25 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) |
| 9175 | We may fix the reference of 'Cicero' by a description, but thereafter the name is rigid [Kripke] |
| Full Idea: We may fix the reference of 'Cicero' by use of some descriptive phrase, such as 'author of these works'. But once we have this reference fixed, we then use the name 'Cicero' rigidly to designate the man who in fact we have identified by his authorship. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.183) | |
| A reaction: Even supposedly rigid names can shift reference, as Evans's example of 'Madagascar' shows (Idea 9041). Reference is a much more social activity than Kripke is willing to admit. There is a 'tradition' of reference (Dummett) for the name 'Cicero'. |
| 9171 | The function of names is simply to refer [Kripke] |
| Full Idea: The function of names is simply to refer. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.167) | |
| A reaction: This is Kripke reverting to the John Stuart Mill view of names. If I say "you are a right Casanova" I don't simply refer to Casanova. In notorious examples like 'Homer' reference is fine, but the object of reference is a bit elusive. |
| 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) |
| 17486 | Supervenience is simply modally robust property co-variance [Hendry] |
| Full Idea: Supervenience is not an ontological relationship, being just modally robust property co-variance. | |
| From: Robin F. Hendry (Chemistry [2008], 'Ontol') | |
| A reaction: I take supervenience to be nothing more than an interesting phenomenon that requires explanation. I suppose Humean Supervenience is a priori metaphysics, since you could hardly explain it. |
| 9174 | It is necessary that this table is not made of ice, but we don't know it a priori [Kripke] |
| Full Idea: Although the statement that this table (if it exists at all) was not made of ice, is necessary, it certainly is not something that we know a priori. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.180) | |
| A reaction: One of the key thoughts in modern philosophy. Kit Fine warns against treating it as a new and exciting toy, but it is a new and exciting toy. Scientific essentialism, which I so want to be true, is built on this proposal. |
| 9172 | A 'rigid designator' designates the same object in all possible worlds [Kripke] |
| Full Idea: By 'rigid designator' I mean a term that designates the same object in all possible worlds. | |
| From: Saul A. Kripke (Identity and Necessity [1971]) | |
| A reaction: I am persistently troubled by the case of objects which are slightly different in another possible world. Does 'Aristotle' refer to him as young or old? Might the very same man have had a mole on his cheek? |
| 9173 | We cannot say that Nixon might have been a different man from the one he actually was [Kripke] |
| Full Idea: It seems that we cannot say "Nixon might have been a different man from the man he in fact was", unless we mean it metaphorically. He might have been a different sort of person. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.176) | |
| A reaction: The problem is that being a 'different sort of person' could become more and more drastic, till Nixon is unrecognisable. I don't see how I can stipulate that a small and dim mouse is Richard Nixon, even in a possible world with magicians. |
| 9176 | Modal statements about this table never refer to counterparts; that confuses epistemology and metaphysics [Kripke] |
| Full Idea: Statements about the modal properties of this table never refer to counterparts. However, if someone confuses the epistemological problems and the metaphysical problems he will be well on the way to the counterpart theory of Lewis. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.184 n16) | |
| A reaction: I can't make out what we should say about a possible object which is very nearly this table. Kripke needs the table to have a clear and unwavering essence, but tables are not that sort of thing. How would Kripke define 'physical object'? |
| 17481 | Nuclear charge (plus laws) explains electron structure and spectrum, but not vice versa [Hendry] |
| Full Idea: Given relevant laws of nature (quantum mechanics, the exclusion principle) nuclear charge determines and explains electronic structure and spectroscopic behaviour, but not vice versa. | |
| From: Robin F. Hendry (Chemistry [2008], 'Micro') | |
| A reaction: I argue that the first necessary condition for essentialism is a direction of explanation, and here we seem to have one. |
| 9177 | Identity theorists must deny that pains can be imagined without brain states [Kripke] |
| Full Idea: The identity theorist has to hold that we are under some illusion in thinking that we can imagine that there could have been pains without brain states. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.190) | |
| A reaction: The origin of Robert Kirk's idea that there might be zombies. Kripke is wrong. Of course Kripke and his friends can imagine disembodied pains; the question is whether being able to imagine them makes them possible, which it doesn't. |
| 9178 | Pain, unlike heat, is picked out by an essential property [Kripke] |
