22 ideas
17641 | Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell] |
17638 | If one proposition is deduced from another, they are more certain together than alone [Russell] |
9108 | From an impossibility anything follows [William of Ockham] |
17632 | Non-contradiction was learned from instances, and then found to be indubitable [Russell] |
9107 | A proposition is true if its subject and predicate stand for the same thing [William of Ockham] |
16300 | Ockham had an early axiomatic account of truth [William of Ockham, by Halbach] |
9106 | The word 'every' only signifies when added to a term such as 'man', referring to all men [William of Ockham] |
17629 | Which premises are ultimate varies with context [Russell] |
17630 | The sources of a proof are the reasons why we believe its conclusion [Russell] |
17640 | Finding the axioms may be the only route to some new results [Russell] |
17627 | It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell] |
17628 | Arithmetic was probably inferred from relationships between physical objects [Russell] |
9113 | Just as unity is not a property of a single thing, so numbers are not properties of many things [William of Ockham] |
9110 | The words 'thing' and 'to be' assert the same idea, as a noun and as a verb [William of Ockham] |
15388 | Universals are single things, and only universal in what they signify [William of Ockham] |
12697 | Indivisibles are not parts, but the extrema of parts [Leibniz] |
9109 | If essence and existence were two things, one could exist without the other, which is impossible [William of Ockham] |
17637 | The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell] |
17639 | Believing a whole science is more than believing each of its propositions [Russell] |
17631 | Induction is inferring premises from consequences [Russell] |
9105 | Some concepts for propositions exist only in the mind, and in no language [William of Ockham] |
17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |