25 ideas
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| Full Idea: Many axioms have been proposed, not on the grounds that they can be directly known, but rather because they produce a desired body of previously recognised results. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], One.5.1) | |
| A reaction: This is the perennial problem with axioms - whether we start from them, or whether we deduce them after the event. There is nothing wrong with that, just as we might infer the existence of quarks because of their results. |
| 7760 | Russell only uses descriptions attributively, and Strawson only referentially [Donnellan, by Lycan] |
| Full Idea: Donnellan objects that Russell's theory of definite descriptions overlooks the referential use (Russell writes as if all descriptions are used attributively), and that Strawson assumes they are all used referentially, to draw attention to things. | |
| From: report of Keith Donnellan (Reference and Definite Descriptions [1966]) by William Lycan - Philosophy of Language Ch.1 | |
| A reaction: This seems like a nice little success for analytical philosophy - clarifying a horrible mess by making a simple distinction that leaves everyone happy. |
| 5811 | A definite description can have a non-referential use [Donnellan] |
| Full Idea: A definite description may also be used non-referentially, even as it occurs in one and the same sentence. | |
| From: Keith Donnellan (Reference and Definite Descriptions [1966], §I) | |
| A reaction: Donnellan says we have to know about the particular occasion on which the description is used, as in itself it will not achieve reference. "Will the last person out switch off the lights" achieves its reference at the end of each day. |
| 5812 | Definite descriptions are 'attributive' if they say something about x, and 'referential' if they pick x out [Donnellan] |
| Full Idea: A speaker who uses a definite description 'attributively' in an assertion states something about whoever or whatever is the so-and-so; a speaker who uses it 'referentially' enables his audience to pick out whom or what he is talking about. | |
| From: Keith Donnellan (Reference and Definite Descriptions [1966], §III) | |
| A reaction: "Smith's murderer is insane" exemplifies the first use before he is caught, and the second use afterwards. The gist is that reference is not a purely linguistic activity, but is closer to pointing at something. This seems right. |
| 5814 | 'The x is F' only presumes that x exists; it does not actually entail the existence [Donnellan] |
| Full Idea: For Russell there is a logical entailment: 'the x is F' entails 'there exists one and only one x'. Whether or not this is true of the attributive use of definite descriptions, it does not seem true of the referential use. The existence is a presumption. | |
| From: Keith Donnellan (Reference and Definite Descriptions [1966], §VI) | |
| A reaction: Can we say 'x does not exist, but x is F'? Strictly, that sounds to me more like a contradiction than a surprising rejection of a presumption. However, 'Father Xmas does not exist, but he has a red coat'. |
| 6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
| Full Idea: Mathematical realism is the doctrine that mathematical objects exist, that much contemporary mathematics is true, and that the existence and truth in question is independent of our constructions, beliefs and proofs. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.12.9) | |
| A reaction: As thus defined, I would call myself a mathematical realist, but everyone must hesitate a little at the word 'exist' and ask, how does it exist? What is it 'made of'? To say that it exists in the way that patterns exist strikes me as very helpful. |
| 6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
| Full Idea: In maths the primary subject-matter is not mathematical objects but structures in which they are arranged; our constants and quantifiers denote atoms, structureless points, or positions in structures; they have no identity outside a structure or pattern. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.1) | |
| A reaction: This seems to me a very promising idea for the understanding of mathematics. All mathematicians acknowledge that the recognition of patterns is basic to the subject. Even animals recognise patterns. It is natural to invent a language of patterns. |
| 6303 | Sets are positions in patterns [Resnik] |
| Full Idea: On my view, sets are positions in certain patterns. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.5) | |
| A reaction: I have always found the ontology of a 'set' puzzling, because they seem to depend on prior reasons why something is a member of a given set, which cannot always be random. It is hard to explain sets without mentioning properties. |
| 6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
| Full Idea: An objection is that structuralism fails to explain why certain mathematical patterns are unified wholes while others are not; for instance, some think that an ontological account of mathematics must explain why a triangle is not a 'random' set of points. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.4) | |
| A reaction: This is an indication that we are not just saying that we recognise patterns in nature, but that we also 'see' various underlying characteristics of the patterns. The obvious suggestion is that we see meta-patterns. |
| 6295 | There are too many mathematical objects for them all to be mental or physical [Resnik] |
| Full Idea: If we take mathematics at its word, there are too many mathematical objects for it to be plausible that they are all mental or physical objects. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], One.1) | |
| A reaction: No one, of course, has ever claimed that they are, but this is a good starting point for assessing the ontology of mathematics. We are going to need 'rules', which can deduce the multitudinous mathematical objects from a small ontology. |
| 6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik] |
| Full Idea: I argue that mathematical knowledge has its roots in pattern recognition and representation, and that manipulating representations of patterns provides the connection between the mathematical proof and mathematical truth. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], One.1) | |
| A reaction: The suggestion that patterns are at the basis of the ontology of mathematics is the most illuminating thought I have encountered in the area. It immediately opens up the possibility of maths being an entirely empirical subject. |
| 6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik] |
| Full Idea: Of the equivalence relationships which occur between patterns, congruence is the strongest, equivalence the next, and mutual occurrence the weakest. None of these is identity, which would require the same position. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.3) | |
| A reaction: This gives some indication of how an account of mathematics as a science of patterns might be built up. Presumably the recognition of these 'degrees of strength' cannot be straightforward observation, but will need an a priori component? |
| 14193 | 'Substance theorists' take modal properties as primitive, without structure, just falling under a sortal [Paul,LA] |
| Full Idea: Some deep essentialists resist the need to explain the structure under de re modal properties, taking them as primitive. One version (which we can call 'substance theory') takes them to fall under a sortal concept, with no further explanation. | |
| From: L.A. Paul (In Defense of Essentialism [2006], §1) | |
| A reaction: A very helpful identification of what Wiggins stands for, and why I disagree with him. The whole point of essences is to provide a notion that fits in with sciences, which means they must have an explanatory role, which needs structures. |
| 14195 | If an object's sort determines its properties, we need to ask what determines its sort [Paul,LA] |
| Full Idea: If the substance essentialist holds that the sort an object belongs to determines its de re modal properties (rather than the other way round), then he needs to give an (ontological, not conceptual) explanation of what determines an object's sort. | |
| From: L.A. Paul (In Defense of Essentialism [2006], §1) | |
| A reaction: See Idea 14193 for 'substance essentialism'. I find it quite incredible that anyone could think that a thing's sort could determine its properties, rather than the other way round. Even if sortals are conventional, they are not arbitrary. |
| 14196 | Substance essentialism says an object is multiple, as falling under various different sortals [Paul,LA] |
| Full Idea: The explanation of material constitution given by substance essentialism is that there are multiple objects. A person is essentially human-shaped (falling under the human sort), while their hunk of tissue is accidentally human-shaped (as tissue). | |
| From: L.A. Paul (In Defense of Essentialism [2006], §1) | |
| A reaction: At this point sortal essentialism begins to look crazy. Persons are dubious examples (with sneaky dualism involved). A bronze statue is essentially harder to dent than a clay one, because of its bronze. If you remake it of clay, it isn't the same statue. |
| 14198 | Absolutely unrestricted qualitative composition would allow things with incompatible properties [Paul,LA] |
| Full Idea: Absolutely unrestricted qualitative composition would imply that objects with incompatible properties and objects such as winged pigs or golden mountains were actual. | |
| From: L.A. Paul (In Defense of Essentialism [2006], §5) | |
| A reaction: Note that this is 'qualitative' composition, and not composition of parts. The objection seems to rule out unrestricted qualitative composition, since you could hardly combine squareness with roundness. |
| 14190 | Deep essentialist objects have intrinsic properties that fix their nature; the shallow version makes it contextual [Paul,LA] |
| Full Idea: Essentialism says that objects have their properties essentially. 'Deep' essentialists take the (nontrivial) essential properties of an object to determine its nature. 'Shallow' essentialists substitute context-dependent truths for the independent ones. | |
| From: L.A. Paul (In Defense of Essentialism [2006], Intro) | |
