29 ideas
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 17377 | All descriptive language is classificatory [Dupré] |
| Full Idea: Classification pervades any descriptive use of language whatever. | |
| From: John Dupré (The Disorder of Things [1993], 1) | |
| A reaction: This is because, as Aristotle well knew, language consists almost entirely of universals (apart from the proper names). Language just is classification. |
| 17376 | We should aim for a classification which tells us as much as possible about the object [Dupré] |
| Full Idea: The most important desideratum of a classificatory scheme is that assigning an object to a particular classification tell us as much as possible about that object. | |
| From: John Dupré (The Disorder of Things [1993], Ch 1) | |
| A reaction: We should probably say that the aim is a successful explanation, rather than a heap of information. If we are totally baffled by a particular type of object, it is presumably important to group the instances together, to focus the bafflement. |
| 15148 | Powers give explanations, without being necessary for some class membership [Chakravartty] |
| Full Idea: Powers explain behaviours regardless of whether they are necessary for membership in a particular class of things. | |
| From: Anjan Chakravarrty (Inessential Aristotle: Powers without Essences [2012], 3) | |
| A reaction: This seems right, and is important for driving a wedge between powers and essences. If there are essences, they are not simply some bunch of powers. |
| 15145 | A kind essence is the necessary and sufficient properties for membership of a class [Chakravartty] |
| Full Idea: The modern concept of a kind essence is a set of intrinsic properties that are individually necessary and jointly sufficient for the membership of something in a class of things, or 'kind'. | |
| From: Anjan Chakravarrty (Inessential Aristotle: Powers without Essences [2012], 2) | |
| A reaction: I am always struck by the problem that the kind itself is constructed from the individuals, so circularity always seems to loom. |
| 17390 | Natural kinds don't need essentialism to be explanatory [Dupré] |
| Full Idea: The importance of natural kinds for explanation does not depend on a doctrine of essences. | |
| From: John Dupré (The Disorder of Things [1993], 3) | |
| A reaction: He suggest as the alternative that laws do the explaining, employing natural kinds. He allows that individual essences might be explanatory. |
| 17389 | A species might have its essential genetic mechanism replaced by a new one [Dupré] |
| Full Idea: Contradicting one of the main points of essentialism, there is no reason in principle why a species should not survive the demise of its current genetic mechanisms (some other species coherence gradually taking over). | |
| From: John Dupré (The Disorder of Things [1993], 2) | |
| A reaction: I would say that this meant that the species had a new essence, because I don't take what is essential to be the same as what is necessary. The new genetics would replace the old as the basic explanation of the species. |
| 17388 | It seems that species lack essential properties, so they can't be natural kinds [Dupré] |
| Full Idea: It is widely agreed among biologists that no essential property can be found to demarcate species, so that if an essential property is necessary for a natural kind, species are not natural kinds. | |
| From: John Dupré (The Disorder of Things [1993], 2) | |
| A reaction: This uses 'essential' to mean 'necessary', but I would use 'essential' to mean 'deeply explanatory'. Biological species are, nevertheless, dubious members of an ontological system. Vegetables are the problem. |
| 15147 | Cluster kinds are explained simply by sharing some properties, not by an 'essence' [Chakravartty] |
| Full Idea: The fact that members of some cluster kinds are subjects of causal generalizations reflects the degree to which they share causally efficacious properties, not the fact that they may be composed of essence kinds per se. | |
| From: Anjan Chakravarrty (Inessential Aristotle: Powers without Essences [2012], 2) | |
| A reaction: I think this is right. I am a fan of individual essences, but not of kind essences. I take kinds, and kind explanations, to be straightforward inductive generalisations from individuals. Extreme stabilities give the illusion of a kind essence. |
| 17374 | The possibility of prediction rests on determinism [Dupré] |
| Full Idea: Determinism is the metaphysical underlay of the possibility of prediction. | |
| From: John Dupré (The Disorder of Things [1993], Intro) | |
| A reaction: Not convinced. There might be micro-indeterminacies which iron out into macro-regularities. |
| 15144 | Explanation of causal phenomena concerns essential kinds - but also lack of them [Chakravartty] |
| Full Idea: Scientific practices such as prediction and explanation regarding causal phenomena are concerned not merely with kinds having essences, but also with kinds lacking them. | |
| From: Anjan Chakravarrty (Inessential Aristotle: Powers without Essences [2012], 1) | |
| A reaction: Not quite clear what he has in mind, but explanation should certainly involve a coherent picture, and not just the citation of some underlying causal mechanism. |
| 17378 | Presumably molecular structure seems important because we never have the Twin Earth experience [Dupré] |
| Full Idea: It is surely the absence of experiences like the one Putnam describes that makes it reasonable to attach to molecular structure at least most of the importance that Putnam ascribes to it. | |
| From: John Dupré (The Disorder of Things [1993], 1) | |
| A reaction: That is, whenever we experience water-like stuff, it always turns out to have the same molecular structure. Twin Earth is a nice thought experiment, except that XZY is virtually inconceivable. |
| 17381 | Phylogenetics involves history, and cladism rests species on splits in lineage [Dupré] |
