of experience [McGinn] |
| 6082 | If causal power is the test for reality, that will exclude necessities and possibilities [McGinn] |
| 6075 | Facts are object-plus-extension, or property-plus-set-of-properties, or object-plus-property [McGinn] |
| 17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
| 18892 | Suppose a world where I'm from different gametes; add my gametes; which one is more me? [McGinn] |
| 12019 | McGinn falsely claims necessity of origin is a special case of the necessity of identity [Forbes,G on McGinn] |
| 6058 | Identity propositions are not always tautological, and have a key epistemic role [McGinn] |
| 6053 | Identity is as basic as any concept could ever be [McGinn] |
| 6043 | Type-identity is close similarity in qualities [McGinn] |
| 6045 | It is best to drop types of identity, and speak of 'identity' or 'resemblance' [McGinn] |
| 6044 | Qualitative identity is really numerical identity of properties [McGinn] |
| 6046 | Qualitative identity can be analysed into numerical identity of the type involved [McGinn] |
| 6054 | Sherlock Holmes does not exist, but he is self-identical [McGinn] |
| 6066 | Existence is a property of all objects, but less universal than self-identity, which covers even conceivable objects [McGinn] |
| 6047 | All identity is necessary, though identity statements can be contingently true [McGinn] |
| 6050 | Leibniz's Law presupposes the notion of property identity [McGinn] |
| 6049 | Leibniz's Law says 'x = y iff for all P, Px iff Py' [McGinn] |
| 6048 | Leibniz's Law is so fundamental that it almost defines the concept of identity [McGinn] |
| 6080 | Modality is not objects or properties, but the type of binding of objects to properties [McGinn] |
| 6079 | If 'possible' is explained as quantification across worlds, there must be possible worlds [McGinn] |
| 6171 | Beliefs are states of the head that explain behaviour, and also items with referential truth-conditions [McGinn] |
| 22415 | Relativity means differing secondary perceptions are not real disagreements [McGinn] |
| 22416 | Phenomenalism is correct for secondary qualities, so scepticism is there impossible [McGinn] |
| 22422 | Maybe all possible sense experience must involve both secondary and primary qualities [McGinn] |
| 22428 | You understood being red if you know the experience involved; not so with thngs being square [McGinn] |
| 22413 | Being red simply consists in looking red [McGinn] |
| 22414 | You don't need to know how a square thing looks or feels to understand squareness [McGinn] |
| 22423 | Touch doesn't provide direct experience of primary qualities, because touch feels temperature [McGinn] |
| 22426 | We can perceive objectively, because primary qualities are not mind-created [McGinn] |
| 22412 | Lockean secondary qualities (unlike primaries) produce particular sensory experiences [McGinn] |
| 22421 | Could there be a mind which lacked secondary quality perception? [McGinn] |
| 22424 | Secondary qualities contain information; their variety would be superfluous otherwise [McGinn] |
| 22425 | The utility theory says secondary qualities give information useful to human beings [McGinn] |
| 7629 | We see objects 'directly' by representing them [McGinn] |
| 6081 | Necessity and possibility are big threats to the empiricist view of knowledge [McGinn] |
| 6071 | Scepticism about reality is possible because existence isn't part of appearances [McGinn] |
| 4691 | If all mental life were conscious, we would be unable to see things, or to process speech [McGinn] |
| 2539 | Mental modules for language, social, action, theory, space, emotion [McGinn] |
| 2545 | Free will is mental causation in action [McGinn] |
| 2543 | Brains aren't made of anything special, suggesting panpsychism [McGinn] |
| 7388 | McGinn invites surrender, by saying it is hopeless trying to imagine conscious machines [Dennett on McGinn] |
| 2540 | Examining mind sees no brain; examining brain sees no mind [McGinn] |
| 3185 | Multiple realisability rules out hidden essences and experts as the source of water- and gold-concepts [McGinn] |
| 18410 | Indexical thought is in relation to my self-consciousness [McGinn] |
| 22417 | Indexicals do not figure in theories of physics, because they are not explanatory causes [McGinn] |
| 22420 | The indexical perspective is subjective, incorrigible and constant [McGinn] |
| 18402 | Indexical concepts are indispensable, as we need them for the power to act [McGinn] |
| 4690 | If meaning is speaker's intentions, it can be reduced to propositional attitudes, and philosophy of mind [McGinn] |
| 6077 | Semantics should not be based on set-membership, but on instantiation of properties in objects [McGinn] |
| 2547 | There is information if there are symbols which refer, and which can combine into a truth or falsehood [McGinn] |
| 6074 | Clearly predicates have extensions (applicable objects), but are the extensions part of their meaning? [McGinn] |
| 22418 | I can know indexical truths a priori, unlike their non-indexical paraphrases [McGinn] |
| 2542 | Causation in the material world is energy-transfer, of motion, electricity or gravity [McGinn] |
| 6072 | If Satan is the most imperfect conceivable being, he must have non-existence [McGinn] |
| 6073 | I think the fault of the Ontological Argument is taking the original idea to be well-defined [McGinn] |