58 ideas
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle. |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| Full Idea: It is surely wise to identify the positions in the natural numbers structure with their counterparts in the integer, rational, real and complex number structures. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
| A reaction: The point is that this might be denied, since 3, 3/1, 3.00.., and -3*i^2 are all arrived at by different methods of construction. Natural 3 has a predecessor, but real 3 doesn't. I agree, intuitively, with Shapiro. Russell (1919) disagreed. |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| Full Idea: A sequence a1,a2,... of rational numbers is 'Cauchy' if for each rational number ε>0 there is a natural number N such that for all natural numbers m, n, if m>N and n>N then -ε < am - an < ε. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 7.2 n4) | |
| A reaction: The sequence is 'Cauchy' if N exists. |
| 17518 | Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers] |
| Full Idea: If we count the concept 'coin in this box', we could regard coin as the 'unit', while taking 'in this box' to limit the scope. Counting coins in two boxes would be not a difference in unit (kind of object), but in scope. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Counting') | |
| A reaction: This is a very nice alternative to the Fregean view of counting, depending totally on the concept, and rests more on a natural concept of object. I prefer Ayers. Compare 'count coins till I tell you to stop'. |
| 17516 | If counting needs a sortal, what of things which fall under two sortals? [Ayers] |
| Full Idea: If we accepted that counting objects always presupposes some sortal, it is surely clear that the class of objects to be counted could be designated by two sortals rather than one. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Realist' vii) | |
| A reaction: His nice example is an object which is both 'a single piece of wool' and a 'sweater', which had better not be counted twice. Wiggins struggles to argue that there is always one 'substance sortal' which predominates. |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| Full Idea: There is a dedicated contingent who hold that the category of 'categories' is the proper foundation for mathematics. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.3 n7) | |
| A reaction: He cites Lawvere (1966) and McLarty (1993), the latter presenting the view as a form of structuralism. I would say that the concept of a category will need further explication, and probably reduce to either sets or relations or properties. |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| Full Idea: Zermelo said that for each number n, its successor is the singleton of n, so 3 is {{{null}}}, and 1 is not a member of 3. Von Neumann said each number n is the set of numbers less than n, so 3 is {null,{null},{null,{null}}}, and 1 is a member of 3. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
| A reaction: See Idea 645 - Zermelo could save Plato from the criticisms of Aristotle! These two accounts are cited by opponents of the set-theoretical account of numbers, because it seems impossible to arbitrate between them. |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| Full Idea: The structuralist vigorously rejects any sort of ontological independence among the natural numbers; the essence of a natural number is its relations to other natural numbers. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
| A reaction: This seems to place the emphasis on ordinals (what order?) rather than on cardinality (how many?). I am strongly inclined to think that this is the correct view, though you can't really have relations if there is nothing to relate. |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| Full Idea: A 'system' is a collection of objects with certain relations among them; a 'pattern' or 'structure' is the abstract form of a system, highlighting the interrelationships and ignoring any features they do not affect how they relate to other objects. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
| A reaction: Note that 'ignoring' features is a psychological account of abstraction, which (thanks to Frege and Geach) is supposed to be taboo - but which I suspect is actually indispensable in any proper account of thought and concepts. |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| Full Idea: The thesis that principles of arithmetic are derivable from the laws of logic runs against a now common view that logic itself has no ontology. There are no particular logical objects. From this perspective logicism is a non-starter. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 5.1) | |
