80 ideas
| 5896 | Speak the truth, for this alone deifies man [Pythagoras, by Porphyry] |
| 3051 | Pythagoras discovered the numerical relation of sounds on a string [Pythagoras, by Diog. Laertius] |
| 4588 | There is no such thing as 'science'; there are just many different sciences [Heil] |
| 18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
| 6298 | Kitcher says maths is an idealisation of the world, and our operations in dealing with it [Kitcher, by Resnik] |
| 12392 | Mathematical a priorism is conceptualist, constructivist or realist [Kitcher] |
| 18078 | The interest or beauty of mathematics is when it uses current knowledge to advance undestanding [Kitcher] |
| 12426 | The 'beauty' or 'interest' of mathematics is just explanatory power [Kitcher] |
| 12395 | Real numbers stand to measurement as natural numbers stand to counting [Kitcher] |
| 12425 | Complex numbers were only accepted when a geometrical model for them was found [Kitcher] |
| 7485 | For Pythagoreans 'one' is not a number, but the foundation of numbers [Pythagoras, by Watson] |
| 18071 | A one-operation is the segregation of a single object [Kitcher] |
| 18066 | The old view is that mathematics is useful in the world because it describes the world [Kitcher] |
| 18083 | With infinitesimals, you divide by the time, then set the time to zero [Kitcher] |
| 12393 | Intuition is no basis for securing a priori knowledge, because it is fallible [Kitcher] |
| 18061 | Mathematical intuition is not the type platonism needs [Kitcher] |
| 12420 | If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher] |
| 12387 | Mathematical knowledge arises from basic perception [Kitcher] |
| 12412 | My constructivism is mathematics as an idealization of collecting and ordering objects [Kitcher] |
| 18065 | We derive limited mathematics from ordinary things, and erect powerful theories on their basis [Kitcher] |
| 18077 | The defenders of complex numbers had to show that they could be expressed in physical terms [Kitcher] |
| 12423 | Analyticity avoids abstract entities, but can there be truth without reference? [Kitcher] |
| 18069 | Arithmetic is an idealizing theory [Kitcher] |
| 18068 | Arithmetic is made true by the world, but is also made true by our constructions [Kitcher] |
| 18070 | We develop a language for correlations, and use it to perform higher level operations [Kitcher] |
| 18072 | Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) [Kitcher] |
| 18063 | Conceptualists say we know mathematics a priori by possessing mathematical concepts [Kitcher] |
| 18064 | If meaning makes mathematics true, you still need to say what the meanings refer to [Kitcher] |
| 4616 | A higher level is 'supervenient' if it is determined by lower levels, but has its own natural laws [Heil] |
| 4603 | Functionalists in Fodor's camp usually say that a genuine property is one that figures in some causal laws [Heil] |
| 4617 | A stone does not possess the property of being a stone; its other properties make it a stone [Heil] |
| 4615 | Complex properties are not new properties, they are merely new combinations of properties [Heil] |
| 4612 | Complex properties are just arrangements of simple properties; they do not "emerge" as separate [Heil] |
| 4587 | From the property predicates P and Q, we can get 'P or Q', but it doesn't have to designate another property [Heil] |
| 4611 | The supporters of 'tropes' treat objects as bundles of tropes, when I think objects 'possess' properties [Heil] |
| 18067 | Abstract objects were a bad way of explaining the structure in mathematics [Kitcher] |
| 4592 | If you can have the boat without its current planks, and the planks with no boat, the planks aren't the boat [Heil] |
| 4586 | You can't embrace the formal apparatus of possible worlds, but reject the ontology [Heil] |
| 4591 | Idealism explains appearances by identifying appearances with reality [Heil] |
| 12390 | A priori knowledge comes from available a priori warrants that produce truth [Kitcher] |
| 12418 | In long mathematical proofs we can't remember the original a priori basis [Kitcher] |
| 12389 | Knowledge is a priori if the experience giving you the concepts thus gives you the knowledge [Kitcher] |
