69 ideas
9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
9605 | If a proposition is false, then its negation is true [Brown,JR] |
9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
9630 | The most brilliant formalist was Hilbert [Brown,JR] |
9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
12747 | Monads are not extended, but have a kind of situation in extension [Leibniz] |
12748 | Only monads are substances, and bodies are collections of them [Leibniz] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
13184 | The division of nature into matter makes distinct appearances, and that presupposes substances [Leibniz] |
13188 | The only indications of reality are agreement among phenomena, and their agreement with necessities [Leibniz] |
12752 | Only unities have any reality [Leibniz] |
13187 | In actual things nothing is indefinite [Leibniz] |
19383 | A man's distant wife dying is a real change in him [Leibniz] |
13179 | A complete monad is a substance with primitive active and passive power [Leibniz] |
12749 | Derivate forces are in phenomena, but primitive forces are in the internal strivings of substances [Leibniz] |
23664 | Powers are quite distinct and simple, and so cannot be defined [Reid] |
23669 | Thinkers say that matter has intrinsic powers, but is also passive and acted upon [Reid] |
23666 | It is obvious that there could not be a power without a subject which possesses it [Reid] |
12722 | Thought terminates in force, rather than extension [Leibniz] |
19379 | The law of the series, which determines future states of a substance, is what individuates it [Leibniz] |
13182 | Changeable accidents are modifications of unchanging essences [Leibniz] |
13178 | Things in different locations are different because they 'express' those locations [Leibniz] |
19411 | In nature there aren't even two identical straight lines, so no two bodies are alike [Leibniz] |
19412 | If two bodies only seem to differ in their position, those different environments will matter [Leibniz] |
19410 | Scientific truths are supported by mutual agreement, as well as agreement with the phenomena [Leibniz] |
23665 | Consciousness is the power of mind to know itself, and minds are grounded in powers [Reid] |
13183 | Primitive forces are internal strivings of substances, acting according to their internal laws [Leibniz] |
23668 | Our own nature attributes free determinations to our own will [Reid] |
19409 | Soul represents body, but soul remains unchanged, while body continuously changes [Leibniz] |
11873 | Our notions may be formed from concepts, but concepts are formed from things [Leibniz] |
9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
13186 | Universals are just abstractions by concealing some of the circumstances [Leibniz] |
9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
20051 | Reid said that agent causation is a unique type of causation [Reid, by Stout,R] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
13185 | Even if extension is impenetrable, this still offers no explanation for motion and its laws [Leibniz] |
8383 | Day and night are constantly conjoined, but they don't cause one another [Reid, by Crane] |
23667 | Regular events don't imply a cause, without an innate conviction of universal causation [Reid] |
23670 | Scientists don't know the cause of magnetism, and only discover its regulations [Reid] |
23671 | Laws are rules for effects, but these need a cause; rules of navigation don't navigate [Reid] |
13177 | An entelechy is a law of the series of its event within some entity [Leibniz] |
13093 | The only permanence in things, constituting their substance, is a law of continuity [Leibniz] |
13096 | The force behind motion is like a soul, with its own laws of continual change [Leibniz] |
13180 | Space is the order of coexisting possibles [Leibniz] |
13181 | Time is the order of inconsistent possibilities [Leibniz] |