| A reaction: If the deep essence determines a things nature, we should not need to say 'nontrivial'. This is my bete noire, the confusion of essential properties with necessary ones, where necessary properties (or predicates, at least) can indeed be trivial. |
| 14191 | Deep essentialists say essences constrain how things could change; modal profiles fix natures [Paul,LA] |
| Full Idea: The deep essentialist holds that most objects have essential properties such that there are many ways they could not be, or many changes through which they could not persist. Objects' modal profiles characterize their natures. | |
| From: L.A. Paul (In Defense of Essentialism [2006], Intro) | |
| A reaction: This is the view I like, especially the last bit. If your modal profile doesn't determine your nature, then what does? Think of how you sum up a person at a funeral. Your modal profile is determined by dispositions and powers. |
| 14192 | Essentialism must deal with charges of arbitrariness, and failure to reduce de re modality [Paul,LA] |
| Full Idea: Two objections to deep essentialism are that it falters when faced with a skeptical objection concerning arbitrariness, and the need for a reductive account of de re modality. | |
| From: L.A. Paul (In Defense of Essentialism [2006], Intro) | |
| A reaction: An immediate response to the second objection might be to say that modal facts about things are not reducible. The charge of arbitrariness (i.e. total arbitrariness, not just a bit of uncertainty) is the main thing a theory of essences must deal with. |
| 14197 | An object's modal properties don't determine its possibilities [Paul,LA] |
| Full Idea: I reject the view that an object's de re modal properties determine its relations to possibilia. | |
| From: L.A. Paul (In Defense of Essentialism [2006], §3) | |
| A reaction: You'll have to read Paul to see why, but I flat disagree with her on this. The whole point of accepting such properties is to determine the modal profile of the thing, and hence see how it can fit into and behave in the world. |
| 14189 | 'Modal realists' believe in many concrete worlds, 'actualists' in just this world, 'ersatzists' in abstract other worlds [Paul,LA] |
| Full Idea: A 'modal realist' believes that there are many concrete worlds, while the 'actualist' believes in only one concrete world, the actual world. The 'ersatzist' is an actualist who takes nonactual possible worlds and their contents to be abstracta. | |
| From: L.A. Paul (In Defense of Essentialism [2006], Intro) | |
| A reaction: My view is something like that modal realism is wrong, and actualism is right, and possible worlds (if they really are that useful) are convenient abstract fictions, constructed (if we have any sense) out of the real possibilities in the actual world. |
| 10435 | A definite description 'the F' is referential if the speaker could thereby be referring to something not-F [Donnellan, by Sainsbury] |
| Full Idea: Donnellan argued that we could recognize a referential use of a definite description 'the F' by the fact that the speaker could thereby refer to something which is not F. | |
| From: report of Keith Donnellan (Reference and Definite Descriptions [1966]) by Mark Sainsbury - The Essence of Reference 18.5 | |
| A reaction: If the expression employed achieved reference whether the speaker wanted it to or not, it would certainly look as if the expression was inherently referring. |
| 10451 | Donnellan is unclear whether the referential-attributive distinction is semantic or pragmatic [Bach on Donnellan] |
| Full Idea: Donnellan seems to be unsure whether to regard his referential-attributive distinction as indicating a semantic ambiguity or merely a pragmatic one. | |
| From: comment on Keith Donnellan (Reference and Definite Descriptions [1966]) by Kent Bach - What Does It Take to Refer? 22.2 L1 | |
| A reaction: I vote for pragmatic. In a single brief conversation a definite description could start as attributive and end as referential, but it seems unlikely that its semantics changed in mid-paragraph. |
| 5813 | A description can successfully refer, even if its application to the subject is not believed [Donnellan] |
| Full Idea: If I think the king is a usurper, "Is the king in his counting house?" succeeds in referring to the right man, even though I do not believe that he fits the description. | |
| From: Keith Donnellan (Reference and Definite Descriptions [1966], §IV) | |
| A reaction: This seems undeniable. If I point at someone, I can refer successfully with almost any description. "Oy! Adolf! Get me a drink!" Reference is an essential aspect of language, and it is not entirely linguistic. |
| 5815 | Whether a definite description is referential or attributive depends on the speaker's intention [Donnellan] |
| Full Idea: Whether or not a definite description is used referentially or attributively is a function of the speaker's intentions in a particular case. | |
| From: Keith Donnellan (Reference and Definite Descriptions [1966], §VII) | |
| A reaction: Donnellan's distinction, and his claim here, seem to me right. However words on a notice could refer on one occasion, and just describe on another. "Anyone entering this cage is mad". |