42 ideas
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] |
17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
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] |
17757 | Members of ordinals are ordinals, and also subsets of ordinals [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] |
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] |
22744 | Parts are not parts if their whole is nothing more than the parts [Sext.Empiricus] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
22748 | Some say motion is perceived by sense, but others say it is by intellect [Sext.Empiricus] |
22746 | If we try to conceive of a line with no breadth, it ceases to exist, and so has no length [Sext.Empiricus] |
22741 | The incorporeal is not in the nature of body, and so could not emerge from it [Sext.Empiricus] |
8412 | A causal interaction is when two processes intersect, and correlated modifications persist afterwards [Salmon] |
8413 | Cause must come first in propagations of causal interactions, but interactions are simultaneous [Salmon] |
8411 | Instead of localised events, I take enduring and extended processes as basic to causation [Salmon] |
22747 | A man walking backwards on a forwards-moving ship is moving in a fixed place [Sext.Empiricus] |
22749 | Time doesn't end with the Universe, because tensed statements about destruction remain true [Sext.Empiricus] |
22750 | Time is divisible, into past, present and future [Sext.Empiricus] |
22742 | Socrates either dies when he exists (before his death) or when he doesn't (after his death) [Sext.Empiricus] |
22751 | If the present is just the limit of the past or the future, it can't exist because they don't exist [Sext.Empiricus] |
22730 | All men agree that God is blessed, imperishable, happy and good [Sext.Empiricus] |
22739 | God must suffer to understand suffering [Sext.Empiricus] |
22738 | The Divine must lack the virtues of continence and fortitude, because they are not needed [Sext.Empiricus] |
22734 | God is defended by agreement, order, absurdity of denying God, and refutations [Sext.Empiricus] |
22736 | God's sensations imply change, and hence perishing, which is absurd, so there is no such God [Sext.Empiricus] |
22740 | God without virtue is absurd, but God's virtues will be better than God [Sext.Empiricus] |
22735 | The original substance lacked motion or shape, and was given these by a cause [Sext.Empiricus] |
22732 | The perfections of God were extrapolations from mankind [Sext.Empiricus] |
22728 | Gods were invented as watchers of people's secret actions [Sext.Empiricus] |
22737 | An incorporeal God could do nothing, and a bodily god would perish, so there is no God [Sext.Empiricus] |
22731 | It is mad to think that what is useful to us, like lakes and rivers, are gods [Sext.Empiricus] |