Combining Philosophers

All the ideas for Rescher,N/Oppenheim,P, Eric R. Scerri and J Pollock / J Cruz

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51 ideas

9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim]
     Full Idea: A whole must possess an attribute peculiar to and characteristic of it as a whole; there must be a characteristic relation of dependence between the parts; and the whole must have some structure which gives it characteristics.
     From: Rescher,N/Oppenheim,P (Logical Analysis of Gestalt Concepts [1955], p.90), quoted by Peter Simons - Parts 9.2
     A reaction: Simons says these are basically sensible conditions, and tries to fill them out. They seem a pretty good start, and I must resist the temptation to rush to borderline cases.
11. Knowledge Aims / A. Knowledge / 1. Knowledge
The main epistemological theories are foundationalist, coherence, probabilistic and reliabilist [Pollock/Cruz]
     Full Idea: The most familiar epistemological theories are foundation theories, coherence theories, probabilistic theories, and reliabilist theories.
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], Pref)
     A reaction: A helpful list. Reliabilism is now the dominant externalist theory. Probability theories will centre on Bayes' Theorem (Idea 2798). The authors want an internalist theory that includes perceptions as well as beliefs. I currently favour coherence.
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
Most people now agree that our reasoning proceeds defeasibly, rather than deductively [Pollock/Cruz]
     Full Idea: One of the most important modern advances in epistemology was the recognition of defeasible reasons; it is now generally acknowledged that most of our reasoning proceeds defeasibly rather than deductively.
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §1.2)
     A reaction: I agree totally. This is why fallibilism is clearly a correct position in epistemology (e.g. Ideas 2736 and 2755). Deduction is not the only grounds given for certainty - there are rationalist foundations (Descartes) and empiricist foundations (Moore).
To believe maximum truths, believe everything; to have infallible beliefs, believe nothing [Pollock/Cruz]
     Full Idea: If we want an agent to believe as many truths as possible, this could be achieved by simply believing everything; if we want an agent to have only true beliefs, this could be achieved by believing nothing.
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §6.6)
     A reaction: I like this. It highlights the pragmatic need for a middle road, in which a core set of beliefs are going to be approved of as 'knowledge', so that we can get on with life. This has to be a social matter, and needs flexibility of Fallibilism.
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / b. Direct realism
Direct realism says justification is partly a function of pure perceptual states, not of beliefs [Pollock/Cruz]
     Full Idea: We defend a version of direct realism, saying that justification must be partly a function of perceptual states themselves, and not just a function of our beliefs about perceptual states.
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §1.5.3)
     A reaction: Judgement suggests that perceptual states give good justification about primary qualities (like mass or shape), but not of secondary qualities (like smell or colour). Perceptions can be downright misleading.
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
Phenomenalism offered conclusive perceptual knowledge, but conclusive reasons no longer seem essential [Pollock/Cruz]
     Full Idea: Phenomenalism offered the prospect of explaining perceptual knowledge within a framework that recognised only conclusive reasons; once it is acknowledged that at least induction uses nonconclusive reasons, it is no longer needed.
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §2.3.3.2)
     A reaction: I'm not sure that that is the only motivation for phenomenalism, which seemed to be attempting to get as close to 'reality' as intellectual honesty would allow. I certainly favour the modern relaxed attitude to knowledge, which needn't be 'conclusive'.
12. Knowledge Sources / B. Perception / 1. Perception
Perception causes beliefs in us, without inference or justification [Pollock/Cruz]
     Full Idea: Perception is a causal process that inputs beliefs into our doxastic system without their being inferred from or justified on the basis of other beliefs we already have.
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §3.2.3)
     A reaction: This topic is much discussed (e.g. by MacDowell). I don't see how something is going to qualify as a 'belief' if it doesn't involve concepts and propositions. The point that we are caused to have many of our beliefs (rather than judging) seems right.
12. Knowledge Sources / B. Perception / 6. Inference in Perception
Sense evidence is not beliefs, because they are about objective properties, not about appearances [Pollock/Cruz]
     Full Idea: We think it is a mistake to suppose that the evidence of our senses comes to us in the form of beliefs; in perception, the beliefs we form are almost invariably about the objective properties of physical objects - not about how they appear to us.
