58 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] |
5831 | The new view is that "water" is a name, and has no definition [Schwartz,SP] |
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] |
17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
17765 | Propositional language can only relate statements as the same or as different [Walicki] |
17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
18724 | In logic nothing is hidden [Wittgenstein] |
17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
18709 | Laws of logic are like laws of chess - if you change them, it's just a different game [Wittgenstein] |
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] |
5829 | We refer to Thales successfully by name, even if all descriptions of him are false [Schwartz,SP] |
5830 | The traditional theory of names says some of the descriptions must be correct [Schwartz,SP] |
17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
18738 | We don't get 'nearer' to something by adding decimals to 1.1412... (root-2) [Wittgenstein] |
18708 | Infinity is not a number, so doesn't say how many; it is the property of a law [Wittgenstein] |
17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
17754 | Inductive proof depends on the choice of the ordering [Walicki] |
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] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
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] |
5826 | The intension of "lemon" is the conjunction of properties associated with it [Schwartz,SP] |
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] |
18711 | A proposition is any expression which can be significantly negated [Wittgenstein] |
18733 | Laws of nature are an aspect of the phenomena, and are just our mode of description [Wittgenstein] |