19 ideas
17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
A reaction: Each expansion brings a limitation, but then you can expand again. |
17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
3291 | Emergent properties appear at high levels of complexity, but aren't explainable by the lower levels [Nagel] |
Full Idea: The supposition that a diamond or organism should truly have emergent properties is that they appear at certain complex levels of organisation, but are not explainable (even in principle) in terms of any more fundamental properties of the system. | |
From: Thomas Nagel (Panpsychism [1979], p.186) |
17471 | Using mechanisms as explanatory schemes began in chemistry [Weisberg/Needham/Hendry] |
Full Idea: The production of mechanisms as explanatory schemes finds its original home in chemistry. | |
From: Weisberg/Needham/Hendry (Philosophy of Chemistry [2011], 5.1) | |
A reaction: This is as opposed to mechanisms in biology or neuroscience, which come later. |
17472 | Thick mechanisms map whole reactions, and thin mechanism chart the steps [Weisberg/Needham/Hendry] |
Full Idea: In chemistry the 'thick' notion of a mechanism traces out positions of electrons and atomic cores, and correlates them with energies, showing the whole reaction. 'Thin' mechanisms focus on a discrete set of intermediate steps. | |
From: Weisberg/Needham/Hendry (Philosophy of Chemistry [2011], 5.1) |
17465 | Lavoisier's elements included four types of earth [Weisberg/Needham/Hendry] |
Full Idea: Four types of earth found a place on Lavoisier's list of elements. | |
From: Weisberg/Needham/Hendry (Philosophy of Chemistry [2011], 1.2) | |
A reaction: A nice intermediate point between the ancient Greek and the modern view of earth. |
3290 | Given the nature of heat and of water, it is literally impossible for water not to boil at the right heat [Nagel] |
Full Idea: Given what heat is and what water is, it is literally impossible for water to be heated beyond a certain point at normal atmospheric pressure without boiling. | |
From: Thomas Nagel (Panpsychism [1979], p.186) |
17468 | Over 100,000,000 compounds have been discovered or synthesised [Weisberg/Needham/Hendry] |
Full Idea: There are well over 100,000,000 chemical compounds that have been discovered or synthesised, all of which have been formally characterised. | |
From: Weisberg/Needham/Hendry (Philosophy of Chemistry [2011], 4.3) |
17470 | Water molecules dissociate, and form large polymers, explaining its properties [Weisberg/Needham/Hendry] |
Full Idea: Water's structure cannot simply be described as a collection of individual molecules. There is a continual dissociation of H2O molecules into hydrogen and hydroxide ions; they former larger polymeric species, explaining conductivity, melting and boiling. | |
From: Weisberg/Needham/Hendry (Philosophy of Chemistry [2011], 4.5) | |
A reaction: [compressed] If philosophers try to state the 'essence of water', they had better not be too glib about it. |
17473 | It is unlikely that chemistry will ever be reduced to physics [Weisberg/Needham/Hendry] |
Full Idea: Most philosophers believe chemistry has not been reduced to physics nor is it likely to be. | |
From: Weisberg/Needham/Hendry (Philosophy of Chemistry [2011], 6) | |
A reaction: [Le Poidevin 2007 argues the opposite] That chemical features are actually metaphysically 'emergent' is a rare view, defended by Hendry. The general view is that the concepts are too different, and approximations render it hopeless. |
17474 | Quantum theory won't tell us which structure a set of atoms will form [Weisberg/Needham/Hendry] |
Full Idea: Quantum mechanics cannot tell us why a given collection of atoms will adopt one molecular structure (and set of chemical properties) or the other. | |
From: Weisberg/Needham/Hendry (Philosophy of Chemistry [2011], 6.1) | |
A reaction: Presumably it the 'chance' process of how the atoms are thrown together. |
17475 | For temperature to be mean kinetic energy, a state of equilibrium is also required [Weisberg/Needham/Hendry] |
Full Idea: Having a particular average kinetic energy is only a necessary condition for having a given temperature, not a sufficient one, because only gases at equilibrium have a well-defined temperature. | |
From: Weisberg/Needham/Hendry (Philosophy of Chemistry [2011], 6.2) | |
A reaction: If you try to pin it all down more precisely, the definition turns out to be circular. |
17469 | 'H2O' just gives the element proportions, not the microstructure [Weisberg/Needham/Hendry] |
Full Idea: 'H2O' is not a description of any microstructure. It is a compositional formula, describing the combining proportions of hydrogen and oxygen to make water. | |
From: Weisberg/Needham/Hendry (Philosophy of Chemistry [2011], 4.5) |
17467 | Isotopes (such as those of hydrogen) can vary in their rates of chemical reaction [Weisberg/Needham/Hendry] |
Full Idea: There are chemically salient differences among the isotopes, best illustrated by the three isotopes of hydrogen: protium, deuterium and tritium, which show different rates of reaction, making heavy water poisonous where ordinary water is not. | |
From: Weisberg/Needham/Hendry (Philosophy of Chemistry [2011], 1.4) | |
A reaction: [They cite Paul Needham 2008] The point is that the isotopes are the natural kinds, rather than the traditional elements. The view is unorthodox, but clearly makes a good point. |
17466 | Mendeleev systematised the elements, and also gave an account of their nature [Weisberg/Needham/Hendry] |
Full Idea: In addition to providing the systematization of the elements used in modern chemistry, Mendeleev also gave an account of the nature of the elements which informs contemporary philosophical understanding. | |
From: Weisberg/Needham/Hendry (Philosophy of Chemistry [2011], 1.3) |