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §2.5.5)
     A reaction: The tricky word here is 'evidence'. At what point in the process of perception does something begin to count as evidence? It must at least involve concepts (and maybe even propositions) if it is going to be thought about in that way.
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
Bayesian epistemology is Bayes' Theorem plus the 'simple rule' (believe P if it is probable) [Pollock/Cruz]
     Full Idea: Bayesian epistemology is based upon the 'simple rule' (believe P if it is sufficiently probable) and Bayes' Theorem.
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §4.3.1)
     A reaction: For Bayes' Theorem, see Idea 2798. There is the question of whether the proposition is subjectively or objectively probable (I believe in ghosts, so any shadow is probably a ghost). There is also the problem of objective evidence for the calculation.
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
Internalism says if anything external varies, the justifiability of the belief does not vary [Pollock/Cruz]
     Full Idea: Internalist theories make justifiability of a belief a function of the internal states of the believer, in the sense that if we vary anything but his internal states the justifiability of the belief does not vary.
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §5.4.3)
     A reaction: This seems to be a nice clear definition of internalism (and, by implication, externalism). It favours externalism. I know my car is in the car park; someone takes it for a joyride, then replaces it; my good justification seems thereby weakened.
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
People rarely have any basic beliefs, and never enough for good foundations [Pollock/Cruz]
     Full Idea: We argue that all foundations theories are false, for the simple reason that people rarely have any epistemological basic beliefs, and never have enough to provide a foundation for the rest of our knowledge.
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §1.5.3)
     A reaction: Once surprising things start to happen in a film, we rapidly jettison our normal basic beliefs, to be ready for surprises. However, it seems to me that quite a lot of beliefs are hard-wired into us, or inescapably arise from the use of our senses.
Foundationalism requires self-justification, not incorrigibility [Pollock/Cruz]
     Full Idea: What foundationalism requires is self-justification, which is weaker than incorrigibility.
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §2.5.3)
     A reaction: The writers oppose foundationalism, but this remark obviously helps the theory. Bonjour votes for a fallible rationalist foundationalism, and an fallible empiricist version seems plausible (because we must check for hallucinations etc.).
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / d. Rational foundations
Reason cannot be an ultimate foundation, because rational justification requires prior beliefs [Pollock/Cruz]
     Full Idea: Reasoning, it seems, can only justify us in holding a belief if we are already justified in holding the beliefs from which we reason, so reasoning cannot provide an ultimate source of justification.
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §2.1)
     A reaction: This sounds slick and conclusive, but it isn't. If we accept that some truths might be 'self-evident' to reason, they could stand independently. And a large body of rational beliefs might be mutually self-supporting, as in the coherence theory of truth.
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
Foundationalism is wrong, because either all beliefs are prima facie justified, or none are [Pollock/Cruz]
     Full Idea: Either no belief is prima facie justified or all beliefs are prima facie justified; …we regard this as a decisive refutation of foundationalism.
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §2.5.5)
     A reaction: The full text must he examined, but it is not at all clear to me how my belief that quantum theory is correct could be even remotely as prima facie justified as my belief that this is my hand. I don't think basic beliefs need be sharply divided off.
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
Negative coherence theories do not require reasons, so have no regress problem [Pollock/Cruz]
     Full Idea: The regress argument has no apparent strength against negative coherence theories, because they do not require reasons for beliefs.
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §3.2.3)
     A reaction: A nice point. Such theories endorse Neurath's picture (Idea 6348). On the whole philosophers like positive support for their beliefs, so the rather passive picture of accepting everything unless it is undermined is not appealing. A fall-back position.
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
Coherence theories fail, because they can't accommodate perception as the basis of knowledge [Pollock/Cruz]
     Full Idea: All coherence theories fail, because they are unable to accommodate perception as the basic source of our knowledge of the world.
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §1.5.3)
     A reaction: An interesting claim, which the authors attempt to justify. They say it is direct realism, because the perceptions justify, without any intervening beliefs. My immediate thought is that they might justify knowledge of primary qualities, but not secondary.
