display all the ideas for this combination of philosophers
22 ideas
| 12815 | Classical mereology doesn't apply well to the objects around us [Simons] |
| Full Idea: The most fundamental criticism of classical mereology is that the theory is not applicable to most of the objects around us, and is accordingly of little use as a formal reconstruction of the concepts of part and whole which we actually employ. | |
| From: Peter Simons (Parts [1987], Intro) | |
| A reaction: This sounds splendidly dismissive, but one might compare it with possible worlds semantics for modal logic, which most people take with a pinch of salt as an actual commitment, but find wonderfully clarifying in modal reasoning. |
| 12832 | Complement: the rest of the Universe apart from some individual, written x-bar [Simons] |
| Full Idea: The 'complement' of each individual in mereology is the rest of the Universe outside it, that is U - x, but written as x-bar [x with a horizontal bar above it]. | |
| From: Peter Simons (Parts [1987], 1.1.10) | |
| A reaction: [Don't have a font for x-bar] See Idea 12831 for the 'Universe'. Simons suggest that the interest of this term is mainly historical and algebraic. |
| 12834 | Criticisms of mereology: parts? transitivity? sums? identity? four-dimensional? [Simons] |
| Full Idea: Main criticisms of mereology: we don't mean 'part' as improper; transitivity of 'part' is sometimes not transitive; no guarantee that there are 'sums'; the identity criteria for individuals are false; we are forced into materialistic four-dimensionalism. | |
| From: Peter Simons (Parts [1987], 3.2) | |
| A reaction: [Compressed summary; for four-dimensionalism see under 'Identity over Time'] Simons says these are in ascending order of importance. |
| 12819 | A 'part' has different meanings for individuals, classes, and masses [Simons] |
| Full Idea: It emerges that 'part', like other formal concepts, is not univocal, but has analogous meanings according to whether we talk of individuals, classes, or masses. | |
| From: Peter Simons (Parts [1987], Intro) | |
| A reaction: He suggests that unrestricted sums are appropriate for the last two, but not for individuals. There must be something univocal about the word - some awareness of a possible whole or larger entity to which the thing could belong. |
| 12822 | Proper or improper part: x < y, 'x is (a) part of y' [Simons] |
| Full Idea: A 'proper or improper part' is expressed by 'x < y', read as 'x is (a) part of y'. The relatively minor deviation from normal usage (of including an improper part, i.e. the whole thing) is warranted by its algebraical convenience. | |
| From: Peter Simons (Parts [1987], 1.1.02) | |
| A reaction: Including an improper part (i.e. the whole thing) is not, Simons points out, uncontroversial, because the part being 'equal' to the whole is read as being 'identical' to the whole, which Simons is unwilling to accept. |
| 12824 | Disjoint: two individuals are disjoint iff they do not overlap, written 'x | y' [Simons] |
| Full Idea: Two individuals are 'disjoint' mereologically if and only if they do not overlap, expressed by 'x | y', read as 'x is disjoint from y'. Disjointedness is symmetric. | |
| From: Peter Simons (Parts [1987], 1.1.04) |
| 12827 | Difference: the difference of individuals is the remainder of an overlap, written 'x - y' [Simons] |
| Full Idea: The 'difference' of two individuals is the largest individual contained in x which has no part in common with y, expressed by 'x - y', read as 'the difference of x and y'. | |
| From: Peter Simons (Parts [1987], 1.1.07) |
| 12823 | Overlap: two parts overlap iff they have a part in common, expressed as 'x o y' [Simons] |
| Full Idea: Two parts 'overlap' mereologically if and only if they have a part in common, expressed by 'x o y', read as 'x overlaps y'. Overlapping is reflexive and symmetric but not transitive. | |
| From: Peter Simons (Parts [1987], 1.1.03) | |
| A reaction: Simons points out that we are uncomfortable with overlapping (as in overlapping national boundaries), because we seem to like conceptual boundaries. We avoid overlap even in ordering primary colour terms, by having a no-man's-land. |
| 12825 | Product: the product of two individuals is the sum of all of their overlaps, written 'x · y' [Simons] |
| Full Idea: For two overlapping individuals their 'product' is the individual which is part of both and such that any common part of both is part of it, expressed by 'x · y', read as 'the product of x and y'. | |
| From: Peter Simons (Parts [1987], 1.1.05) | |
| A reaction: That is, the 'product' is the sum of any common parts between two individuals. In set theory all sets intersect at the null set, but mereology usually avoids the 'null individual'. |
| 12826 | Sum: the sum of individuals is what is overlapped if either of them are, written 'x + y' [Simons] |
| Full Idea: The 'sum' of two individuals is that individual which something overlaps iff it overlaps at least one of x and y, expressed by 'x + y', read as 'the sum of x and y'. It is central to classical extensional mereologies that any two individuals have a sum. | |
| From: Peter Simons (Parts [1987], 1.1.06) | |
| A reaction: This rather technical definition (defining an individual by the possibility of it being overlapped) does not always coincide with the smallest individual containing them both. |
| 12828 | General sum: the sum of objects satisfying some predicate, written σx(Fx) [Simons] |
| Full Idea: The 'general sum' of all objects satisfying a certain predicate is denoted by a variable-binding operator, expressed by 'σx(Fx)', read as 'the sum of objects satisfying F'. | |
| From: Peter Simons (Parts [1987], 1.1.08) | |
