110 ideas
11283 | There is pure deductive reasoning, and explanatory demonstration reasoning [Aristotle, by Politis] |
1672 | Maybe everything could be demonstrated, if demonstration can be reciprocal or circular [Aristotle] |
1684 | Two falsehoods can be contrary to one another [Aristotle] |
12145 | Definitions are of what something is, and that is universal [Aristotle] |
12075 | An Aristotelian definition is causal [Aristotle, by Witt] |
12384 | Definition by division needs predicates, which are well ordered and thorough [Aristotle] |
9066 | You can define objects by progressively identifying what is the same and what is different [Aristotle] |
12382 | What it is and why it is are the same; screening defines and explains an eclipse [Aristotle] |
1668 | An axiom is a principle which must be understood if one is to learn anything [Aristotle] |
12376 | Demonstrations by reductio assume excluded middle [Aristotle] |
12373 | Something holds universally when it is proved of an arbitrary and primitive case [Aristotle] |
12363 | Everything is either asserted or denied truly [Aristotle] |
1618 | We study bound variables not to know reality, but to know what reality language asserts [Quine] |
8455 | Canonical notation needs quantification, variables and predicates, but not names [Quine, by Orenstein] |
8456 | Quine extended Russell's defining away of definite descriptions, to also define away names [Quine, by Orenstein] |
1611 | Names can be converted to descriptions, and Russell showed how to eliminate those [Quine] |
13004 | Aristotle's axioms (unlike Euclid's) are assumptions awaiting proof [Aristotle, by Leibniz] |
12377 | Mathematics is concerned with forms, not with superficial properties [Aristotle] |
12372 | The essence of a triangle comes from the line, mentioned in any account of triangles [Aristotle] |
12369 | A unit is what is quantitatively indivisible [Aristotle] |
1613 | Logicists cheerfully accept reference to bound variables and all sorts of abstract entities [Quine] |
1616 | Formalism says maths is built of meaningless notations; these build into rules which have meaning [Quine] |
1615 | Intuitionism says classes are invented, and abstract entities are constructed from specified ingredients [Quine] |
1614 | Conceptualism holds that there are universals but they are mind-made [Quine] |
10241 | For Quine, there is only one way to exist [Quine, by Shapiro] |
4064 | The idea of a thing and the idea of existence are two sides of the same coin [Quine, by Crane] |
19277 | Quine rests existence on bound variables, because he thinks singular terms can be analysed away [Quine, by Hale] |
12210 | Quine's ontology is wrong; his question is scientific, and his answer is partly philosophical [Fine,K on Quine] |
8496 | What actually exists does not, of course, depend on language [Quine] |
1610 | To be is to be the value of a variable, which amounts to being in the range of reference of a pronoun [Quine] |
8459 | Fictional quantification has no ontology, so we study ontology through scientific theories [Quine, by Orenstein] |
8497 | An ontology is like a scientific theory; we accept the simplest scheme that fits disorderly experiences [Quine] |
16261 | If commitment rests on first-order logic, we obviously lose the ontology concerning predication [Maudlin on Quine] |
7698 | If to be is to be the value of a variable, we must already know the values available [Jacquette on Quine] |
18910 | To seek truth, study the real connections between subjects and attributes [Aristotle] |
1612 | Realism, conceptualism and nominalism in medieval universals reappear in maths as logicism, intuitionism and formalism [Quine] |
1675 | Separate Forms aren't needed for logic, but universals (one holding of many) are essential [Aristotle] |
1677 | We can forget the Forms, as they are irrelevant, and not needed in giving demonstrations [Aristotle] |
15402 | There is no entity called 'redness', and that some things are red is ultimate and irreducible [Quine] |
4443 | Quine has argued that predicates do not have any ontological commitment [Quine, by Armstrong] |
8498 | Treating scattered sensations as single objects simplifies our understanding of experience [Quine] |
14193 | 'Substance theorists' take modal properties as primitive, without structure, just falling under a sortal [Paul,LA] |
14195 | If an object's sort determines its properties, we need to ask what determines its sort [Paul,LA] |
14196 | Substance essentialism says an object is multiple, as falling under various different sortals [Paul,LA] |
1687 | Why are being terrestrial and a biped combined in the definition of man, but being literate and musical aren't? [Aristotle] |
1681 | Units are positionless substances, and points are substances with position [Aristotle] |
14198 | Absolutely unrestricted qualitative composition would allow things with incompatible properties [Paul,LA] |
14190 | Deep essentialist objects have intrinsic properties that fix their nature; the shallow version makes it contextual [Paul,LA] |
12146 | Definitions recognise essences, so are not themselves essences [Aristotle] |
14191 | Deep essentialists say essences constrain how things could change; modal profiles fix natures [Paul,LA] |
17039 | The predicates of a thing's nature are necessary to it [Aristotle] |
11994 | Aristotelian essences are properties mentioned at the starting point of a science [Aristotle, by Kung] |
14192 | Essentialism must deal with charges of arbitrariness, and failure to reduce de re modality [Paul,LA] |
14197 | An object's modal properties don't determine its possibilities [Paul,LA] |
12381 | What is necessary cannot be otherwise [Aristotle] |
1690 | A stone travels upwards by a forced necessity, and downwards by natural necessity [Aristotle] |
8856 | Quine's indispensability argument said arguments for abstracta were a posteriori [Quine, by Yablo] |
14189 | 'Modal realists' believe in many concrete worlds, 'actualists' in just this world, 'ersatzists' in abstract other worlds [Paul,LA] |
12443 | Can an unactualized possible have self-identity, and be distinct from other possibles? [Quine] |
12072 | For Aristotle knowledge is explanatory, involving understanding, and principles or causes [Aristotle, by Witt] |
12073 | 'Episteme' means grasping causes, universal judgments, explanation, and teaching [Aristotle, by Witt] |
12378 | The reason why is the key to knowledge [Aristotle] |
12364 | We understand a thing when we know its explanation and its necessity [Aristotle] |
12370 | Some understanding, of immediate items, is indemonstrable [Aristotle] |
12366 | We only understand something when we know its explanation [Aristotle] |
1685 | No one has mere belief about something if they think it HAS to be true [Aristotle] |
1673 | Knowledge proceeds from principles, so it is hard to know if we know [Aristotle] |
18209 | We can never translate our whole language of objects into phenomenalism [Quine] |
12379 | You cannot understand anything through perception [Aristotle] |
16725 | Some knowledge is lost if you lose a sense, and there is no way the knowledge can be replaced [Aristotle] |
23309 | Aristotle's concepts of understanding and explanation mean he is not a pure empiricist [Aristotle, by Frede,M] |
1693 | Animals may have some knowledge if they retain perception, but understanding requires reasons to be given [Aristotle] |
9067 | Many memories of the same item form a single experience [Aristotle] |
1671 | Sceptics say justification is an infinite regress, or it stops at the unknowable [Aristotle] |
1670 | When you understand basics, you can't be persuaded to change your mind [Aristotle] |
1691 | Aim to get definitions of the primitive components, thus establishing the kind, and work towards the attributes [Aristotle] |
12383 | There must be definitions before demonstration is possible [Aristotle] |
1674 | All demonstration is concerned with existence, axioms and properties [Aristotle] |
24068 | Demonstration is more than entailment, as the explanatory order must match the causal order [Aristotle, by Koslicki] |
17310 | Aristotle gets asymmetric consequence from demonstration, which reflects real causal priority [Aristotle, by Koslicki] |
21359 | Aristotle doesn't actually apply his theory of demonstration to his practical science [Leroi on Aristotle] |
1667 | Premises must be true, primitive and immediate, and prior to and explanatory of conclusions [Aristotle] |
12365 | We can know by demonstration, which is a scientific deduction leading to understanding [Aristotle] |
10918 | Demonstrative understanding rests on necessary features of the thing in itself [Aristotle] |
12374 | Demonstrations must be necessary, and that depends on the middle term [Aristotle] |
12148 | Demonstrations are syllogisms which give explanations [Aristotle] |
1679 | Universal demonstrations are about thought; particular demonstrations lead to perceptions [Aristotle] |
1680 | Demonstration is better with fewer presuppositions, and it is quicker if these are familiar [Aristotle] |
12147 | The principles of demonstrations are definitions [Aristotle] |
12371 | A demonstration is a deduction which proceeds from necessities [Aristotle] |
1683 | We learn universals from many particulars [Aristotle] |
12367 | What is most universal is furthest away, and the particulars are nearest [Aristotle] |
12380 | Universals are valuable because they make the explanations plain [Aristotle] |
12385 | Are particulars explained more by universals, or by other particulars? [Aristotle] |
1689 | Explanation is of the status of a thing, inferences to it, initiation of change, and purpose [Aristotle] |
1686 | What we seek and understand are facts, reasons, existence, and identity [Aristotle] |
12357 | Explanation and generality are inseparable [Aristotle, by Wedin] |
1669 | The foundation or source is stronger than the thing it causes [Aristotle] |
1678 | Universals give better explanations, because they are self-explanatory and primitive [Aristotle] |
9068 | Perception creates primitive immediate principles by building a series of firm concepts [Aristotle] |
9069 | A perception lodging in the soul creates a primitive universal, which becomes generalised [Aristotle] |
9070 | We learn primitives and universals by induction from perceptions [Aristotle] |
1619 | There is an attempt to give a verificationist account of meaning, without the error of reducing everything to sensations [Dennett on Quine] |
1609 | I do not believe there is some abstract entity called a 'meaning' which we can 'have' [Quine] |
1617 | The word 'meaning' is only useful when talking about significance or about synonymy [Quine] |
19159 | Quine relates predicates to their objects, by being 'true of' them [Quine, by Davidson] |
12368 | Negation takes something away from something [Aristotle] |
1692 | If you shouldn't argue in metaphors, then you shouldn't try to define them either [Aristotle] |
12375 | Whatever holds of a kind intrinsically holds of it necessarily [Aristotle] |
1688 | Properties must be proved, but not essence; but existents are not a kind, so existence isn't part of essence [Aristotle] |