| A reaction: This criticism strikes me as utterly devastating. There are two routes to go: prove that logic does have an ontology of objects (what would they be?), or - better - deny that arithmetic contains any 'objects'. Or give up logicism. |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| Full Idea: Term Formalism is the view that mathematics is just about characters or symbols - the systems of numerals and other linguistic forms. ...This will cover integers and rational numbers, but what are real numbers supposed to be, if they lack names? | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.1) | |
| A reaction: Real numbers (such as pi and root-2) have infinite decimal expansions, so we can start naming those. We could also start giving names like 'Harry' to other reals, though it might take a while. OK, I give up. |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| Full Idea: Game Formalism likens mathematics to chess, where the 'content' of mathematics is exhausted by the rules of operating with its language. ...This, however, leaves the problem of why the mathematical games are so useful to the sciences. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.2) | |
| A reaction: This thought pushes us towards structuralism. It could still be a game, but one we learned from observing nature, which plays its own games. Chess is, after all, modelled on warfare. |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| Full Idea: The Deductivist version of formalism (sometimes called 'if-thenism') says that the practice of mathematics consists of determining logical consequences of otherwise uninterpreted axioms. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.2) | |
| A reaction: [Hilbert is the source] More plausible than Term or Game Formalism (qv). It still leaves the question of why it seems applicable to nature, and why those particular axioms might be chosen. In some sense, though, it is obviously right. |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| Full Idea: Critics commonly complain that the intuitionist restrictions cripple the mathematician. On the other hand, intuitionist mathematics allows for many potentially important distinctions not available in classical mathematics, and is often more subtle. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 7.1) | |
| A reaction: The main way in which it cripples is its restriction on talk of infinity ('Cantor's heaven'), which was resented by Hilbert. Since high-level infinities are interesting, it would be odd if we were not allowed to discuss them. |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| Full Idea: I classify conceptualists according to what they say about properties or concepts. If someone classified properties as existing independent of language I would classify her as a realist in ontology of mathematics. Or they may be idealists or nominalists. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 2.2.1) | |
| A reaction: In other words, Shapiro wants to eliminate 'conceptualist' as a useful label in philosophy of mathematics. He's probably right. All thought involves concepts, but that doesn't produce a conceptualist theory of, say, football. |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| Full Idea: A definition of a mathematical entity is 'impredicative' if it refers to a collection that contains the defined entity. The definition of 'least upper bound' is impredicative as it refers to upper bounds and characterizes a member of this set. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: The big question is whether mathematics can live with impredicative definitions, or whether they threaten to be viciously circular, and undermine the whole enterprise. |
| 17520 | Events do not have natural boundaries, and we have to set them [Ayers] |
| Full Idea: In order to know which event has been ostensively identified by a speaker, the auditor must know the limits intended by the speaker. ...Events do not have natural boundaries. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Concl') | |
| A reaction: He distinguishes events thus from natural objects, where the world, to a large extent, offers us the boundaries. Nice point. |
| 17519 | To express borderline cases of objects, you need the concept of an 'object' [Ayers] |
| Full Idea: The only explanation of the power to produce borderline examples like 'Is this hazelnut one object or two?' is the possession of the concept of an object. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Counting') |
| 17511 | Recognising continuity is separate from sortals, and must precede their use [Ayers] |
| Full Idea: The recognition of the fact of continuity is logically independent of the possession of sortal concepts, whereas the formation of sortal concepts is at least psychologically dependent upon the recognition of continuity. | |
