30 ideas
| 9108 | From an impossibility anything follows [William of Ockham] |
| 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] |
| 10807 | Mathematics reduces to set theory, which reduces, with some mereology, to the singleton function [Lewis] |
| 10809 | We can accept the null set, but not a null class, a class lacking members [Lewis] |
| 10811 | The null set plays the role of last resort, for class abstracts and for existence [Lewis] |
| 10812 | The null set is not a little speck of sheer nothingness, a black hole in Reality [Lewis] |
| 14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
| 14240 | The empty set is something, not nothing! [Oliver/Smiley] |
| 14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
| 14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
| 10813 | What on earth is the relationship between a singleton and an element? [Lewis] |
| 10814 | Are all singletons exact intrinsic duplicates? [Lewis] |
| 14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
| 10806 | Megethology is the result of adding plural quantification to mereology [Lewis] |
| 10816 | We can use mereology to simulate quantification over relations [Lewis] |
| 9106 | The word 'every' only signifies when added to a term such as 'man', referring to all men [William of Ockham] |
| 14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
| 14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
| 14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
| 14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
| 10808 | Mathematics is generalisations about singleton functions [Lewis] |
| 14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
| 10815 | We don't need 'abstract structures' to have structural truths about successor functions [Lewis] |
| 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] |
| 10810 | I say that absolutely any things can have a mereological fusion [Lewis] |
| 9109 | If essence and existence were two things, one could exist without the other, which is impossible [William of Ockham] |
| 9105 | Some concepts for propositions exist only in the mind, and in no language [William of Ockham] |