64 ideas
| 20186 | Unlike knowledge, wisdom cannot be misused [Zagzebski] |
| 19694 | Wisdom is the property of a person, not of their cognitive state [Zagzebski, by Whitcomb] |
| 20221 | Precision is only one of the virtues of a good definition [Zagzebski] |
| 20220 | Objection by counterexample is weak, because it only reveals inaccuracies in one theory [Zagzebski] |
| 15716 | If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert] |
| 18844 | You would cripple mathematics if you denied Excluded Middle [Hilbert] |
| 17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
| 17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
| 12456 | I aim to establish certainty for mathematical methods [Hilbert] |
| 12461 | We believe all mathematical problems are solvable [Hilbert] |
| 8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
| 13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
| 12462 | Only the finite can bring certainty to the infinite [Hilbert] |
| 9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
| 12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
| 12455 | The idea of an infinite totality is an illusion [Hilbert] |
| 12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| 9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
| 18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
| 18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
| 17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
| 17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
| 17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
| 17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
| 10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
| 10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
| 22293 | Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter] |
| 12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
| 10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
| 18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
| 12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
| 20188 | Modern epistemology is too atomistic, and neglects understanding [Zagzebski] |
| 20223 | Epistemology is excessively atomic, by focusing on justification instead of understanding [Zagzebski] |
| 20217 | Truth is valuable, but someone knowing the truth is more valuable [Zagzebski] |
| 20191 | Some beliefs are fairly voluntary, and others are not at all so [Zagzebski] |
| 20222 | Knowledge either aims at a quantity of truths, or a quality of understanding of truths [Zagzebski] |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| 20225 | For internalists Gettier situations are where internally it is fine, but there is an external mishap [Zagzebski] |
| 20226 | Gettier problems are always possible if justification and truth are not closely linked [Zagzebski] |
| 20228 | We avoid the Gettier problem if the support for the belief entails its truth [Zagzebski] |
| 20227 | Gettier cases arise when good luck cancels out bad luck [Zagzebski] |
| 20194 | Intellectual virtues are forms of moral virtue [Zagzebski] |
| 20206 | Intellectual and moral prejudice are the same vice (and there are other examples) [Zagzebski] |
| 20208 | We can name at least thirteen intellectual vices [Zagzebski] |
| 20210 | A reliable process is no use without the virtues to make use of them [Zagzebski] |
| 20215 | A justified belief emulates the understanding and beliefs of an intellectually virtuous person [Zagzebski] |
| 20187 | Epistemic perfection for reliabilism is a truth-producing machine [Zagzebski] |
| 20218 | The self is known as much by its knowledge as by its action [Zagzebski] |
| 20205 | The feeling accompanying curiosity is neither pleasant nor painful [Zagzebski] |
| 20202 | Motives involve desires, but also how the desires connect to our aims [Zagzebski] |
| 20216 | Modern moral theory concerns settling conflicts, rather than human fulfilment [Zagzebski] |
| 20193 | Moral luck means our praise and blame may exceed our control or awareness [Zagzebski] |
| 20199 | Nowadays we doubt the Greek view that the flourishing of individuals and communities are linked [Zagzebski] |
| 20207 | Every moral virtue requires a degree of intelligence [Zagzebski] |
| 20196 | Virtue theory is hopeless if there is no core of agreed universal virtues [Zagzebski] |
| 20200 | A virtue must always have a corresponding vice [Zagzebski] |
| 20201 | Eight marks distingush skills from virtues [Zagzebski, by PG] |
| 20203 | Virtues are deep acquired excellences of persons, which successfully attain desire ends [Zagzebski] |
| 20214 | Virtue theory can have lots of rules, as long as they are grounded in virtues and in facts [Zagzebski] |
| 20213 | We need phronesis to coordinate our virtues [Zagzebski] |
| 20209 | For the virtue of honesty you must be careful with the truth, and not just speak truly [Zagzebski] |
| 20197 | The courage of an evil person is still a quality worth having [Zagzebski] |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |