32 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. |
| 12452 | Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer] |
| Full Idea: Not to the mathematician, but to the psychologist, belongs the task of explaining why ...we are averse to so-called contradictory systems in which the negative as well as the positive of certain propositions are valid. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.79) | |
| A reaction: Was the turning point of Graham Priest's life the day he read this sentence? I don't agree. I take the principle of non-contradiction to be a highly generalised observation of how the world works (and Russell agrees with me). |
| 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. |
| 15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |
| Full Idea: From the intuitionist standpoint the dogma of the universal validity of the principle of excluded third in mathematics can only be considered as a phenomenon of history of civilization, like the rationality of pi or rotation of the sky about the earth. | |
| From: Luitzen E.J. Brouwer (works [1930]), quoted by Shaughan Lavine - Understanding the Infinite VI.2 | |
| A reaction: [Brouwer 1952:510-11] |
| 18946 | Unreflectively, we all assume there are nonexistents, and we can refer to them [Reimer] |
| Full Idea: As speakers of the language, we unreflectively assume that there are nonexistents, and that reference to them is possible. | |
| From: Marga Reimer (The Problem of Empty Names [2001], p.499), quoted by Sarah Sawyer - Empty Names 4 | |
| A reaction: Sarah Swoyer quotes this as a good solution to the problem of empty names, and I like it. It introduces a two-tier picture of our understanding of the world, as 'unreflective' and 'reflective', but that seems good. We accept numbers 'unreflectively'. |
| 18119 | Mathematics is a mental activity which does not use language [Brouwer, by Bostock] |
| Full Idea: Brouwer made the rather extraordinary claim that mathematics is a mental activity which uses no language. | |
| From: report of Luitzen E.J. Brouwer (Mathematics, Science and Language [1928]) by David Bostock - Philosophy of Mathematics 7.1 | |
| A reaction: Since I take language to have far less of a role in thought than is commonly believed, I don't think this idea is absurd. I would say that we don't use language much when we are talking! |
| 18247 | Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro] |
| Full Idea: In his early writing, Brouwer took a real number to be a Cauchy sequence determined by a rule. Later he augmented rule-governed sequences with free-choice sequences, but even then the attitude is that Cauchy sequences are potential, not actual infinities. | |
| From: report of Luitzen E.J. Brouwer (works [1930]) by Stewart Shapiro - Philosophy of Mathematics 6.6 | |
| A reaction: This is the 'constructivist' view of numbers, as espoused by intuitionists like Brouwer. |
| 12451 | Scientific laws largely rest on the results of counting and measuring [Brouwer] |
| Full Idea: A large part of the natural laws introduced by science treat only of the mutual relations between the results of counting and measuring. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.77) | |
| A reaction: His point, I take it, is that the higher reaches of numbers have lost touch with the original point of the system. I now see the whole issue as just depending on conventions about the agreed extension of the word 'number'. |
| 18118 | Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock] |
| Full Idea: Brouwer regards as somehow 'wicked' the idea that mathematics can be applied to a non-mental subject matter, the physical world, and that it might develop in response to the needs which that application reveals. | |
| From: report of Luitzen E.J. Brouwer (Mathematics, Science and Language [1928]) by David Bostock - Philosophy of Mathematics 7.1 | |
| A reaction: The idea is that mathematics only concerns creations of the human mind. It presumably has no more application than, say, noughts-and-crosses. |
| 12454 | Intuitionists only accept denumerable sets [Brouwer] |
| Full Idea: The intuitionist recognises only the existence of denumerable sets. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80) | |
| A reaction: That takes you up to omega, but not beyond, presumably because it then loses sight of the original intuition of 'bare two-oneness' (Idea 12453). I sympathise, but the word 'number' has shifted its meaning a lot these days. |
| 12453 | Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer] |
| Full Idea: Neo-intuitionism sees the falling apart of moments, reunited while remaining separated in time, as the fundamental phenomenon of human intellect, passing by abstracting to mathematical thinking, the intuition of bare two-oneness. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80) | |
| A reaction: [compressed] A famous and somewhat obscure idea. He goes on to say that this creates one and two, and all the finite ordinals. |
| 8728 | Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer] |
| Full Idea: Mathematics rigorously treated from the point of view of deducing theorems exclusively by means of introspective construction, is called intuitionistic mathematics. It deviates from classical mathematics, which believes in unknown truths. | |
| From: Luitzen E.J. Brouwer (Consciousness, Philosophy and Mathematics [1948]), quoted by Stewart Shapiro - Thinking About Mathematics 1.2 | |
| A reaction: Clearly intuitionist mathematics is a close cousin of logical positivism and the verification principle. This view would be anathema to Frege, because it is psychological. Personally I believe in the existence of unknown truths, big time! |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 10117 | Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman] |
| Full Idea: The concern of mathematical intuitionists was that the use of certain forms of inference generates, not contradiction, but unjustified assertions. | |
| From: report of Luitzen E.J. Brouwer (Intuitionism and Formalism [1912]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: This seems to be the real origin of the verificationist idea in the theory of meaning. It is a hugely revolutionary idea - that ideas are not only ruled out of court by contradiction, but that there are other criteria which should also be met. |
| 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. |