113 ideas
3879 | Philosophy aims to provide a theory of everything [Scruton] |
12865 | Analytic philosophers may prefer formal systems because natural language is such mess [Simons] |
3891 | If p entails q, then p is sufficient for q, and q is necessary for p [Scruton] |
3894 | We may define 'good' correctly, but then ask whether the application of the definition is good [Scruton] |
3883 | A true proposition is consistent with every other true proposition [Scruton] |
3884 | The pragmatist does not really have a theory of truth [Scruton] |
12815 | Classical mereology doesn't apply well to the objects around us [Simons] |
12819 | A 'part' has different meanings for individuals, classes, and masses [Simons] |
12832 | Complement: the rest of the Universe apart from some individual, written x-bar [Simons] |
12834 | Criticisms of mereology: parts? transitivity? sums? identity? four-dimensional? [Simons] |
12827 | Difference: the difference of individuals is the remainder of an overlap, written 'x - y' [Simons] |
12828 | General sum: the sum of objects satisfying some predicate, written σx(Fx) [Simons] |
12822 | Proper or improper part: x < y, 'x is (a) part of y' [Simons] |
12823 | Overlap: two parts overlap iff they have a part in common, expressed as 'x o y' [Simons] |
12824 | Disjoint: two individuals are disjoint iff they do not overlap, written 'x | y' [Simons] |
12825 | Product: the product of two individuals is the sum of all of their overlaps, written 'x · y' [Simons] |
12826 | Sum: the sum of individuals is what is overlapped if either of them are, written 'x + y' [Simons] |
12829 | General product: the nucleus of all objects satisfying a predicate, written πx(Fx) [Simons] |
12830 | Universe: the mereological sum of all objects whatever, written 'U' [Simons] |
12831 | Atom: an individual with no proper parts, written 'At x' [Simons] |
12844 | Dissective: stuff is dissective if parts of the stuff are always the stuff [Simons] |
12816 | Classical mereology doesn't handle temporal or modal notions very well [Simons] |
12821 | The part-relation is transitive and asymmetric (and thus irreflexive) [Simons] |
18847 | Each wheel is part of a car, but the four wheels are not a further part [Simons] |
12813 | Two standard formalisations of part-whole theory are the Calculus of Individuals, and Mereology [Simons] |
12846 | A 'group' is a collection with a condition which constitutes their being united [Simons] |
12861 | 'The wolves' are the matter of 'the pack'; the latter is a group, with different identity conditions [Simons] |
12848 | The same members may form two groups [Simons] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
12876 | Philosophy is stuck on the Fregean view that an individual is anything with a proper name [Simons] |
12845 | Some natural languages don't distinguish between singular and plural [Simons] |
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] |
3907 | Could you be intellectually acquainted with numbers, but unable to count objects? [Scruton] |
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] |
3908 | If maths contains unprovable truths, then maths cannot be reduced to a set of proofs [Scruton] |
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] |
12838 | Four-dimensional ontology has no change, since that needs an object, and time to pass [Simons] |
12842 | There are real relational changes, as well as bogus 'Cambridge changes' [Simons] |
12841 | I don't believe in processes [Simons] |
12836 | Fans of process ontology cheat, since river-stages refer to 'rivers' [Simons] |
12880 | Moments are things like smiles or skids, which are founded on other things [Simons] |
12881 | A smiling is an event with causes, but the smile is a continuant without causes [Simons] |
12883 | Moving disturbances are are moments which continuously change their basis [Simons] |
12882 | A wave is maintained by a process, but it isn't a process [Simons] |
12840 | I do not think there is a general identity condition for events [Simons] |
12839 | Relativity has an ontology of things and events, not on space-time diagrams [Simons] |
12879 | Independent objects can exist apart, and maybe even entirely alone [Simons] |
12847 | Mass nouns admit 'much' and 'a little', and resist 'many' and 'few'. [Simons] |
12862 | Gold is not its atoms, because the atoms must be all gold, but gold contains neutrons [Simons] |
12863 | Mass terms (unlike plurals) are used with indifference to whether they can exist in units [Simons] |
12859 | A mixture can have different qualities from its ingredients. [Simons] |
12858 | Mixtures disappear if nearly all of the mixture is one ingredient [Simons] |
3906 | If possible worlds are needed to define properties, maybe we should abandon properties [Scruton] |