| Full Idea: The phylogenetic conception of classification reflects the facts of evolutionary history. Cladism insists that every taxonomic distinction should reflect an evolutionary event of lineage bifurcation. | |
| From: John Dupré (The Disorder of Things [1993], 1) | |
| A reaction: Devitt attacks cladism nicely. It rules out species change without bifurcation, and it insists on species change even in a line which remains unchanged after a split. |
| 17385 | Kinds don't do anything (including evolve) because they are abstract [Dupré] |
| Full Idea: A kind, being an abstract object, cannot do anything, including evolve. | |
| From: John Dupré (The Disorder of Things [1993], 2) | |
| A reaction: Maybe. We might have an extensional view of the kind, so that 'gold' is the set of extant gold atoms. But possible gold atoms are also gold, and defunct ones too. Virtually every word in English is abtract if you think about it long enough. |
| 15146 | Some kinds, such as electrons, have essences, but 'cluster kinds' do not [Chakravartty] |
| Full Idea: Many of the kinds we theorize about and experiment on today simply do not have essences. We can distinguish 'essence kinds', such as electrons, and 'cluster kinds', such as biological species. | |
| From: Anjan Chakravarrty (Inessential Aristotle: Powers without Essences [2012], 2) | |
| A reaction: This is an important point for essentialists. He offers a strict criterion, in Idea 15145, for mind membership, but we might allow species to have essences by just relaxing the criteria a bit, and acknowledging some vagueness, especially over time. |
| 17375 | Natural kinds are decided entirely by the intentions of our classification [Dupré] |
| Full Idea: The question of which natural kind a thing belongs to ....can be answered only in relation to some specification of the goal underlying the intent to classify the object. | |
| From: John Dupré (The Disorder of Things [1993], Intro) | |
| A reaction: I don't think I believe this. The situation is complex, and our intents are relevant, but to find an intent which no longer classifies tigers into the same category is wilful silliness. |
| 17379 | Borders between species are much less clear in vegetables than among animals [Dupré] |
| Full Idea: The richest source of illustrations is the vegetable kingdom, where specific differences tend to be much less clear than among animals, and considerable developmental plasticity is the rule. | |
| From: John Dupré (The Disorder of Things [1993], 1) | |
| A reaction: Nice. Just as the idea that laws of nature are mathematical suits physics, but founders on biology, so natural kinds founder in an area of biology to which we pay less attention. He cites prickly pears and lilies. I'm thinking oranges, satsumas etc. |
| 17384 | Even atoms of an element differ, in the energy levels of their electrons [Dupré] |
| Full Idea: Even if we claim that it is really isotopes not atoms that are the natural kinds (thus divorcing chemistry from ordinary language), atoms are said to differ with respect to such features as energy levels of the electrons. | |
| From: John Dupré (The Disorder of Things [1993], 2) | |
| A reaction: So we can't just pick out the features of one atom, and say that is the essence. Essence always involves some selection. I say the essence arises from the explanation of the atom's behaviour. |
| 17387 | Ecologists favour classifying by niche, even though that can clash with genealogy [Dupré] |
| Full Idea: To the extent that the occupants of a particular niche do not coincide with the members of a particular genealogical line, a possibility widely acknowledged to occur, ecologists must favour a method of classification lacking genealogical grounding. | |
| From: John Dupré (The Disorder of Things [1993], 2) | |
| A reaction: Zoo keepers probably classify by cages, or which zoo owns what, but that doesn't mean that they reject genealogy. Don't assume ecologists are rejecting any underlying classification that differs from theirs. Compare classification by economists. |
| 17382 | Cooks, unlike scientists, distinguish garlic from onions [Dupré] |
| Full Idea: It would be a severe culinary misfortune if no distinction were drawn between garlic and onions, a distinction that is not reflected in scientific taxonomy. | |
| From: John Dupré (The Disorder of Things [1993], 1) | |
| A reaction: Not every persuasive. We distinguish some cows from others because they taste better, but no one thinks that is a serious way in which to classify cows. |
| 17380 | Wales may count as fish [Dupré] |
| Full Idea: The claim that whales are not fish is a debatable one | |
| From: John Dupré (The Disorder of Things [1993], 1) | |
| A reaction: A very nice challenge to an almost unquestioned orthodoxy. |
| 15151 | Many causal laws do not refer to kinds, but only to properties [Chakravartty] |
| Full Idea: Causal laws often do not make reference to kinds of objects at all, but rather summarize relations between quantitative, causally efficacious properties of objects. | |
| From: Anjan Chakravarrty (Inessential Aristotle: Powers without Essences [2012], 3) | |
| A reaction: This would only be a serious challenge if it was not possible to translate talk of properties into talk of kinds, and vice versa. |
| 17383 | Species are the lowest-level classification in biology [Dupré] |
| Full Idea: Species are, by definition, the lowest-level classificatory unit, or basal taxonomic unit, for biological organisms. | |
| From: John Dupré (The Disorder of Things [1993], 2) | |
| A reaction: I think this is the 'infima species' for Aristotelians. What about 'male' and 'female' in each species? |
| 17386 | The theory of evolution is mainly about species [Dupré] |
| Full Idea: Species are what the theory of evolution is centrally about. | |
| From: John Dupré (The Disorder of Things [1993], 2) |