| A reaction: This, it seems, is introduced to restrict some infinite classes which aspire to be sums. |
| 12829 | General product: the nucleus of all objects satisfying a predicate, written πx(Fx) [Simons] |
| Full Idea: The 'general product' or 'nucleus' of all objects satisfying a certain predicate is denoted by a variable-binding operator, expressed by 'πx(Fx)', read as 'the product of objects satisfying F'. | |
| From: Peter Simons (Parts [1987], 1.1.08) | |
| A reaction: See Idea 12825 for 'product'. 'Nucleus' is a helpful word here. Thought: is the general product a candidate for a formal definition of essence? It would be a sortal essence - roughly, what all beetles have in common, just by being beetles. |
| 12830 | Universe: the mereological sum of all objects whatever, written 'U' [Simons] |
| Full Idea: The 'Universe' in mereology is the sum of all objects whatever, a unique individual of which all individuals are part. This is denoted by 'U'. Strictly, there can be no 'empty Universe', since the Universe is not a container, but the whole filling. | |
| From: Peter Simons (Parts [1987], 1.1.09) | |
| A reaction: This, of course, contrasts with set theory, which cannot have a set of all sets. At the lower end, set theory does have a null set, while mereology has no null individual. See David Lewis on combining the two theories. |
| 12831 | Atom: an individual with no proper parts, written 'At x' [Simons] |
| Full Idea: An 'atom' in mereology is an individual with no proper parts. We shall use the expression 'At x' to mean 'x is an atom'. | |
| From: Peter Simons (Parts [1987], 1.1.11) | |
| A reaction: Note that 'part' in standard mereology includes improper parts, so every object has at least one part, namely itself. |
| 12844 | Dissective: stuff is dissective if parts of the stuff are always the stuff [Simons] |
| Full Idea: Water is said not to be 'dissective', since there are parts of any quantity of water which are not water. | |
| From: Peter Simons (Parts [1987], 4.2) | |
| A reaction: This won't seem to do for any physical matter, but presumably parts of numbers are always numbers. |
| 12813 | Two standard formalisations of part-whole theory are the Calculus of Individuals, and Mereology [Simons] |
| Full Idea: The standardly accepted formal theory of part-whole is classical extensional mereology, which is known in two logical guises, the Calculus of Individuals of Leonard and Goodman, and the Mereology of Lesniewski. | |
| From: Peter Simons (Parts [1987], Intro) | |
| A reaction: Simons catalogues several other modern attempts at axiomatisation in his chapter 2. |
| 12821 | The part-relation is transitive and asymmetric (and thus irreflexive) [Simons] |
| Full Idea: Formally, the part-relation is transitive and asymmetric (and thus irreflexive). Hence nothing is a proper part of itself, things aren't proper parts of one another, and if one is part of two which is part of three then one is part of three. | |
| From: Peter Simons (Parts [1987], 1.1.1) |
| 18847 | Each wheel is part of a car, but the four wheels are not a further part [Simons] |
| Full Idea: The four wheels of a car are parts of it (each is part of it), but there is not a fifth part consisting of the four wheels. | |
| From: Peter Simons (Parts [1987], 4.6) | |
| A reaction: This raises questions about the transitivity of parthood. If there are parts of parts of wholes, the basic parts are OK, and the whole is OK, but how can there also be an intermediate part? Try counting the parts of this whole! |
| 12816 | Classical mereology doesn't handle temporal or modal notions very well [Simons] |
| Full Idea: The underlying logic of classical extensional mereology does not have the resources to deal with temporal and modal notions such as temporary part, temporal part, essential part, or essential permanent part. | |
| From: Peter Simons (Parts [1987], Intro) | |
| A reaction: Simons tries to rectify this in the later chapters of his book, with modifications rather than extensions. Since everyone struggles with temporal and modal issues of identity, we shouldn't judge too harshly. |
| 12846 | A 'group' is a collection with a condition which constitutes their being united [Simons] |
| Full Idea: We call a 'collection' of jewels a 'group' term. Several random musicians are unlikely to be an orchestra. If they come together regularly in a room to play, such conditions are constitutive of an orchestra. | |
| From: Peter Simons (Parts [1987], 4.4) | |
| A reaction: Clearly this invites lots of borderline cases. Eleven footballers don't immediately make a team, as followers of the game know well. |
| 12848 | The same members may form two groups [Simons] |
| Full Idea: Groups may coincide in membership without being identical - extensionality goes. | |
| From: Peter Simons (Parts [1987], 4.9) | |
| A reaction: Thus an eleven-person orchestra may also constitute a football team. What if a pile of stones is an impediment to you, and useful to me? Is it then two groups? Suppose they hum while playing football? (Don't you just love philosophy?) |
| 12861 | 'The wolves' are the matter of 'the pack'; the latter is a group, with different identity conditions [Simons] |
| Full Idea: 'The wolves' is a plural term referring to just these animals, whereas 'the pack' of wolves refers to a group, and the group and plurality, while they may coincide in membership, have different identity conditions. The wolves are the matter of the pack. | |
| From: Peter Simons (Parts [1987], 6.4) | |
| A reaction: Even a cautious philosopher like Simons is ready to make bold ontological commitment to 'packs', on the basis of something called 'identity conditions'. I think it is just verbal. You can qualify 'the wolves' and 'the pack' to make them identical. |