40 ideas
2666 | Carneades' pinnacles of philosophy are the basis of knowledge (the criterion of truth) and the end of appetite (good) [Carneades, by Cicero] |
21390 | Future events are true if one day we will say 'this event is happening now' [Carneades] |
21672 | We say future things are true that will possess actuality at some following time [Carneades, by Cicero] |
10676 | The Axiom of Choice is a non-logical principle of set-theory [Hossack] |
10686 | The Axiom of Choice guarantees a one-one correspondence from sets to ordinals [Hossack] |
23623 | Predicativism says only predicated sets exist [Hossack] |
23624 | The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack] |
23625 | Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack] |
10687 | Maybe we reduce sets to ordinals, rather than the other way round [Hossack] |
10677 | Extensional mereology needs two definitions and two axioms [Hossack] |
23628 | The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack] |
23627 | 'Before' and 'after' are not two relations, but one relation with two orders [Hossack] |
10671 | Plural definite descriptions pick out the largest class of things that fit the description [Hossack] |
10666 | Plural reference will refer to complex facts without postulating complex things [Hossack] |
10669 | Plural reference is just an abbreviation when properties are distributive, but not otherwise [Hossack] |
10675 | A plural comprehension principle says there are some things one of which meets some condition [Hossack] |
10673 | Plural language can discuss without inconsistency things that are not members of themselves [Hossack] |
10680 | The theory of the transfinite needs the ordinal numbers [Hossack] |
10684 | I take the real numbers to be just lengths [Hossack] |
23626 | Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack] |
10674 | A plural language gives a single comprehensive induction axiom for arithmetic [Hossack] |
10681 | In arithmetic singularists need sets as the instantiator of numeric properties [Hossack] |
10685 | Set theory is the science of infinity [Hossack] |
23621 | Numbers are properties, not sets (because numbers are magnitudes) [Hossack] |
23622 | We can only mentally construct potential infinities, but maths needs actual infinities [Hossack] |
10668 | We are committed to a 'group' of children, if they are sitting in a circle [Hossack] |
10664 | Complex particulars are either masses, or composites, or sets [Hossack] |
10678 | The relation of composition is indispensable to the part-whole relation for individuals [Hossack] |
12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
10665 | Leibniz's Law argues against atomism - water is wet, unlike water molecules [Hossack] |
10682 | The fusion of five rectangles can decompose into more than five parts that are rectangles [Hossack] |
15825 | Carneades denied the transitivity of identity [Carneades, by Chisholm] |
21389 | Carneades distinguished logical from causal necessity, when talking of future events [Long on Carneades] |
21671 | Voluntary motion is intrinsically within our power, and this power is its cause [Carneades, by Cicero] |
21391 | Some actions are within our power; determinism needs prior causes for everything - so it is false [Carneades, by Cicero] |
21674 | Even Apollo can only foretell the future when it is naturally necessary [Carneades, by Cicero] |
10663 | A thought can refer to many things, but only predicate a universal and affirm a state of affairs [Hossack] |
7398 | Carneades said that after a shipwreck a wise man would seize the only plank by force [Carneades, by Tuck] |
21392 | People change laws for advantage; either there is no justice, or it is a form of self-injury [Carneades, by Lactantius] |
10683 | We could ignore space, and just talk of the shape of matter [Hossack] |