| From: M.R. Ayers (Individuals without Sortals [1974], Intro) | |
| A reaction: I take this to be entirely correct. I might add that unity must also be recognised. |
| 17510 | Speakers need the very general category of a thing, if they are to think about it [Ayers] |
| Full Idea: If a speaker indicates something, then in order for others to catch his reference they must know, at some level of generality, what kind of thing is indicated. They must categorise it as event, object, or quality. Thinking about something needs that much. | |
| From: M.R. Ayers (Individuals without Sortals [1974], Intro) | |
| A reaction: Ayers defends the view that such general categories are required, but not the much narrower sortal terms defended by Geach and Wiggins. I'm with Ayers all the way. 'What the hell is that?' |
| 17522 | We use sortals to classify physical objects by the nature and origin of their unity [Ayers] |
| Full Idea: Sortals are the terms by which we intend to classify physical objects according to the nature and origin of their unity. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Concl') | |
| A reaction: This is as opposed to using sortals for the initial individuation. I take the perception of the unity to come first, so resemblance must be mentioned, though it can be an underlying (essentialist) resemblance. |
| 17515 | Seeing caterpillar and moth as the same needs continuity, not identity of sortal concepts [Ayers] |
| Full Idea: It is unnecessary to call moths 'caterpillars' or caterpillars 'moths' to see that they can be the same individual. It may be that our sortal concepts reflect our beliefs about continuity, but our beliefs about continuity need not reflect our sortals. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Realist' vi) | |
| A reaction: Something that metamorphosed through 15 different stages could hardly required 15 different sortals before we recognised the fact. Ayers is right. |
| 17517 | Could the same matter have more than one form or principle of unity? [Ayers] |
| Full Idea: The abstract question arises of whether the same matter could be subject to more than one principle of unity simultaneously, or unified by more than one 'form'. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Realist' vii) | |
| A reaction: He suggests that the unity of the sweater is destroyed by unravelling, and the unity of the thread by cutting. |
| 17513 | If there are two objects, then 'that marble, man-shaped object' is ambiguous [Ayers] |
| Full Idea: The statue is marble and man-shaped, but so is the piece of marble. So not only are the two objects in the same place, but two marble and man-shaped objects in the same place, so 'that marble, man-shaped object' must be ambiguous or indefinite. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Prob') | |
| A reaction: It strikes me as basic that it can't be a piece of marble if you subtract its shape, and it can't be a statue if you subtract its matter. To treat a statue as an object, separately from its matter, is absurd. |
| 17523 | Sortals basically apply to individuals [Ayers] |
| Full Idea: Sortals, in their primitive use, apply to the individual. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Concl') | |
| A reaction: If the sortal applies to the individual, any essence must pertain to that individual, and not to the class it has been placed in. |
| 17514 | Temporal 'parts' cannot be separated or rearranged [Ayers] |
| Full Idea: Temporally extended 'parts' are still mysteriously inseparable and not subject to rearrangement: a thing cannot be cut temporally in half. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Prob') | |
| A reaction: A nice warning to anyone accepting a glib analogy between spatial parts and temporal parts. |
| 17521 | You can't have the concept of a 'stage' if you lack the concept of an object [Ayers] |
| Full Idea: It would be impossible for anyone to have the concept of a stage who did not already possess the concept of a physical object. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Concl') |
| 17509 | Some say a 'covering concept' completes identity; others place the concept in the reference [Ayers] |
| Full Idea: Some hold that the 'covering concept' completes the incomplete concept of identity, determining the kind of sameness involved. Others strongly deny the identity itself is incomplete, and locate the covering concept within the necessary act of reference. | |
| From: M.R. Ayers (Individuals without Sortals [1974], Intro) | |
| A reaction: [a bit compressed; Geach is the first view, and Quine the second; Wiggins is somewhere between the two] |
| 17512 | If diachronic identities need covering concepts, why not synchronic identities too? [Ayers] |
