15 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] |
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. |
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. |
21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
Full Idea: Cantor proved that the number of sets in a collection of terms is larger than the number of terms. Hence Cantor's Paradox says the number of sets in the collection of all sets must be larger than the number of sets in the collection of all sets. | |
From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
A reaction: The sets must count as terms in the next iteration, but that is a normal application of the Power Set axiom. |
21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
Full Idea: The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1. | |
From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
A reaction: Formulated by Burali-Forti in 1897. |
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'. |
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] |
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) |
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. |
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). |
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. |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |