37 ideas
| 14480 | Maybe analytic truths do not require truth-makers, as they place no demands on the world [Thomasson] |
| Full Idea: It is a venerable view that analytic claims do not require truth-makers, as they place no demands on the world, but this claim has often been challenged. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 03.4) | |
| A reaction: She offers two challenges (bottom p.68), but I would have thought that the best response is that the meanings of the words themselves constitute truthmakers - perhaps via the essence of each word, as Fine suggests. |
| 10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
| Full Idea: Set theory has three roles: as a means of taming the infinite, as a supplier of the subject-matter of mathematics, and as a source of its modes of reasoning. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], Intro 1) | |
| A reaction: These all seem to be connected with mathematics, but there is also ontological interest in set theory. Potter emphasises that his second role does not entail a commitment to sets 'being' numbers. |
| 10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
| Full Idea: It is rare to find any direct reason given for believing that the empty set exists, except for variants of Dedekind's argument from convenience. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.3) |
| 13044 | Infinity: There is at least one limit level [Potter] |
| Full Idea: Axiom of Infinity: There is at least one limit level. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.9) | |
| A reaction: A 'limit ordinal' is one which has successors, but no predecessors. The axiom just says there is at least one infinity. |
| 10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
| Full Idea: It is only quite recently that the idea has emerged of deriving our conception of collections from a relation of dependence between them. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.2) | |
| A reaction: This is the 'iterative' view of sets, which he traces back to Gödel's 'What is Cantor's Continuum Problem?' |
| 13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
| Full Idea: We group under the heading 'limitation of size' those principles which classify properties as collectivizing or not according to how many objects there are with the property. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 13.5) | |
| A reaction: The idea was floated by Cantor, toyed with by Russell (1906), and advocated by von Neumann. The thought is simply that paradoxes start to appear when sets become enormous. |
| 10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
| Full Idea: Mereology tends to elide the distinction between the cards in a pack and the suits. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 02.1) | |
| A reaction: The example is a favourite of Frege's. Potter is giving a reason why mathematicians opted for set theory. I'm not clear, though, why a pack cannot have either 4 parts or 52 parts. Parts can 'fall under a concept' (such as 'legs'). I'm puzzled. |
| 10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
| Full Idea: In second-order logic only the formation rules are completely formalizable, not the inference rules. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 01.2) | |
| A reaction: He cites Gödel's First Incompleteness theorem for this. |
| 14471 | Analytical entailments arise from combinations of meanings and inference rules [Thomasson] |
| Full Idea: 'Analytically entail' means entail in virtue of the meanings of the expressions involved and rules of inference. So 'Jones bought a house' analytically entails 'Jones bought a building'. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 01.2) | |
| A reaction: Quine wouldn't like this, but it sounds OK to me. Thomasson uses this as a key tool in her claim that common sense objects must exist. |
| 10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
| Full Idea: A 'supposition' axiomatic theory is as concerned with truth as a 'realist' one (with undefined terms), but the truths are conditional. Satisfying the axioms is satisfying the theorem. This is if-thenism, or implicationism, or eliminative structuralism. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 01.1) | |
| A reaction: Aha! I had failed to make the connection between if-thenism and eliminative structuralism (of which I am rather fond). I think I am an if-thenist (not about all truth, but about provable truth). |
| 10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
| Full Idea: Even if set theory's role as a foundation for mathematics turned out to be wholly illusory, it would earn its keep through the calculus it provides for counting infinite sets. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.8) |
| 17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
| Full Idea: It is a remarkable fact that all the arithmetical properties of the natural numbers can be derived from such a small number of assumptions (as the Peano Axioms). | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 05.2) | |
| A reaction: If one were to defend essentialism about arithmetic, this would be grist to their mill. I'm just saying. |
| 14493 | Existence might require playing a role in explanation, or in a causal story, or being composed in some way [Thomasson] |
| Full Idea: A higher standard for saying that entities exist might require that they play an essential role in explanation, or must figure in any complete causal story, or exist according to some uniform and nonarbitrary principle of composition. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 11.2) | |
| A reaction: I am struck by the first of these three. If I am defending the notion that essence depends on Aristotle's account of explanation, then if we add that existence also depends on explanation, we get a criterion for the existence of essences. Yay. |
| 14491 | Rival ontological claims can both be true, if there are analytic relationships between them [Thomasson] |
| Full Idea: Where there are analytic interrelations among our claims, distinct ontological claims may be true without rivalry, redundancy, or reduction. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 10) | |
| A reaction: Thus we might, I suppose, that it is analytically necessary that a lump of clay has a shape, and that a statue be made of something. Interesting. |
| 14489 | Theories do not avoid commitment to entities by avoiding certain terms or concepts [Thomasson] |
| Full Idea: A theory does not avoid commitment to any entities by avoiding use of certain terms or concepts. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 09.4) | |
| A reaction: This is a salutary warning to those who apply the notion of ontological commitment rather naively. |
| 13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
| Full Idea: A set is called a 'relation' if every element of it is an ordered pair. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.7) | |
| A reaction: This is the modern extensional view of relations. For 'to the left of', you just list all the things that are to the left, with the things they are to the left of. But just listing the ordered pairs won't necessarily reveal how they are related. |
| 14485 | Ordinary objects may be not indispensable, but they are nearly unavoidable [Thomasson] |
| Full Idea: I do not argue that ordinary objects are indispensable, but rather that they are (nearly) unavoidable. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 09) | |
| A reaction: Disappointing, given the blurb and title of the book, but put in those terms it will be hard to disagree. Clearly ordinary objects figure in the most useful way for us to talk. I wonder whether we have a clear ontology of 'simples' in which they vanish. |
| 14487 | The simple existence conditions for objects are established by our practices, and are met [Thomasson] |
| Full Idea: The existence conditions for ordinary objects are established by our practices, and they are quite minimal, so it is rather obvious that they are fulfilled, and so there are such things. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 09.3) | |
| A reaction: This is one of her main arguments. The same argument would have worked for witches or ghosts in certain cultures. |
| 21651 | It is analytic that if simples are arranged chair-wise, then there is a chair [Thomasson, by Hofweber] |
| Full Idea: Thomasson argues that the existence of ordinary objects follows analytically from the distribution of simples, assuming that there are any simples. It is an analytic truth that if there are simples arranged chair-wise, then there is a chair. | |
| From: report of Amie L. Thomasson (Ordinary Objects [2007]) by Thomas Hofweber - Ontology and the Ambitions of Metaphysics 07.3 | |
| A reaction: But how do you distinguish when simples are arranged nearly chair-wise from the point where they click into place as actually chair-wise? What is the criterion? |
| 14486 | Eliminativists haven't found existence conditions for chairs, beyond those of the word 'chair' [Thomasson] |
| Full Idea: The eliminativist cannot claim to have 'discovered' some real existence conditions for chairs beyond those entailed by the semantic rules associated with ordinary use of the word 'chair'. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 09.3) | |
| A reaction: It is difficult to understand atoms arranged 'chairwise' or 'baseballwise' if you don't already know what a chair or a baseball are. |
| 14467 | Ordinary objects are rejected, to avoid contradictions, or for greater economy in thought [Thomasson] |
| Full Idea: Objections to ordinary objects are the Causal Redundancy claim (objects lack causal powers), the Anti-Colocation view (statues and lumps overlap), Sorites arguments, a more economical ontology, or a more scientific ontology. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], Intro) | |
| A reaction: [my summary of two paragraphs] The chief exponents of these views are Van Inwagen and Merricks. Before you glibly accept ordinary objects, you must focus on producing a really strict ontology. These arguments all have real force. |
| 14479 | To individuate people we need conventions, but conventions are made up by people [Thomasson] |
| Full Idea: The conventionalist faces paradox if they hold that conventions are logically prior to people (since this plurality requires conventions of individuation), and people are logically prior to conventions (if they make up the conventions). | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 03.3) | |
| A reaction: [Sidelle is the spokesman for conventionalism] The best defence would be to deny the second part, and say that conventions emerge from whatever is there, but only conventions can individuate the bits of what is there. |
| 14481 | Wherever an object exists, there are intrinsic properties instantiating every modal profile [Thomasson] |
| Full Idea: In a 'modally plenitudinous' ontology, wherever there is an object at all, there are objects with intrinsic modal properties instantiating every consistent modal profile. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 03.5) | |
| A reaction: [She cites K.Bennett, Hawley, Rea, Sidelle] I love this. At last a label for the view I have been espousing. I am a Modal Plenitudinist. I must get a badge made. |
| 13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
| Full Idea: The argument that the relation of dependence is well-founded ...is a version of the classical arguments for substance. ..Any conceptual scheme which genuinely represents a world cannot contain infinite backward chains of meaning. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.3) | |
| A reaction: Thus the iterative conception of set may imply a notion of substance, and Barwise's radical attempt to ditch the Axiom of Foundation (Idea 13039) was a radical attempt to get rid of 'substances'. Potter cites Wittgenstein as a fan of substances here. |
| 14482 | If the statue and the lump are two objects, they require separate properties, so we could add their masses [Thomasson] |
| Full Idea: An objection to the idea that statues are not identical to material lumps of stuff is the proliferation of instances of properties shared by those objects. If the mass of the statue is 500kg, and the mass of the lump is 500kg, do we have 1000kg? | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 04.3) | |
| A reaction: [compressed; she cites Rea 1997 and Zimmerman 1995] To wriggle out of this we would have to understand 'object' rather differently, so that an independent mass is not intrinsic to it. I leave this as an exercise for the reader. |
| 14483 | Given the similarity of statue and lump, what could possibly ground their modal properties? [Thomasson] |
| Full Idea: The 'grounding problem' is that given all that the statue and the lump have in common, what could possibly ground their different modal properties? | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 04.4) | |
| A reaction: Their modal properties are, of course, different, because only one of them could survive squashing. Thomasson suggests their difference of sort, but I'm not sure what that means, separately from what they actually are. |
| 13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
| Full Idea: A collection has a determinate number of members, whereas a fusion may be carved up into parts in various equally valid (although perhaps not equally interesting) ways. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 02.1) | |
| A reaction: This seems to sum up both the attraction and the weakness of mereology. If you doubt the natural identity of so-called 'objects', then maybe classical mereology is the way to go. |
| 14476 | Identity claims between objects are only well-formed if the categories are specified [Thomasson] |
| Full Idea: Identity claims are only well-formed and truth-evaluable if the terms flanking the statement are associated with a certain category of entity each is to refer to, which disambiguates the reference and identity-criteria. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 03) | |
| A reaction: The first of her two criteria for identity. She is buying the full Wiggins package. |
| 14477 | Identical entities must be of the same category, and meet the criteria for the category [Thomasson] |
| Full Idea: Identity claims are only true if the entities referred to are of the same category, and meet the criteria of identity appropriate for things of that category. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 03) | |
| A reaction: This may be a little too optimistic about having a set of clear-cut and reasonably objective categories to work with, but attempts at establishing metaphysical categories have not gone especially well. |
| 10709 | Priority is a modality, arising from collections and members [Potter] |
| Full Idea: We must conclude that priority is a modality distinct from that of time or necessity, a modality arising in some way out of the manner in which a collection is constituted from its members. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.3) | |
| A reaction: He is referring to the 'iterative' view of sets, and cites Aristotle 'Metaphysics' 1019a1-4 as background. |
| 14478 | Modal Conventionalism says modality is analytic, not intrinsic to the world, and linguistic [Thomasson] |
| Full Idea: Modal Conventionalism has at least three theses: 1) modal truths are either analytic truths, or combine analytic and empirical truths, 2) modal properties are not intrinsic features of the world, 3) modal propositions depend on linguistic conventions. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 03.2) | |
| A reaction: [She cites Alan Sidelle 1989 for this view] I disagree mainly with number 2), since I take dispositions to be key intrinsic features of nature, and I interpret dispositions as modal properties. |
| 14466 | A chief task of philosophy is making reflective sense of our common sense worldview [Thomasson] |
| Full Idea: Showing how, reflectively, we can make sense of our unreflective common sense worldview is arguably one of the chief tasks of philosophy. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], Intro) | |
| A reaction: Maybe. The obvious problem is that when you look at weird and remote cultures like the Aztecs, what counts as 'common sense' might be a bit different. She is talking of ordinary objects, though, where her point is reasonable. |
| 14475 | How can causal theories of reference handle nonexistence claims? [Thomasson] |
| Full Idea: Pure causal theories of reference have problems in handling nonexistence claims | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 02.3) | |
| A reaction: This is a very sound reason for shifting from a direct causal baptism view to one in which the baptism takes place by a social consensus. So there is a consensus about 'unicorns', but obviously no baptism. See Evans's 'Madagascar' example. |
| 14474 | Pure causal theories of reference have the 'qua problem', of what sort of things is being referred to [Thomasson] |
| Full Idea: Pure causal theories of reference face the 'qua problem' - that it may be radically indeterminate what the term refers to unless there is some very basic concept of what sort of thing is being referred to. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 02.3) | |
| A reaction: She cites Dummett and Wiggins on this. There is an obvious problem that when I say 'look at that!' there are all sorts of conventions at work if my reference is to succeed. |
| 14488 | Analyticity is revealed through redundancy, as in 'He bought a house and a building' [Thomasson] |
| Full Idea: The analytic interrelations among elements of language become evident through redundancy. It is redundant to utter 'He bought a house and a building', since buying a house analytically entails that he bought a building. | |
| From: Amie L. Thomasson (Ordinary Objects [2007], 09.4) | |
| A reaction: This appears to concern necessary class membership. It is only linguistically redundant if the class membership is obvious. Houses are familiar, uranium samples are not. |
| 22474 | Unlike aesthetic evaluation, moral evaluation needs a concept of responsibility [Foot] |
| Full Idea: Moral, as opposed to aesthetic, evaluation does require some distinction between actions for which we are responsible and those for which we are not responsible. | |
| From: Philippa Foot (Nietzsche's Immoralism [1991], p.154) | |
| A reaction: It is hard to disagree with this, but difficult to give a precise account of responsibility, probably because it is not an all-or-nothing matter. If we accept responsibility for our controlled actions, why not for our considered aesthetic judgements? |
| 22472 | The practice of justice may well need a recognition of human equality [Foot] |
| Full Idea: I wonder whether the practice of justice may not absolutely require a certain recognition of equality between human beings, not a pretence of the equality of talents, but something deeper. | |
| From: Philippa Foot (Nietzsche's Immoralism [1991], p.152) | |
| A reaction: {My 'something deeper' is expressed by Foot in a quotation from Gertrude Stein]. This may well be the most fundamental division which runs across a society - between those who accept and those reject human equality. |