16 ideas
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. |
14508 | A 'thisness' is a thing's property of being identical with itself (not the possession of self-identity) [Adams,RM] |
Full Idea: A thisness is the property of being identical with a certain particular individual - not the property that we all share, of being identical with some individual, but my property of being identical with me, your property of being identical with you etc. | |
From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 1) | |
A reaction: These philosophers tell you that a thisness 'is' so-and-so, and don't admit that he (and Plantinga) are putting forward a new theory about haecceities, and one I find implausible. I just don't believe in the property of 'being-identical-to-me'. |
14511 | There are cases where mere qualities would not ensure an intrinsic identity [Adams,RM] |
Full Idea: I have argued that there are possible cases in which no purely qualitative conditions would be both necessary and sufficient for possessing a given thisness. | |
From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 6) | |
A reaction: Are we perhaps confusing our epistemology with our ontology here? We can ensure that something has identity, or ensure that its identity is knowable. If it is 'something', then it has identity. Er, that's it? |
12031 | Essences are taken to be qualitative properties [Adams,RM] |
Full Idea: Essences have normally been understood to be constituted by qualitative properties. | |
From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 1) | |
A reaction: I add this simple point, because it might be challenged by the view that an essence is a substance, rather than the properties of anything. I prefer that, and would add that substances are individuated by distinctive causal powers. |
12034 | If the universe was cyclical, totally indiscernible events might occur from time to time [Adams,RM] |
Full Idea: There is a temporal argument for the possibility of non-identical indiscernibles, if there could be a cyclical universe, in which each event was preceded and followed by infinitely many other events qualitatively indiscernible from itself. | |
From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 3) | |
A reaction: The argument is a parallel to Max Black's indiscernible spheres in space. Adams offers the reply that time might be tightly 'curved', so that the repetition was indeed the same event again. |
14510 | Two events might be indiscernible yet distinct, if there was a universe cyclical in time [Adams,RM] |
Full Idea: Similar to the argument from spatial dispersal, we can argue against the Identity of Indiscernibles from temporal dispersal. It seems there could be a cyclic universe, ..and thus there could be distinct but indiscernible events, separated temporally. | |
From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 3) | |
A reaction: See Idea 14509 for spatial dispersal. If cosmologists decided that a cyclical universe was incoherent, would that ruin the argument? Presumably there might even be indistinguishable events in the one universe (in principle!). |
16455 | Black's two globes might be one globe in highly curved space [Adams,RM] |
Full Idea: If God creates a globe reached by travelling two diameters in a straight line from another globe, this can be described as two globes in Euclidean space, or a single globe in a tightly curved non-Euclidean space. | |
From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 3) | |
A reaction: [my compression of Adams's version of Hacking's response to Black, as spotted by Stalnaker] Hence we save the identity of indiscernibles, by saying we can't be sure that two indiscernibles are not one thing, unusually described. |
14507 | Are possible worlds just qualities, or do they include primitive identities as well? [Adams,RM] |
Full Idea: Is the world - and are all possible worlds - constituted by purely qualitative facts, or does thisness hold a place beside suchness as a fundamental feature of reality? | |
From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], Intro) | |
A reaction: 'Thisness' and 'suchness' aim to capture Aristotelian notions of the entity and its attributes. Aristotle talks of 'a this'. Adams is after adding 'haecceities' to the world. My intuitive answer is no, there are no 'pure' identities. We add those. |
11964 | Possible worlds are world-stories, maximal descriptions of whole non-existent worlds [Adams,RM, by Molnar] |
Full Idea: According to a theory proposed by Adams, possible worlds are world-stories, that is maximally complete consistent sets of propositions which between them describe non-existent whole worlds. | |
From: report of Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979]) by George Molnar - Powers 12.2.2 | |
A reaction: Presumably this places an additional constraint on the view that a world is just a maximal set of propositions. It seems to require coherence as well as consistency. Suppose an object destroys all others objects. Is that a world? |
16451 | Adams says anti-haecceitism reduces all thisness to suchness [Adams,RM, by Stalnaker] |
Full Idea: The anti-haecceitist thesis (according to Adams's version) is that all thisnesses are reducible to, or supervenient upon, suchnesses. | |
From: report of Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979]) by Robert C. Stalnaker - Mere Possibilities 3.5 |
11901 | Haecceitism may or may not involve some logical connection to essence [Adams,RM, by Mackie,P] |
Full Idea: Moderate Haecceitism says that thisnesses and transworld identities are primitive, but logically connected with suchnesses. ..Extreme Haecceitism involves the rejection of all logical connections between suchness and thisness, for persons. | |
From: report of Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979]) by Penelope Mackie - How Things Might Have Been | |
A reaction: I am coming to the conclusion that they are not linked. That thisness is a feature of our conceptual thinking, and is utterly atomistic and content-free, while suchness is rich and a feature of reality. |
14512 | Moderate Haecceitism says transworld identities are primitive, but connected to qualities [Adams,RM] |
Full Idea: My position, according to which thisnesses and transworld identities are primitive but logically connected to suchnesses, we may call 'Moderate Haecceitism'. | |
From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 6) | |
A reaction: The rather tentative connection to qualities is to block the possibility of Aristotle being a poached egg, which he (quite reasonably!) holds to be counterintuitive. It all feels like a mess to me. |
8840 | There are five possible responses to the problem of infinite regress in justification [Cleve] |
Full Idea: Sceptics respond to the regress problem by denying knowledge; Foundationalists accept justifications without reasons; Positists say reasons terminate is mere posits; Coherentists say mutual support is justification; Infinitists accept the regress. | |
From: James Van Cleve (Why coherence is not enough [2005], I) | |
A reaction: A nice map of the territory. The doubts of Scepticism are not strong enough for anyone to embrace the view; Foundationalist destroy knowledge (?), as do Positists; Infinitism is a version of Coherentism - which is the winner. |
8841 | Modern foundationalists say basic beliefs are fallible, and coherence is relevant [Cleve] |
Full Idea: Contemporary foundationalists are seldom of the strong Cartesian variety: they do not insist that basic beliefs be absolutely certain. They also tend to allow that coherence can enhance justification. | |
From: James Van Cleve (Why coherence is not enough [2005], III) | |
A reaction: It strikes me that they have got onto a slippery slope. How certain are the basic beliefs? How do you evaluate their certainty? Could incoherence in their implications undermine them? Skyscrapers need perfect foundations. |
12032 | Direct reference is by proper names, or indexicals, or referential uses of descriptions [Adams,RM] |
Full Idea: Direct reference is commonly effected by the use of proper names and indexical expressions, and sometimes by what has been called (by Donnellan) the 'referential' use of descriptions. | |
From: Robert Merrihew Adams (Primitive Thisness and Primitive Identity [1979], 2) | |
A reaction: One might enquire whether the third usage should be described as 'direct', but then I am not sure that there is much of a distinction between references which are or are not 'direct'. Either you (or a sentence) refer or you (or it) don't. |