87 ideas
| 9408 | Science studies phenomena, but only metaphysics tells us what exists [Mumford] |
| 2056 | Philosophers are always switching direction to something more interesting [Plato] |
| 2083 | Either a syllable is its letters (making parts as knowable as whole) or it isn't (meaning it has no parts) [Plato] |
| 2086 | Understanding mainly involves knowing the elements, not their combinations [Plato] |
| 9429 | Many forms of reasoning, such as extrapolation and analogy, are useful but deductively invalid [Mumford] |
| 2082 | A rational account is essentially a weaving together of things with names [Plato] |
| 2052 | Eristic discussion is aggressive, but dialectic aims to help one's companions in discussion [Plato] |
| 15854 | A primary element has only a name, and no logos, but complexes have an account, by weaving the names [Plato] |
| 9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
| 9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
| 9705 | 'fld R' indicates the 'field' of all objects in the relation [Enderton] |
| 9704 | 'ran R' indicates the 'range' of objects being related to [Enderton] |
| 9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
| 9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
| 9699 | The 'powerset' of a set is all the subsets of a given set [Enderton] |
| 9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
| 9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton] |
| 9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
| 9701 | A 'relation' is a set of ordered pairs [Enderton] |
| 9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
| 9708 | A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton] |
| 9709 | A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton] |
| 9711 | A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton] |
| 9706 | A 'function' is a relation in which each object is related to just one other object [Enderton] |
| 9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton] |
| 9717 | A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton] |
| 9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
| 9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
| 9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
| 9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
| 9721 | A logical truth or tautology is a logical consequence of the empty set [Enderton] |
| 9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
| 9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
| 9720 | A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton] |
| 9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
| 9996 | Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton] |
| 9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
| 10216 | We master arithmetic by knowing all the numbers in our soul [Plato] |
| 9427 | For Humeans the world is a world primarily of events [Mumford] |
| 2060 | There seem to be two sorts of change: alteration and motion [Plato] |
| 9446 | Properties are just natural clusters of powers [Mumford] |
| 9435 | A 'porridge' nominalist thinks we just divide reality in any way that suits us [Mumford] |
| 9447 | If properties are clusters of powers, this can explain why properties resemble in degrees [Mumford] |
| 2084 | If a word has no parts and has a single identity, it turns out to be the same kind of thing as a letter [Plato] |
| 15844 | A sum is that from which nothing is lacking, which is a whole [Plato] |
| 15843 | The whole can't be the parts, because it would be all of the parts, which is the whole [Plato] |
| 12248 | How can we show that a universally possessed property is an essential property? [Mumford] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 2080 | Things are only knowable if a rational account (logos) is possible [Plato] |
| 16126 | Expertise is knowledge of the whole by means of the parts [Plato] |
| 2050 | It is impossible to believe something which is held to be false [Plato] |
| 2076 | How can a belief exist if its object doesn't exist? [Plato] |
| 2045 | Perception is infallible, suggesting that it is knowledge [Plato] |
| 2067 | Our senses could have been separate, but they converge on one mind [Plato] |
| 2068 | With what physical faculty do we perceive pairs of opposed abstract qualities? [Plato] |
| 2069 | Thought must grasp being itself before truth becomes possible [Plato] |
| 2078 | You might mistake eleven for twelve in your senses, but not in your mind [Plato] |
| 2089 | An inadequate rational account would still not justify knowledge [Plato] |
| 2085 | Parts and wholes are either equally knowable or equally unknowable [Plato] |
| 2091 | Without distinguishing marks, how do I know what my beliefs are about? [Plato] |
| 2087 | A rational account might be seeing an image of one's belief, like a reflection in a mirror [Plato] |
| 2090 | A rational account involves giving an image, or analysis, or giving a differentiating mark [Plato] |
| 2081 | Maybe primary elements can be named, but not receive a rational account [Plato] |
| 2088 | A rational account of a wagon would mean knowledge of its hundred parts [Plato] |
| 2047 | What evidence can be brought to show whether we are dreaming or not? [Plato] |
| 2053 | If you claim that all beliefs are true, that includes beliefs opposed to your own [Plato] |
| 2054 | Clearly some people are superior to others when it comes to medicine [Plato] |
| 2059 | How can a relativist form opinions about what will happen in the future? [Plato] |
| 9430 | Singular causes, and identities, might be necessary without falling under a law [Mumford] |
| 9445 | We can give up the counterfactual account if we take causal language at face value [Mumford] |
| 9443 | It is only properties which are the source of necessity in the world [Mumford] |
| 9444 | There are four candidates for the logical form of law statements [Mumford] |
| 9416 | Regularities are more likely with few instances, and guaranteed with no instances! [Mumford] |
| 9415 | Would it count as a regularity if the only five As were also B? [Mumford] |
| 9431 | Pure regularities are rare, usually only found in idealized conditions [Mumford] |
| 9441 | Regularity laws don't explain, because they have no governing role [Mumford] |
| 9421 | The best systems theory says regularities derive from laws, rather than constituting them [Mumford] |
| 9422 | If the best system describes a nomological system, the laws are in nature, not in the description [Mumford] |
| 9432 | Laws of nature are necessary relations between universal properties, rather than about particulars [Mumford] |
| 9433 | If laws can be uninstantiated, this favours the view of them as connecting universals [Mumford] |
| 9434 | Laws of nature are just the possession of essential properties by natural kinds [Mumford] |
| 9437 | To distinguish accidental from essential properties, we must include possible members of kinds [Mumford] |
| 9411 | There are no laws of nature in Aristotle; they became standard with Descartes and Newton [Mumford] |
| 9439 | The Central Dilemma is how to explain an internal or external view of laws which govern [Mumford] |
| 9412 | You only need laws if you (erroneously) think the world is otherwise inert [Mumford] |
| 2058 | God must be the epitome of goodness, and we can only approach a divine state by being as good as possible [Plato] |
| 2057 | There must always be some force of evil ranged against good [Plato] |