25 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. |
| 8195 | Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense [Dummett] |
| Full Idea: I once wrote that there are three linguistic devices that make it possible for us to frame undecidable statements: quantification over infinity totalities, as expressed by word such as 'never'; the subjunctive conditional form; and the past tense. | |
| From: Michael Dummett (Truth and the Past [2001], 4) | |
| A reaction: Dummett now repudiates the third one. Statements containing vague concepts also appear to be undecidable. Personally I have no problems with deciding (to a fair extent) about 'never x', and 'if x were true', and 'it was x'. |
| 8194 | Surely there is no exact single grain that brings a heap into existence [Dummett] |
| Full Idea: There is surely no number n such that "n grains of sand do not make a heap, although n+1 grains of sand do" is true. | |
| From: Michael Dummett (Truth and the Past [2001], 4) | |
| A reaction: It might be argued that there is such a number, but no human being is capable of determing it. Might God know the value of n? On the whole Dummett's view seems the most plausible. |
| 8190 | Intuitionists rely on the proof of mathematical statements, not their truth [Dummett] |
| Full Idea: The intuitionist account of the meaning of mathematical statements does not employ the notion of a statement's being true, but only that of something's being a proof of the statement. | |
| From: Michael Dummett (Truth and the Past [2001], 2) | |
| A reaction: I remain unconvinced that anyone could give an account of proof that didn't discreetly employ the notion of truth. What are we to make of "we suspect this is true, but no one knows how to prove it?" (e.g. Goldbach's Conjecture). |
| 8198 | A 'Cambridge Change' is like saying 'the landscape changes as you travel east' [Dummett] |
| Full Idea: The idea of 'Cambridge Change' is like saying 'the landscape changes as you travel east'. | |
| From: Michael Dummett (Truth and the Past [2001], 5) | |
| A reaction: The phrase was coined in Oxford. It is a useful label with which realists can insult solipsists, idealists and other riff-raff. Four Dimensionalists seem to see time in this way. Events sit there, and we travel past them. But there are indexical events. |
| 8192 | I no longer think what a statement about the past says is just what can justify it [Dummett] |
| Full Idea: In distinguishing between what can establish a statement about the past as true and what it is that that statement says, we are repudiating antirealism about the past. | |
| From: Michael Dummett (Truth and the Past [2001], 3) | |
| A reaction: This is a late shift of ground from the champion of antirealism. If Dummett's whole position is based on a 'justificationist' theory of meaning, he must surely have a different theory of meaning now for statements about the past? |
| 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. |
| 8199 | The existence of a universe without sentience or intelligence is an unintelligible fantasy [Dummett] |
| Full Idea: The existence of a universe from which sentience was permanently absent is an unintelligible fantasy. What exists is what can be known to exist. What is true is what can be known to be true. Reality is what can be experienced and known. | |
| From: Michael Dummett (Truth and the Past [2001], 5) | |
| A reaction: This strikes me as nonsense. The fact that we cannot think about a universe without introducing a viewpoint does not mean that we cannot 'intellectually imagine' its existence devoid of viewpoints. Nothing could ever experience a star's interior. |
| 8193 | Verification is not an individual but a collective activity [Dummett] |
| Full Idea: Verification is not an individual but a collective activity. | |
| From: Michael Dummett (Truth and the Past [2001], 3) | |
| A reaction: This generates problems. Are deceased members of the community included? (Yes, says Dummett). If someone speaks to angels (Blake!), do they get included? Is a majority necessary? What of weird loners? Etc. |
| 8189 | Truth-condition theorists must argue use can only be described by appeal to conditions of truth [Dummett] |
| Full Idea: To demonstrate the necessity of a truth-conditional theory of meaning, a proponent of such a theory must argue that use cannot be described without appeal to the conditions for the truth of statements. | |
| From: Michael Dummett (Truth and the Past [2001], 1) | |
| A reaction: Unlike Dummett, I find that argument rather appealing. How do you decide the possible or appropriate use for a piece of language, if you don't already know what it means. Basing it all on social conventions means it could be meaningless ritual. |
| 8191 | The truth-conditions theory must get agreement on a conception of truth [Dummett] |
| Full Idea: It is not enough for the truth-condition theorist to argue that we need the concept of truth: he must show that we should have the same conception of truth that he has. | |
| From: Michael Dummett (Truth and the Past [2001], 2) | |
| A reaction: Davidson invites us to accept Tarski's account of truth. It invites the question of what the theory would be like with a very robust correspondence account of truth, or a flabby rather subjective coherence view, or the worst sort of pragmatic view. |
| 4867 | Whether nature is beautiful or orderly is entirely in relation to human imagination [Spinoza] |
| Full Idea: I do not attribute to nature either beauty or deformity, order or confusion. Only in relation to our imagination can things be called beautiful or deformed, ordered or confused. | |
| From: Baruch de Spinoza (Letters to Oldenburg [1665], 1665?) | |
| A reaction: This is clearly a statement of Hume's famous later opinion that there are no values ('ought') in nature ('is'). It is a rejection of Aristotelian and Greek teleology. It is hard to argue with, but I have strong sales resistance, rooted in virtue theory. |
| 8197 | Maybe past (which affects us) and future (which we can affect) are both real [Dummett] |
| Full Idea: Maybe both the past and the future are real, determined by our current temporal perspective. Past is then events capable of having a causal influence upon events near us, and future is events we can affect, but from which we receive no information. | |
| From: Michael Dummett (Truth and the Past [2001], 5) | |
| A reaction: This is the Four-Dimensional view, which is opposed to Presentism. Might immediate unease is that it gives encouragement to fortune-tellers, whom I have always dismissed with 'You can't see the future, because it doesn't exist'. |
| 8196 | The present cannot exist alone as a mere boundary; past and future truths are rendered meaningless [Dummett] |
| Full Idea: The idea that only the present is real cannot be sustained. St Augustine pointed out that the present has no duration; it is a mere boundary between past and future, and dependent on them. It also denies truth-value to statements about past or future. | |
| From: Michael Dummett (Truth and the Past [2001], 5) | |
| A reaction: To defend Presentism, I suspect that one must focus entirely on the activities of consciousness and short-term memory. All truths, of past or future, must refer totally to such mental events. But what could an event be if there is no enduring time? |
| 4866 | God is a being with infinite attributes, each of them infinite or perfect [Spinoza] |
| Full Idea: I define God as a being consisting in infinite attributes, whereof each is infinite or supremely perfect. | |
| From: Baruch de Spinoza (Letters to Oldenburg [1665], 1661) | |
| A reaction: This seems to me the glorious culmination of the hyperbolic conception of God that expands steadily from wood spirits through Zeus, to eventually mop up everything in nature, and then everything that can be imagined beyond nature. All very silly. |
| 4868 | Trying to prove God's existence through miracles is proving the obscure by the more obscure [Spinoza] |
| Full Idea: Those who endeavour to establish God's existence and the truth of religion by means of miracles seek to prove the obscure by what is more obscure. | |
| From: Baruch de Spinoza (Letters to Oldenburg [1665], 1675?) | |
| A reaction: Nicely put. On the whole this has to be right, but one must leave open a possibility. If there is a God, and He seeks to prove Himself by a deed, are we saying this is impossible? Divine intervention might be the best explanation of something. |