69 ideas
18730 | The history of philosophy only matters if the subject is a choice between rival theories [Wittgenstein] |
18704 | Philosophy tries to be rid of certain intellectual puzzles, irrelevant to daily life [Wittgenstein] |
18710 | Philosophers express puzzlement, but don't clearly state the puzzle [Wittgenstein] |
18732 | We don't need a theory of truth, because we use the word perfectly well [Wittgenstein] |
18714 | We already know what we want to know, and analysis gives us no new facts [Wittgenstein] |
9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
18706 | Words of the same kind can be substituted in a proposition without producing nonsense [Wittgenstein] |
18735 | Talking nonsense is not following the rules [Wittgenstein] |
18719 | Grammar says that saying 'sound is red' is not false, but nonsense [Wittgenstein] |
18731 | There is no theory of truth, because it isn't a concept [Wittgenstein] |
18707 | All thought has the logical form of reality [Wittgenstein] |
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] |
18724 | In logic nothing is hidden [Wittgenstein] |
18709 | Laws of logic are like laws of chess - if you change them, it's just a different game [Wittgenstein] |
9605 | If a proposition is false, then its negation is true [Brown,JR] |
18736 | Contradiction is between two rules, not between rule and reality [Wittgenstein] |
18723 | We may correctly use 'not' without making the rule explicit [Wittgenstein] |
18718 | Saying 'and' has meaning is just saying it works in a sentence [Wittgenstein] |
18727 | A person's name doesn't mean their body; bodies don't sit down, and their existence can be denied [Wittgenstein] |
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] |
18738 | We don't get 'nearer' to something by adding decimals to 1.1412... (root-2) [Wittgenstein] |
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] |
18708 | Infinity is not a number, so doesn't say how many; it is the property of a law [Wittgenstein] |
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] |
3663 | How can you contemplate Platonic entities without causal transactions with them? [Putnam] |
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] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
18737 | There are no positive or negative facts; these are just the forms of propositions [Wittgenstein] |
18715 | Using 'green' is a commitment to future usage of 'green' [Wittgenstein] |
18726 | For each necessity in the world there is an arbitrary rule of language [Wittgenstein] |
18712 | Understanding is translation, into action or into other symbols [Wittgenstein] |
18280 | We live in sense-data, but talk about physical objects [Wittgenstein] |
18729 | Part of what we mean by stating the facts is the way we tend to experience them [Wittgenstein] |
18734 | If you remember wrongly, then there must be some other criterion than your remembering [Wittgenstein] |
18721 | Explanation and understanding are the same [Wittgenstein] |
18720 | Explanation gives understanding by revealing the full multiplicity of the thing [Wittgenstein] |
18716 | A machine strikes us as being a rule of movement [Wittgenstein] |
18713 | If an explanation is good, the symbol is used properly in the future [Wittgenstein] |
18717 | Thought is an activity which we perform by the expression of it [Wittgenstein] |
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] |
18725 | A proposition draws a line around the facts which agree with it [Wittgenstein] |
18728 | The meaning of a proposition is the mode of its verification [Wittgenstein] |
18705 | Words function only in propositions, like levers in a machine [Wittgenstein] |
9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
18711 | A proposition is any expression which can be significantly negated [Wittgenstein] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
18733 | Laws of nature are an aspect of the phenomena, and are just our mode of description [Wittgenstein] |