| Full Idea: 'Heat' is a rigid designator, which is picked out by the contingent property of being felt in a certain way; pain, on the other hand, is picked out by an essential (indeed necessary and sufficient) property. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.190 n19) | |
| A reaction: Hm. I could pick out your pain by your contingent whimpering behaviour. I can spot my own potential pain by a combination of bodily damage and pain killing tablets. I suspect him of the same blunder as Descartes on this one. |
| 17478 | Maybe two kinds are the same if there is no change of entropy on isothermal mixing [Hendry] |
| Full Idea: One suggestion is that any two different substance, however alike, exhibit a positive entropy change on mixing. So absence of entropy change on isothermal mixing provides a criterion of sameness of kind. | |
| From: Robin F. Hendry (Chemistry [2008], 'Micro') | |
| A reaction: [He cites Paul Needham 2000] This sounds nice, because at a more amateur level we can say that stuff is the same if mixing two samples of it produces no difference. I call it the Upanishads Test. |
| 17484 | Maybe the nature of water is macroscopic, and not in the microstructure [Hendry] |
| Full Idea: Some deny that that microstructure is what makes it water; substance identity and difference should be determined instead by macroscopic similarities and differences. | |
| From: Robin F. Hendry (Chemistry [2008], 'Micro') | |
| A reaction: Very plausible. Is the essential nature of human beings to be found in the structure of our cells? |
| 17479 | The nature of an element must survive chemical change, so it is the nucleus, not the electrons [Hendry] |
| Full Idea: Whatever earns something membership of the extension of 'krypton' must be a property that can survive chemical change and, therefore, the gain and loss of electrons. Hence what makes it krypton must be a nuclear property. | |
| From: Robin F. Hendry (Chemistry [2008], 'Micro') | |
| A reaction: A very nice illuminating example of essentialism in chemistry. The 'nature' is what survives through change, just like what Aristotle said, innit? |
| 17485 | Maybe water is the smallest part of it that still counts as water (which is H2O molecules) [Hendry] |
| Full Idea: If they do count as water, individual H2O molecules are the smallest items that can qualify as water on their own account. Hydroxyl ions and protons, in contrast, qualify as water only as part of a larger body. | |
| From: Robin F. Hendry (Chemistry [2008], 'Micro') | |
| A reaction: As Aristotle might say, this is the homoeomerous aspect of water. This is Hendry's own proposal, and seems rather good. |
| 17482 | Compounds can differ with the same collection of atoms, so structure matters too [Hendry] |
| Full Idea: The distinctness of the isomers ethanol (CH3CH2OH, boiling at 78.4°) and dimethyl ether (CH3OCH3, boiling at -24.9°) must lie in their different molecular structures. ...But structure has continuously varying quantities, like bond length and angle. | |
| From: Robin F. Hendry (Chemistry [2008], 'Micro') | |
| A reaction: [compressed] This seems to imply that what matters is an idealised abstraction of the structure (i.e. its topology), which is a reason for denying that chemistry is reducible to mere physics. |
| 17483 | Water continuously changes, with new groupings of molecules [Hendry] |
| Full Idea: Macroscopic bodies of water are complex and dynamic congeries of different molecular species, in which there is a constant dissociation of individual molecules, re-association of ions, and formation, growth and disassociation of oligomers. | |
| From: Robin F. Hendry (Chemistry [2008], 'Micro') | |
| A reaction: The point is that these activities are needed to explain the behaviour of water (such as its conductivity). |
| 17476 | Elements survive chemical change, and are tracked to explain direction and properties [Hendry] |
| Full Idea: Elements survive chemical change, and chemical explanations track them from one composite substance to another, thereby explaining both the direction of the chemical change, and the properties of the substances they compose. | |
| From: Robin F. Hendry (Chemistry [2008], Intro) | |
| A reaction: [The 16,000th idea of this database, entered on Guy Fawkes' Day 2013] |
| 17477 | Defining elements by atomic number allowed atoms of an element to have different masses [Hendry] |
| Full Idea: In 1923 elements were defined as populations of atoms with the same nuclear charge (i.e. atomic number), allowing that atoms of the same element may have different masses. | |
| From: Robin F. Hendry (Chemistry [2008], 'Chem') | |
| A reaction: The point is that it allowed isotopes of the same element to come under one heading. This is fine for the heavier elements, but a bit dubious for the very light ones (where an isotope makes a bigger difference). |
| 17480 | Generally it is nuclear charge (not nuclear mass) which determines behaviour [Hendry] |
| Full Idea: In general, nuclear charge is the overwhelming determinant of an element's chemical behaviour, while nuclear mass is a negligible factor. | |
| From: Robin F. Hendry (Chemistry [2008], 'Micro') | |
| A reaction: The exception is the isotopes of very light elements light hydrogen. |