Coherence theories isolate justification from the world [Pollock/Cruz]
     Full Idea: The Isolation Argument objects that coherence theories cut justification off from the world.
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §3.2.4)
     A reaction: I don't see this as a strong objection. Justification can be in the way beliefs cohere together, but the beliefs themselves consist of holding propositions to be true, and truth asserts a connection to the world (I say).
13. Knowledge Criteria / C. External Justification / 1. External Justification
Externalism comes as 'probabilism' (probability of truth) and 'reliabilism' (probability of good cognitive process) [Pollock/Cruz]
     Full Idea: There are two major kinds of externalist theory in the literature - probabilism (which expresses justification in terms of probability of the belief being true), and reliabilism (which refers to the probability of the cognitive processes being right).
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §4.1)
     A reaction: A useful clarification. Reliabilism has an obvious problem, that a process can be reliable, but only luckily correct on this occasion (a clock which has, unusually, stopped). A ghost is more probably there if I believe in ghosts.
13. Knowledge Criteria / C. External Justification / 2. Causal Justification
One belief may cause another, without being the basis for the second belief [Pollock/Cruz]
     Full Idea: If I fall flat on my back running to a class, my belief that I was late for class may cause me to have the belief that there are birds in the trees, but I do not believe the latter on the basis of the former.
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §2.3.1)
     A reaction: A nice example, which fairly conclusively demolishes any causal theory of justification. My example is believing correctly that the phone ring is from mother, because she said she would call. Maybe causation is needed somewhere in the right theory.
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
We can't start our beliefs from scratch, because we wouldn't know where to start [Pollock/Cruz]
     Full Idea: We cannot forsake all of our beliefs and start over again, because then we could not know how to start.
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §3.1)
     A reaction: A point with which it is hard to disagree, but even Descartes agreed with it (Idea 3604). Presumably all your beliefs can take it in turn to be doubted, while others are held true, or you can whittle the beliefs which can't be abandoned down to a minimum.
14. Science / A. Basis of Science / 4. Prediction
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.
14. Science / B. Scientific Theories / 4. Paradigm
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.
14. Science / C. Induction / 1. Induction
Enumerative induction gives a universal judgement, while statistical induction gives a proportion [Pollock/Cruz]
     Full Idea: Enumerative induction examines a sample of objects, observes they all have a property, and infers that they all have that property; statistical induction observes a proportion of the objects having the property, and infers that proportion in general.
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §1.4.6)
     A reaction: There is also induction by elimination, where it is either p or q, and observation keeps saying it isn't p. A small sample is very unreliable, but a huge sample (e.g. cigarettes and cancer) is almost certain, so where is the small/huge boundary?
14. Science / C. Induction / 6. Bayes's Theorem
Since every tautology has a probability of 1, should we believe all tautologies? [Pollock/Cruz]
     Full Idea: It follows from the probability calculus that every tautology has probability 1; it then follows in Bayesian epistemology that we are justified in believing every tautology.
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §4.3.1.5)
     A reaction: If I say 'a bachelor is a small ant' you wouldn't believe it, but if I said 'I define a bachelor as a small ant' you would have to believe it. 'Bachelors are unmarried' men is a description of English usage, so is not really a simple tautology.
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
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.
14. Science / D. Explanation / 3. Best Explanation / a. Best explanation
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.
Scientific confirmation is best viewed as inference to the best explanation [Pollock/Cruz]
     Full Idea: The confirmation of scientific theories is probably best viewed in terms of inference to the best explanation.
     From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §2.3.3.3)
     A reaction: A simple claim, but one with which I strongly agree. 'Inference', of course, implies that there is some fairly strict logical thinking going on, which may not be so. I suspect that dogs can move to the best explanation. It is, though, a rational process.
26. Natural Theory / B. Natural Kinds / 1. Natural Kinds
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')
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.
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
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.
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
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')
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')
27. Natural Reality / F. Chemistry / 1. Chemistry
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')
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.
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.
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')
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.
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.
27. Natural Reality / F. Chemistry / 2. Modern Elements
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)
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.
27. Natural Reality / F. Chemistry / 3. Periodic Table
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.
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.
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.
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.
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.
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.
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]
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.
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.
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')
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')