54 ideas
10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
10900 | Logically true sentences are true in all structures [Zalabardo] |
10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
3942 | I do not believe in the existence of anything, if I see no reason to believe it [Berkeley] |
3952 | I know that nothing inconsistent can exist [Berkeley] |
3959 | There is no other substance, in a strict sense, than spirit [Berkeley] |
3946 | A thing is shown to be impossible if a contradiction is demonstrated within its definition [Berkeley] |
3958 | Since our ideas vary when the real things are said to be unchanged, they cannot be true copies [Berkeley] |
3943 | If existence is perceived directly, by which sense; if indirectly, how is it inferred from direct perception? [Berkeley] |
3931 | Sensible objects are just sets of sensible qualities [Berkeley] |
5192 | Berkeley did not deny material things; he merely said they must be defined through sensations [Berkeley, by Ayer] |
5174 | Berkeley needed a phenomenalist account of the self, as well as of material things [Ayer on Berkeley] |
1103 | 'To be is to be perceived' is a simple confusion of experience with its objects [Russell on Berkeley] |
6403 | For Berkelely, reality is ideas and a community of minds, including God's [Berkeley, by Grayling] |
3936 | Time is measured by the succession of ideas in our minds [Berkeley] |
3930 | There is no such thing as 'material substance' [Berkeley] |
3939 | I conceive a tree in my mind, but I cannot prove that its existence can be conceived outside a mind [Berkeley] |
3945 | There is nothing in nature which needs the concept of matter to explain it [Berkeley] |
3947 | Perceptions are ideas, and ideas exist in the mind, so objects only exist in the mind [Berkeley] |
3933 | Primary qualities (such as shape, solidity, mass) are held to really exist, unlike secondary qualities [Berkeley] |
3934 | A mite would see its own foot as large, though we would see it as tiny [Berkeley] |
3935 | The apparent size of an object varies with its distance away, so that can't be a property of the object [Berkeley] |
3937 | 'Solidity' is either not a sensible quality at all, or it is clearly relative to our senses [Berkeley] |
3940 | Distance is not directly perceived by sight [Berkeley] |
3957 | Immediate objects of perception, which some treat as appearances, I treat as the real things themselves [Berkeley] |
3953 | Real things and imaginary or dreamed things differ because the latter are much fainter [Berkeley] |
3938 | Geometry is originally perceived by senses, and so is not purely intellectual [Berkeley] |
3944 | It is possible that we could perceive everything as we do now, but nothing actually existed. [Berkeley] |
3932 | A hot hand and a cold hand will have different experiences in the same tepid water [Berkeley] |
3948 | Experience tells me that other minds exist independently from my own [Berkeley] |
3941 | How can that which is unthinking be a cause of thought? [Berkeley] |
5374 | Berkeley probably used 'idea' to mean both the act of apprehension and the thing apprehended [Russell on Berkeley] |
3954 | Immorality is not in the action, but in the deviation of the will from moral law [Berkeley] |
19399 | Prime matter is nothing when it is at rest [Leibniz] |
3950 | There must be a God, because all sensible things must be perceived by him [Berkeley] |
3951 | There must be a God, because I and my ideas are not independent [Berkeley] |
3949 | It has been proved that creation is the workmanship of God, from its beauty and usefulness [Berkeley] |
3956 | People are responsible because they have limited power, though this ultimately derives from God [Berkeley] |
3955 | If sin is not just physical, we don't consider God the origin of sin because he causes physical events [Berkeley] |