| Full Idea: Why are covering concepts required for diachronic identities, when they must be supposed unnecessary for synchronic identities? | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Prob') |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| Full Idea: Rationalism is a long-standing school that can be characterized as an attempt to extend the perceived methodology of mathematics to all of knowledge. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.1) | |
| A reaction: Sometimes called 'Descartes's Dream', or the 'Enlightenment Project', the dream of proving everything. Within maths, Hilbert's Programme aimed for the same certainty. Idea 22 is the motto for the opposition to this approach. |
| 17405 | If a theory can be fudged, so can observations [Scerri] |
| Full Idea: A theorist may have designed his theory to fit the facts, but is it not equally possible for observers to be influenced by a theory in their report of experimental facts? | |
| From: Eric R. Scerri (The Periodic Table [2007], 05 'Power') | |
| A reaction: This is in reply to Lipton's claim that prediction is better than accommodation because of the 'fudging' problem. The reply is that you might fudge to achieve a prediction. If it was correct, that wouldn't avoid the charge of fudging. |
| 17397 | The periodic system is the big counterexample to Kuhn's theory of revolutionary science [Scerri] |
| Full Idea: The history of the periodic system appears to be the supreme counterexample to Kuhn's thesis, whereby scientific developments proceed in a sudden, revolutionary fashion. | |
| From: Eric R. Scerri (The Periodic Table [2007], 03 'Rapid') | |
| A reaction: What is lovely about the periodic table is that it seems so wonderfully right, and hence no revolution has ever been needed. The big theories of physics and cosmology are much more precarious. |
| 17393 | Scientists eventually seek underlying explanations for every pattern [Scerri] |
| Full Idea: Whenever scientists are presented with a useful pattern or system of classification, it is only a matter of time before the begin to ask whether there may be some underlying explanation for the pattern. | |
| From: Eric R. Scerri (The Periodic Table [2007], Intro 'Evol') | |
| A reaction: Music to my ears, against the idea that the sole aim of science is accurately describe the patterns. |
| 17403 | The periodic table suggests accommodation to facts rates above prediction [Scerri] |
| Full Idea: Rather than proving the value of prediction, the development and acceptance of the periodic table may give us a powerful illustration of the importance of accommodation, that is, the ability of a new scientific theory to explain already known facts. | |
| From: Eric R. Scerri (The Periodic Table [2007], 05 'Intro') | |
| A reaction: The original table made famous predictions, but also just as many wrong ones (Scerri:143), and Scerri thinks this aspect has been overrated. |
| 17394 | Natural kinds are what are differentiated by nature, and not just by us [Scerri] |
| Full Idea: Natural kinds are realistic scientific entities that are differentiated by nature itself rather than by our human attempts at classification. | |
| From: Eric R. Scerri (The Periodic Table [2007], Intro 'Evol') |
| 17421 | If elements are natural kinds, might the groups of the periodic table also be natural kinds? [Scerri] |
| Full Idea: Elements defined by their atomic numbers are frequently assumed to represent 'natural kinds' in chemistry. ...The question arises as to whether groups of elements appearing in the periodic table might also represent natural kinds. | |
| From: Eric R. Scerri (The Periodic Table [2007], 10 'Elements') | |
| A reaction: Scerri says the distinction is not as sharp as that between the elements. As a realist, he believes there is 'one ideal periodic classification', which would then make the periods into kinds. |
| 17396 | The colour of gold is best explained by relativistic effects due to fast-moving inner-shell electrons [Scerri] |
| Full Idea: Many seemingly mundane properties of elements such as the characteristic color of gold ....can best be explained by relativistic effects due to fast-moving inner-shell electrons. | |
| From: Eric R. Scerri (The Periodic Table [2007], 01 'Under') | |
| A reaction: John Locke - I wish you were reading this! That we could work out the hidden facts of gold, and thereby explain and predict the surface properties we experience, is exactly what Locke thought to be forever impossible. |
| 17420 | The stability of nuclei can be estimated through their binding energy [Scerri] |
| Full Idea: The stability of nuclei can be estimated through their binding energy, a quantity given by the difference between their masses and the masses of their constituent particles. | |
