18 ideas
| 10653 | Maybe set theory need not be well-founded [Varzi] |
| Full Idea: There are some proposals for non-well-founded set theory (tolerating cases of self-membership and membership circularities). | |
| From: Achille Varzi (Mereology [2003], 2.1) | |
| A reaction: [He cites Aczel 1988, and Barwise and Moss 1996] |
| 10648 | Mereology need not be nominalist, though it is often taken to be so [Varzi] |
| Full Idea: While mereology was originally offered with a nominalist viewpoint, resulting in a conception of mereology as an ontologically parsimonious alternative to set theory, there is no necessary link between analysis of parthood and nominalism. | |
| From: Achille Varzi (Mereology [2003], 1) | |
| A reaction: He cites Lesniewski and Leonard-and-Goodman. Do you allow something called a 'whole' into your ontology, as well as the parts? He observes that while 'wholes' can be concrete, they can also be abstract, if the parts are abstract. |
| 10655 | Are there mereological atoms, and are all objects made of them? [Varzi] |
| Full Idea: It is an open question whether there are any mereological atoms (with no proper parts), and also whether every object is ultimately made up of atoms. | |
| From: Achille Varzi (Mereology [2003], 3) | |
| A reaction: Such a view would have to presuppose (metaphysically) that the divisibility of matter has limits. If one follows this route, then are there only 'natural' wholes, or are we 'unrestricted' in our view of how the atoms combine? I favour the natural route. |
| 10659 | There is something of which everything is part, but no null-thing which is part of everything [Varzi] |
| Full Idea: It is common in mereology to hold that there is something of which everything is part, but few hold that there is a 'null entity' that is part of everything. | |
| From: Achille Varzi (Mereology [2003], 4.1) | |
| A reaction: This comes out as roughly the opposite of set theory, which cannot do without the null set, but is not keen on the set of everything. |
| 10190 | From the axiomatic point of view, mathematics is a storehouse of abstract structures [Bourbaki] |
| Full Idea: From the axiomatic point of view, mathematics appears as a storehouse of abstract forms - the mathematical structures. | |
| From: Nicholas Bourbaki (The Architecture of Mathematics [1950], 221-32), quoted by Fraser MacBride - Review of Chihara's 'Structural Acc of Maths' p.79 | |
| A reaction: This seems to be the culmination of the structuralist view that developed from Dedekind and Hilbert, and was further developed by philosophers in the 1990s. |
| 10502 | We can rise by degrees through abstraction, with higher levels representing more things [Arnauld,A/Nicole,P] |
| Full Idea: I can start with a triangle, and rise by degrees to all straight-lined figures and to extension itself. The lower degree will include the higher degree. Since the higher degree is less determinate, it can represent more things. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: [compressed] This attempts to explain the generalising ability of abstraction cited in Idea 10501. If you take a complex object and eliminate features one by one, it can only 'represent' more particulars; it could hardly represent fewer. |
| 10661 | 'Composition is identity' says multitudes are the reality, loosely composing single things [Varzi] |
| Full Idea: The thesis known as 'composition is identity' is that identity is mereological composition; a fusion is just the parts counted loosely, but it is strictly a multitude and loosely a single thing. | |
| From: Achille Varzi (Mereology [2003], 4.3) | |
| A reaction: [He cites D.Baxter 1988, in Mind] It is not clear, from this simple statement, what the difference is between multitudes that are parts of a thing, and multitudes that are not. A heavy weight seems to hang on the notion of 'composed of'. |
| 10647 | Parts may or may not be attached, demarcated, arbitrary, material, extended, spatial or temporal [Varzi] |
| Full Idea: The word 'part' can used whether it is attached, or arbitrarily demarcated, or gerrymandered, or immaterial, or unextended, or spatial, or temporal. | |
| From: Achille Varzi (Mereology [2003], 1) |
| 10651 | If 'part' is reflexive, then identity is a limit case of parthood [Varzi] |
| Full Idea: Taking reflexivity as constitutive of the meaning of 'part' amounts to regarding identity as a limit case of parthood. | |
| From: Achille Varzi (Mereology [2003], 2.1) | |
| A reaction: A nice thought, but it is horribly 'philosophical', and a long way from ordinary usage and common sense (which is, I'm sorry to say, a BAD thing). |
| 10649 | 'Part' stands for a reflexive, antisymmetric and transitive relation [Varzi] |
| Full Idea: It seems obvious that 'part' stands for a partial ordering, a reflexive ('everything is part of itself'), antisymmetic ('two things cannot be part of each other'), and transitive (a part of a part of a thing is part of that thing) relation. | |
