45 ideas
18951 | For scientific purposes there is a precise concept of 'true-in-L', using set theory [Putnam] |
Full Idea: For a language L there is a predicate 'true-in-L' which one can employ for all scientific purposes in place of intuitive truth, and this predicate admits of a precise definition using only the vocabulary of L itself plus set theory. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.2) | |
A reaction: He refers, of course, to Tarski's theory. I'm unclear of the division between 'scientific purposes' and the rest of life (which is why some people embrace 'minimal' theories of ordinary truth). I'm struck by set theory being a necessary feature. |
18953 | Modern notation frees us from Aristotle's restriction of only using two class-names in premises [Putnam] |
Full Idea: In modern notation we can consider potential logical principles that Aristotle never considered because of his general practice of looking at inferences each of whose premises involved exactly two class-names. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.3) | |
A reaction: Presumably you can build up complex inferences from a pair of terms, just as you do with pairs in set theory. |
18949 | The universal syllogism is now expressed as the transitivity of subclasses [Putnam] |
Full Idea: On its modern interpretation, the validity of the inference 'All S are M; All M are P; so All S are P' just expresses the transitivity of the relation 'subclass of'. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.1) | |
A reaction: A simple point I've never quite grasped. Since lots of syllogisms can be expressed as Venn Diagrams, in which the circles are just sets, it's kind of obvious really. So why does Sommers go back to 'terms'? See 'Term Logic'. |
18952 | '⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)' [Putnam] |
Full Idea: The symbol '⊃' (read 'if...then') is used with the definition 'Px ⊃ Qx' ('if Px then Qx') is short for '¬(Px & ¬Qx)'. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.3) | |
A reaction: So ⊃ and → are just abbreviations, and not really a proper part of the language. Notoriously, though, this is quite a long way from what 'if...then' means in ordinary English, and it leads to paradoxical oddities. |
18958 | In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type [Putnam] |
Full Idea: In the theory of types, 'x ∈ y' is well defined only if x and y are of the appropriate type, where individuals count as the zero type, sets of individuals as type one, sets of sets of individuals as type two. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.6) |
18954 | Before the late 19th century logic was trivialised by not dealing with relations [Putnam] |
Full Idea: It was essentially the failure to develop a logic of relations that trivialised the logic studied before the end of the nineteenth century. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.3) | |
A reaction: De Morgan, Peirce and Frege were, I believe, the people who put this right. |
18956 | Asserting first-order validity implicitly involves second-order reference to classes [Putnam] |
Full Idea: The natural understanding of first-order logic is that in writing down first-order schemata we are implicitly asserting their validity, that is, making second-order assertions. ...Thus even quantification theory involves reference to classes. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.3) | |
A reaction: If, as a nominalist, you totally rejected classes, presumably you would get by in first-order logic somehow. To say 'there are no classes so there is no logical validity' sounds bonkers. |
18962 | Unfashionably, I think logic has an empirical foundation [Putnam] |
Full Idea: Today, the tendency among philosophers is to assume that in no sense does logic itself have an empirical foundation. I believe this tendency is wrong. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.9) | |
A reaction: I agree, not on the basis of indispensability to science, but on the basis of psychological processes that lead from experience to logic. Russell and Quine are Putnam's allies here, and Frege is his opponent. Putnam developed a quantum logic. |
18961 | We can identify functions with certain sets - or identify sets with certain functions [Putnam] |
Full Idea: Instead of identifying functions with certain sets, I might have identified sets with certain functions. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.9) |
18955 | Having a valid form doesn't ensure truth, as it may be meaningless [Putnam] |
Full Idea: I don't think all substitution-instances of a valid schema are 'true'; some are clearly meaningless, such as 'If all boojums are snarks and all snarks are egglehumphs, then all boojums are egglehumphs'. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.3) | |
A reaction: This seems like a very good challenge to Quine's claim that it is only form which produces a logical truth. Keep deductive and semantic consequence separate, with two different types of 'logical truth'. |
18959 | Sets larger than the continuum should be studied in an 'if-then' spirit [Putnam] |
Full Idea: Sets of a very high type or very high cardinality (higher than the continuum, for example) should today be investigated in an 'if-then' spirit. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.7) | |
A reaction: This attitude goes back to Hilbert, but it fits with Quine's view of what is indispensable for science. It is hard to see a reason for the cut-off, just looking at the logic of expanding sets. |
17945 | Forms are not a theory of universals, but an attempt to explain how predication is possible [Nehamas] |
Full Idea: The theory of Forms is not a theory of universals but a first attempt to explain how predication, the application of a single term to many objects - now considered one of the most elementary operations of language - is possible. | |
From: Alexander Nehamas (Introduction to 'Virtues of Authenticity' [1999], p.xxvii) |
17946 | Only Tallness really is tall, and other inferior tall things merely participate in the tallness [Nehamas] |
Full Idea: Only Tallness and nothing else really is tall; everything else merely participates in the Forms and, being excluded from the realm of Being, belongs to the inferior world of Becoming. | |
From: Alexander Nehamas (Introduction to 'Virtues of Authenticity' [1999], p.xxviii) | |
A reaction: This is just as weird as the normal view (and puzzle of participation), but at least it makes more sense of 'metachein' (partaking). |
18957 | Nominalism only makes sense if it is materialist [Putnam] |
Full Idea: Nominalists must at heart be materialists, or so it seems to me: otherwise their scruples are unintelligible. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.5) | |
A reaction: This is modern nominalism - the rejection of abstract objects. I largely plead guilty to both charges. |
18950 | Physics is full of non-physical entities, such as space-vectors [Putnam] |
Full Idea: Physics is full of references to such 'non-physical' entities as state-vectors, Hamiltonians, Hilbert space etc. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.2) | |
A reaction: I take these to be concepts which are 'abstracted' from the physical facts, and so they don't strike me as being much of an ontological problem, or an objection to nominalism (which Putnam takes them to be). |
17944 | 'Episteme' is better translated as 'understanding' than as 'knowledge' [Nehamas] |
Full Idea: The Greek 'episteme' is usually translated as 'knowledge' but, I argue, closer to our notion of understanding. | |
From: Alexander Nehamas (Introduction to 'Virtues of Authenticity' [1999], p.xvi) | |
A reaction: He agrees with Julia Annas on this. I take it to be crucial. See the first sentence of Aristotle's 'Metaphysics'. It is explanation which leads to understanding. |
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. |
18960 | Most predictions are uninteresting, and are only sought in order to confirm a theory [Putnam] |
Full Idea: Scientists want successful predictions in order to confirm their theories; they do not want theories in order to obtain the predictions, which are in some cases of not the slightest interest in themselves. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.8) | |
A reaction: Equally, we might only care about the prediction, and have no interest at all in the theory. Farmers want weather predictions, not a PhD in meteorology. |
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. |
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') |
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') |
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. |
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. |
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') |
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. |
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. |
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) |
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') |
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. |
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] |
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. |
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. |
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. |
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. |
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. |
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') |