| From: Eric R. Scerri (The Periodic Table [2007], 10 'Stabil') |
| 17411 | If all elements are multiples of one (of hydrogen), that suggests once again that matter is unified [Scerri] |
| Full Idea: The work of Moseley and others rehabilitated Prout's hypothesis that all elements were composites of hydrogen, being exact multiples of 1. ..This revitalized some philososophical notions of the unity of all matter, criticised by Mendeleev and others. | |
| From: Eric R. Scerri (The Periodic Table [2007], 06 'Philos') |
| 17404 | Chemistry does not work from general principles, but by careful induction from large amounts of data [Scerri] |
| Full Idea: Unlike in physics, chemical reasoning does not generally proceed unambiguously from general principles. It is a more inductive science in which large amounts of observational data must be carefully weighed. | |
| From: Eric R. Scerri (The Periodic Table [2007], 05 'Mendel') | |
| A reaction: This is why essentialist thinking was important for Mendeleev, because it kept his focus on the core facts beneath the messy and incomplete data. |
| 17407 | The electron is the main source of chemical properties [Scerri] |
| Full Idea: It is the electron that is mainly responsible for the chemical properties of the elements. | |
| From: Eric R. Scerri (The Periodic Table [2007], 06 'Intro') |
| 17409 | Does radioactivity show that only physics can explain chemistry? [Scerri] |
| Full Idea: Some authors believe that the interpretation of the properties of the elements passed from chemistry to physics as a result of the discovery of radioactivity. ...I believe this view to be overly reductionist. | |
| From: Eric R. Scerri (The Periodic Table [2007], 06 'Radio') | |
| A reaction: It is all a matter of the explanations, and how far down they have to go. If most non-radiocative chemistry doesn't need to mention the physics, then chemistry is largely autonomous. |
| 17392 | How can poisonous elements survive in the nutritious compound they compose? [Scerri] |
| Full Idea: A central mystery of chemistry is how the elements survive in the compounds they form. For example, how can poisonous grey metal sodium combine with green poisonous gas chlorine, to make salt, which is non-poisonous and essential for life? | |
| From: Eric R. Scerri (The Periodic Table [2007], Intro 'Elem') | |
| A reaction: A very nice question which had never occurred to me. If our digestive system pulled the sodium apart from the chlorine, we would die. |
| 17391 | Periodicity and bonding are the two big ideas in chemistry [Scerri] |
| Full Idea: The two big ideas in chemistry are chemical periodicity and chemical bonding, and they are deeply interconnected. | |
| From: Eric R. Scerri (The Periodic Table [2007], Intro 'Per') |
| 17415 | A big chemistry idea is that covalent bonds are shared electrons, not transfer of electrons [Scerri] |
| Full Idea: One of the most influential ideas in modern chemistry is of a covalent bond as a shared pair of electrons (not as transfer of electrons and the formation of ionic bonds). | |
| From: Eric R. Scerri (The Periodic Table [2007], 08 'Intro') | |
| A reaction: Gilbert Newton Lewis was responsible for this. |
| 17418 | It is now thought that all the elements have literally evolved from hydrogen [Scerri] |
| Full Idea: The elements are now believed to have literally evolved from hydrogen by various mechanisms. | |
| From: Eric R. Scerri (The Periodic Table [2007], 10 'Evol) |
| 17398 | 19th C views said elements survived abstractly in compounds, but also as 'material ingredients' [Scerri] |
| Full Idea: In the 19th century abstract elements were believed to be permanent and responsible for observed properties in compounds, but (departing from Aristotle) they were also 'material ingredients', thus linking the metaphysical and material realm. | |
| From: Eric R. Scerri (The Periodic Table [2007], 04 'Nature') | |
| A reaction: I'm not sure I can make sense of this gulf between the metaphysical and the material realm, so this was an account heading for disaster. |
| 17406 | Moseley, using X-rays, showed that atomic number ordered better than atomic weight [Scerri] |
| Full Idea: By using X-rays, Henry Moseley later discovered that a better ordering principle for the periodic system is atomic numbers rather than atomic weight, by subjecting many different elements to bombardment. | |
| From: Eric R. Scerri (The Periodic Table [2007], 06 'Intro') | |
| A reaction: Moseley was killed in the First World War at the age of 26. It is interesting that they more or less worked out the whole table, before they discovered the best principle on which to found it. |
| 17408 | Some suggested basing the new periodic table on isotopes, not elements [Scerri] |