12850 | To individuate something we must pick it out, but also know its limits of variation [Simons] |
12860 | Sortal nouns for continuants tell you their continuance- and cessation-conditions [Simons] |
12886 | A whole requires some unique relation which binds together all of the parts [Simons] |
12835 | Does Tibbles remain the same cat when it loses its tail? [Simons] |
12857 | Tibbles isn't Tib-plus-tail, because Tibbles can survive its loss, but the sum can't [Simons] |
12820 | Without extensional mereology two objects can occupy the same position [Simons] |
12866 | Composition is asymmetric and transitive [Simons] |
12867 | A hand constitutes a fist (when clenched), but a fist is not composed of an augmented hand [Simons] |
12864 | We say 'b is part of a', 'b is a part of a', 'b are a part of a', or 'b are parts of a'. [Simons] |
12814 | Classical mereology says there are 'sums', for whose existence there is no other evidence [Simons] |
12817 | 'Mereological extensionality' says objects with the same parts are identical [Simons] |
12833 | If there are c atoms, this gives 2^c - 1 individuals, so there can't be just 2 or 12 individuals [Simons] |
12849 | Sums are more plausible for pluralities and masses than they are for individuals [Simons] |
12877 | Sums of things in different categories are found within philosophy. [Simons] |
12888 | The wholeness of a melody seems conventional, but of an explosion it seems natural [Simons] |
12871 | Objects have their essential properties because of the kind of objects they are [Simons] |
12870 | We must distinguish the de dicto 'must' of propositions from the de re 'must' of essence [Simons] |
12873 | Original parts are the best candidates for being essential to artefacts [Simons] |
12874 | An essential part of an essential part is an essential part of the whole [Simons] |
12837 | Four dimensional-objects are stranger than most people think [Simons] |
12856 | Intermittent objects would be respectable if they occurred in nature, as well as in artefacts [Simons] |
12885 | Objects like chess games, with gaps in them, are thereby less unified [Simons] |
12854 | An entrepreneur and a museum curator would each be happy with their ship at the end [Simons] |
12855 | The 'best candidate' theories mistakenly assume there is one answer to 'Which is the real ship?' [Simons] |
12872 | The zygote is an essential initial part, for a sexually reproduced organism [Simons] |
3888 | Hume assumes that necessity can only be de dicto, not de re [Scruton] |
3903 | The conceivable can't be a test of the possible, if there are things which are possible but inconceivable [Scruton] |
12889 | The limits of change for an individual depend on the kind of individual [Simons] |
3897 | Epistemology is about the justification of belief, not the definition of knowledge [Scruton] |
3881 | In the Cogito argument consciousness develops into self-consciousness [Scruton] |
3887 | Maybe our knowledge of truth and causation is synthetic a priori [Scruton] |
3901 | Touch only seems to reveal primary qualities [Scruton] |
3885 | We only conceive of primary qualities as attached to secondary qualities [Scruton] |
3910 | If primary and secondary qualities are distinct, what has the secondary qualities? [Scruton] |
3899 | The representational theory says perceptual states are intentional states [Scruton] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
3898 | My belief that it will rain tomorrow can't be caused by its raining tomorrow [Scruton] |
3880 | Logical positivism avoids scepticism, by closing the gap between evidence and conclusion [Scruton] |
3878 | Why should you believe someone who says there are no truths? [Scruton] |
3892 | Every event having a cause, and every event being determined by its cause, are not the same [Scruton] |
3911 | The very concept of a substance denies the possibility of mutual interaction and dependence [Scruton] |
3882 | Wittgenstein makes it impossible to build foundations from something that is totally private [Scruton] |
12843 | With activities if you are doing it you've done it, with performances you must finish to have done it [Simons] |
12875 | One false note doesn't make it a performance of a different work [Simons] |
3896 | Any social theory of morality has the problem of the 'free rider', who only pretends to join in [Scruton] |
3886 | Membership is the greatest source of obligation [Scruton] |
3895 | The categorical imperative is not just individual, but can be used for negotiations between strangers [Scruton] |
3890 | 'Cause' used to just mean any valid explanation [Scruton] |
3904 | Measuring space requires no movement while I do it [Scruton] |
3905 | 'Existence' is not a predicate of 'man', but of the concept of man, saying it has at least one instance [Scruton] |