22 ideas
7807 | The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra] |
21560 | Any linguistic expression may lack meaning when taken out of context [Russell] |
21561 | 'The number one is bald' or 'the number one is fond of cream cheese' are meaningless [Russell] |
18130 | Axiom of Reducibility: there is always a function of the lowest possible order in a given level [Russell, by Bostock] |
9618 | Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR] |
16014 | It is controversial whether only 'numerical identity' allows two things to be counted as one [Noonan] |
9830 | Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett] |
17265 | Philosophical proofs in mathematics establish truths, and also show their grounds [Bolzano, by Correia/Schnieder] |
21562 | There is no complexity without relations, so no propositions, and no truth [Russell] |
16024 | I could have died at five, but the summation of my adult stages could not [Noonan] |
16023 | Stage theorists accept four-dimensionalism, but call each stage a whole object [Noonan] |
16016 | Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular [Noonan] |
16017 | Identity is usually defined as the equivalence relation satisfying Leibniz's Law [Noonan] |
16015 | Problems about identity can't even be formulated without the concept of identity [Noonan] |
16020 | Identity can only be characterised in a second-order language [Noonan] |
16019 | Leibniz's Law must be kept separate from the substitutivity principle [Noonan] |
16018 | Indiscernibility is basic to our understanding of identity and distinctness [Noonan] |
9185 | Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett] |
22276 | Bolzano saw propositions as objective entities, existing independently of us [Bolzano, by Potter] |
17264 | Propositions are abstract structures of concepts, ready for judgement or assertion [Bolzano, by Correia/Schnieder] |
12232 | A 'proposition' is the sense of a linguistic expression, and can be true or false [Bolzano] |
12233 | The ground of a pure conceptual truth is only in other conceptual truths [Bolzano] |