| 12416 | We have some self-knowledge a priori, such as knowledge of our own existence [Kitcher] |
| 12413 | A 'warrant' is a process which ensures that a true belief is knowledge [Kitcher] |
| 20473 | If experiential can defeat a belief, then its justification depends on the defeater's absence [Kitcher, by Casullo] |
| 4610 | Different generations focus on either the quality of mind, or its scientific standing, or the content of thought [Heil] |
| 4618 | If minds are realised materially, it looks as if the material laws will pre-empt any causal role for mind [Heil] |
| 4621 | Whatever exists has qualities, so it is no surprise that states of minds have qualities [Heil] |
| 4623 | Propositional attitudes are not the only intentional states; there is also mental imagery [Heil] |
| 4626 | The widespread externalist view says intentionality has content because of causal links of agent to world [Heil] |
| 18075 | Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher] |
| 4622 | Error must be possible in introspection, because error is possible in all judgements [Heil] |
| 4590 | If causation is just regularities in events, the interaction of mind and body is not a special problem [Heil] |
| 4614 | Disposition is a fundamental feature of reality, since basic particles are capable of endless possible interactions [Heil] |
| 4595 | No mental state entails inevitable behaviour, because other beliefs or desires may intervene [Heil] |
| 4599 | Hearts are material, but functionalism says the property of being a heart is not a material property [Heil] |
| 4624 | If you are a functionalist, there appears to be no room for qualia [Heil] |
| 4601 | Higher-level sciences cannot be reduced, because their concepts mark boundaries invisible at lower levels [Heil] |
| 4602 | Higher-level sciences designate real properties of objects, which are not reducible to lower levels [Heil] |
| 4593 | 'Property dualism' says mind and body are not substances, but distinct families of properties [Heil] |
| 4597 | Early identity theory talked of mind and brain 'processes', but now the focus is properties [Heil] |
| 4609 | It seems contradictory to be asked to believe that we can be eliminativist about beliefs [Heil] |
| 4596 | The appeal of the identity theory is its simplicity, and its solution to the mental causation problem [Heil] |
| 4598 | Functionalists emphasise that mental processes are not to be reduced to what realises them [Heil] |
| 4619 | 'Multiple realisability' needs to clearly distinguish low-level realisers from what is realised [Heil] |
| 4620 | Multiple realisability is not a relation among properties, but an application of predicates to resembling things [Heil] |
| 4594 | A scientist could know everything about the physiology of headaches, but never have had one [Heil] |
| 4625 | Is mental imagery pictorial, or is it propositional? [Heil] |
| 4607 | Folk psychology and neuroscience are no more competitors than cartography and geology are [Heil] |
| 4605 | Truth-conditions correspond to the idea of 'literal meaning' [Heil] |
| 4606 | To understand 'birds warble' and 'tigers growl', you must also understand 'tigers warble' [Heil] |
| 4604 | If propositions are abstract entities, how do human beings interact with them? [Heil] |
| 3053 | Pythagoras taught that virtue is harmony, and health, and universal good, and God [Pythagoras, by Diog. Laertius] |
| 5244 | For Pythagoreans, justice is simply treating all people the same [Pythagoras, by Aristotle] |
| 375 | When musical harmony and rhythm were discovered, similar features were seen in bodily movement [Pythagoras, by Plato] |
| 638 | Pythagoreans define timeliness, justice and marriage in terms of numbers [Pythagoras, by Aristotle] |
| 553 | Pythagoreans think mathematical principles are the principles of all of nature [Pythagoras, by Aristotle] |
| 554 | Pythagoreans say things imitate numbers, but Plato says things participate in numbers [Pythagoras, by Aristotle] |
| 644 | For Pythagoreans the entire universe is made of numbers [Pythagoras, by Aristotle] |
| 7467 | The modern idea of an immortal soul was largely created by Pythagoras [Pythagoras, by Watson] |