34 ideas
8623 | Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege] |
13907 | If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon] |
18739 | Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew] |
18741 | Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew] |
18744 | Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew] |
6297 | Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik] |
9603 | An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR] |
9894 | A unit is that according to which each existing thing is said to be one [Euclid] |
8738 | Postulate 2 says a line can be extended continuously [Euclid, by Shapiro] |
22278 | Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid] |
8673 | Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend] |
10250 | Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid] |
10302 | Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays] |
14157 | Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid] |
1600 | Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik] |
18740 | If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew] |
14329 | Some dispositional properties (such as mental ones) may have no categorical base [Price,HH] |
18745 | A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew] |
18747 | The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew] |
18748 | Epistemic logic introduced impossible worlds [Horsten/Pettigrew] |
18746 | Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew] |
18750 | Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew] |
9032 | Before we can abstract from an instance of violet, we must first recognise it [Price,HH] |
9034 | There may be degrees of abstraction which allow recognition by signs, without full concepts [Price,HH] |
9035 | If judgement of a characteristic is possible, that part of abstraction must be complete [Price,HH] |
9036 | There is pre-verbal sign-based abstraction, as when ice actually looks cold [Price,HH] |
9037 | Intelligent behaviour, even in animals, has something abstract about it [Price,HH] |
9033 | Recognition must precede the acquisition of basic concepts, so it is the fundamental intellectual process [Price,HH] |
10645 | We reach concepts by clarification, or by definition, or by habitual experience [Price,HH] |
9030 | Abstractions can be interpreted dispositionally, as the ability to recognise or imagine an item [Price,HH] |
9029 | If ideas have to be images, then abstract ideas become a paradoxical problem [Price,HH] |
10646 | Our understanding of 'dog' or 'house' arises from a repeated experience of concomitances [Price,HH] |
9031 | The basic concepts of conceptual cognition are acquired by direct abstraction from instances [Price,HH] |
10644 | A 'felt familiarity' with universals is more primitive than abstraction [Price,HH] |