55 ideas
4742 | Correspondence may be one-many or many one, as when either p or q make 'p or q' true [Armstrong] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
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] |
9497 | Without modality, Armstrong falls back on fictionalism to support counterfactual laws [Bird on Armstrong] |
15550 | Properties are contingently existing beings with multiple locations in space and time [Armstrong, by Lewis] |
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] |
4743 | The truth-maker for a truth must necessitate that truth [Armstrong] |
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] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
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] |
4798 | In recent writings, Armstrong makes a direct identification of necessitation with causation [Armstrong, by Psillos] |
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] |