| Full Idea: Some chemists even suggested that the periodic table would have to be abandoned in favor of a classification system that included a separate place for every single isotope. | |
| From: Eric R. Scerri (The Periodic Table [2007], 06 'Intro') | |
| A reaction: The extreme case is tin, which has 21 isotopes, so is tin a fundamental, or is each of the isotopes a fundamental? Does there have to be a right answer to that? All tin isotopes basically react in the same way, so we stick with the elements table. |
| 17412 | Elements are placed in the table by the number of positive charges - the atomic number [Scerri] |
| Full Idea: The serial number of an element in the periodic table, its atomic number, corresponds to the number of positive charges in the atom. | |
| From: Eric R. Scerri (The Periodic Table [2007], 07 'Models') | |
| A reaction: Note that this is a feature of the nucleus, despite that fact that the electrons decide the chemical properties. A nice model for Locke's views on essentialism. |
| 17414 | Pauli explained the electron shells, but not the lengths of the periods in the table [Scerri] |
| Full Idea: Pauli explained the maximum number of electrons successive shells can accommodate, ...but it does not explain the lengths of the periods, which is the really crucial property of the periodic table. | |
| From: Eric R. Scerri (The Periodic Table [2007], 07 'Pauli') | |
| A reaction: Paulis' Exclusion Principle says no two electrons in an atom can have the same set of four quantum numbers. He added 'spin' as a fourth number. It means 'electrons cannot be distinguished' (243). Scerri says the big problem is still not fully explained. |
| 17413 | Elements in the table are grouped by having the same number of outer-shell electrons [Scerri] |
| Full Idea: The modern notion is that atoms fall into the same group of the periodic table if they possess the same numbers of outer-shell electrons. | |
| From: Eric R. Scerri (The Periodic Table [2007], 07 'Quantum') | |
| A reaction: Scerri goes on to raise questions about this, on p.242. By this principle helium should be an alkaline earth element, but it isn't. |
| 17416 | Orthodoxy says the periodic table is explained by quantum mechanics [Scerri] |
| Full Idea: The prevailing reductionist climate implies that quantum mechanics inevitably provides a more fundamental explanation for the periodic system. | |
| From: Eric R. Scerri (The Periodic Table [2007], 08 'Concl') | |
| A reaction: Scerri has argued that chemists did much better than physicists in working out how the outer electron shells of atoms worked, by induction from data, rather than inference from basic principles. |
| 17422 | The best classification needs the deepest and most general principles of the atoms [Scerri] |
| Full Idea: An optimal classification can be obtained by identifying the deepest and most general principles that govern the atoms of the elements. | |
| From: Eric R. Scerri (The Periodic Table [2007], 10 'Continuum') | |
| A reaction: He adds (p.286) that the best system will add the 'greatest degree of regularity' to these best principles. |
| 17395 | Elements were ordered by equivalent weight; later by atomic weight; finally by atomic number [Scerri] |
| Full Idea: Historically, the ordering of elements across periods was determined by equivalent weight, then later by atomic weight, and eventually by atomic number. | |
| From: Eric R. Scerri (The Periodic Table [2007], 01 'React') | |
| A reaction: So they used to be ordered by quantities (measured by real numbers), but eventually were ordered by unit items (counted by natural numbers). There need to be distinct protons (unified) to be counted. |
| 17417 | To explain the table, quantum mechanics still needs to explain order of shell filling [Scerri] |
| Full Idea: The order of shell filling has not yet been deduced from first principles, and this issue cannot be avoided if one is to really ask whether quantum mechanics explains the periodic system in a fundamental manner. | |
| From: Eric R. Scerri (The Periodic Table [2007], 09 'From') |
| 17419 | Since 99.96% of the universe is hydrogen and helium, the periodic table hardly matters [Scerri] |
| Full Idea: All the elements other than hydrogen and helium make up just 0.04% of the universe. Seen from this perspective, the periodic table appears to rather insignificant. | |
| From: Eric R. Scerri (The Periodic Table [2007], 10 'Astro') |
| 17410 | Moseley showed the elements progress in units, and thereby clearly identified the gaps [Scerri] |
| Full Idea: Moseley's work showed that the successive elements in the periodic table have an atomic number greater by one unit. The gaps could then be identified definitively, as 43, 61, 72, 75, 85, 87, and 91. | |
| From: Eric R. Scerri (The Periodic Table [2007], 06 'Henry') | |
| A reaction: [compressed] |