| From: Achille Varzi (Mereology [2003], 2.1) | |
| A reaction: I'm never clear why the reflexive bit of the relation should be taken as 'obvious', since it seems to defy normal usage and common sense. It would be absurd to say 'I'll give you part of the cake' and hand you the whole of it. See Idea 10651. |
| 10654 | The parthood relation will help to define at least seven basic predicates [Varzi] |
| Full Idea: With a basic parthood relation, we can formally define various mereological predicates, such as overlap, underlap, proper part, over-crossing, under-crossing, proper overlap, and proper underlap. | |
| From: Achille Varzi (Mereology [2003], 2.2) | |
| A reaction: [Varzi offers some diagrams, but they need interpretation] |
| 10658 | Sameness of parts won't guarantee identity if their arrangement matters [Varzi] |
| Full Idea: We might say that sameness of parts is not sufficient for identity, as some entities may differ exclusively with respect to the arrangement of the parts, as when we compare 'John loves Mary' with 'Mary loves John'. | |
| From: Achille Varzi (Mereology [2003], 3.2) | |
| A reaction: Presumably wide dispersal should also prevent parts from fixing wholes, but there is so much vagueness here that it is tempting to go for unrestricted composition, and then work back to the common sense position. |
| 10652 | Conceivability may indicate possibility, but literary fantasy does not [Varzi] |
| Full Idea: Conceivability may well be a guide to possibility, but literary fantasy is by itself no evidence of conceivability. | |
| From: Achille Varzi (Mereology [2003], 2.1) | |
| A reaction: Very nice. People who cite 'conceivability' in this context often have a disgracefully loose usage for the word. Really, really conceivable is probably our only guide to possibility. |
| 18258 | We can only know the exterior world via our ideas [Arnauld,A/Nicole,P] |
| Full Idea: We can have knowledge of what is outside us only through the mediation of ideas in us. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], p.63), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc' |
| 16784 | Forms make things distinct and explain the properties, by pure form, or arrangement of parts [Arnauld,A/Nicole,P] |
| Full Idea: The form is what renders a thing such and distinguishes it from others, whether it is a being really distinct from the matter, according to the Schools, or whether it is only the arrangement of the parts. By this form one must explain its properties. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], III.18 p240), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 27.6 | |
| A reaction: If we ask 'what explains the properties of this thing' it is hard to avoid coming up with something that might be called the 'form'. Note that they allow either substantial or corpuscularian forms. It is hard to disagree with the idea. |
| 10499 | We know by abstraction because we only understand composite things a part at a time [Arnauld,A/Nicole,P] |
| Full Idea: The mind cannot perfectly understand things that are even slightly composite unless it considers them a part at a time. ...This is generally called knowing by abstraction. (..the human body, for example). | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: This adds the interesting thought that the mind is forced to abstract, rather than abstraction being a luxury extra feature. Knowledge through analysis is knowledge by abstraction. Also a nice linking of abstraction to epistemology. |
| 10501 | A triangle diagram is about all triangles, if some features are ignored [Arnauld,A/Nicole,P] |
| Full Idea: If I draw an equilateral triangle on a piece of paper, ..I shall have an idea of only a single triangle. But if I ignore all the particular circumstances and focus on the three equal lines, I will be able to represent all equilateral triangles. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: [compressed] They observed that we grasp composites through their parts, and now that we can grasp generalisations through particulars, both achieved by the psychological act of abstraction, thus showing its epistemological power. |
| 10500 | No one denies that a line has width, but we can just attend to its length [Arnauld,A/Nicole,P] |
| Full Idea: Geometers by no means assume that there are lines without width or surfaces without depth. They only think it is possible to consider the length without paying attention to the width. We can measure the length of a path without its width. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: A nice example which makes the point indubitable. The modern 'rigorous' account of abstraction that starts with Frege seems to require more than one object, in order to derive abstractions like direction or number. Path widths are not comparatives. |