31 ideas
| 18085 | Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy] |
| Full Idea: When the successive absolute values of a variable decrease indefinitely in such a way as to become less than any given quantity, that variable becomes what is called an 'infinitesimal'. Such a variable has zero as its limit. | |
| From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4 | |
| A reaction: The creator of the important idea of the limit still talked in terms of infinitesimals. In the next generation the limit took over completely. |
| 18084 | When successive variable values approach a fixed value, that is its 'limit' [Cauchy] |
| Full Idea: When the values successively attributed to the same variable approach indefinitely a fixed value, eventually differing from it by as little as one could wish, that fixed value is called the 'limit' of all the others. | |
| From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4 | |
| A reaction: This seems to be a highly significan proposal, because you can now treat that limit as a number, and adds things to it. It opens the door to Cantor's infinities. Is the 'limit' just a fiction? |
| 8502 | Realism doesn't explain 'a is F' any further by saying it is 'a has F-ness' [Devitt] |
| Full Idea: Realists feel that the one-place predication 'a is F' leaves something unexplained, yet all that is offered is a two-place predication (a relational statement). There is an equal problem about 'a having F-ness'. | |
| From: Michael Devitt ('Ostrich Nominalism' or 'Mirage Realism'? [1980], p.97) | |
| A reaction: I think this is a key argument on the nominalist side - the denial that the theory of universals actually makes any progress at all in giving an explanation of what is going on around here. Platonist have the problem of 'partaking'. |
| 8503 | The particular/universal distinction is unhelpful clutter; we should accept 'a is F' as basic [Devitt] |
| Full Idea: Talk of 'particulars' and 'universals' clutters the landscape without adding to our understanding. We should rest with the basic fact that a is F. | |
| From: Michael Devitt ('Ostrich Nominalism' or 'Mirage Realism'? [1980], p.98) | |
| A reaction: Ramsey was first to challenge the basic distinction. I find the approach of Quine and Devitt unsatisfactory. We abandon explanation when it is totally hopeless, but that is usually in the face of complexity. Properties are difficult but simple. |
| 8501 | Quineans take predication about objects as basic, not reference to properties they may have [Devitt] |
| Full Idea: For 'a and b have the same property, F-ness' the Quinean Nominalist has a paraphrase to hand: 'a and b are both F'. ..In denying that this object need have properties, the Quinean is not denying that it really is F. | |
| From: Michael Devitt ('Ostrich Nominalism' or 'Mirage Realism'? [1980], p.95) | |
| A reaction: The question that remains is why 'F' is used of both a and b. We don't call a and b 'a', because they are different. Quine falls back on resemblance. I suspect Quineans of hiding behind the semantics. |
| 17368 | Essentialism concerns the nature of a group, not its category [Devitt] |
| Full Idea: Essentialism is concerned with the nature of a group, whatever the category it falls under. | |
| From: Michael Devitt (Resurrecting Biological Essentialism [2008], 6) | |
| A reaction: This seems to me such a simple and obvious point that I am amazed that anyone rejects it, yet lots of people seem to think that an essence is just some sort of category. |
| 17370 | Things that gradually change, like species, can still have essences [Devitt] |
| Full Idea: An intrinsic essence does not have to be 'neat and tidy'. ...Essentialism can accept the gradual change of one thing into another. | |
| From: Michael Devitt (Resurrecting Biological Essentialism [2008], 11) | |
| A reaction: My thesis is that essentialism is a response to the needs of explanation, so as long as there is some core explanation to be found, even in something transitory, then the concept of an essence can apply to it. |
| 9354 | Why should necessities only be knowable a priori? That Hesperus is Phosporus is known empirically [Devitt] |
| Full Idea: Why should we accept that necessities can only be known a priori? Prima facie, some necessities are known empirically; for example, that water is necessarily H2O, and that Hesperus is necessarily Phosphorus. | |
| From: Michael Devitt (There is no a Priori [2005], §2) | |
| A reaction: An important question, whatever your view. If the only thing we can know a priori is necessities, it doesn't follow that necessities can only be known a priori. It gets interesting if we say that some necessities can never be known a priori. |
| 19565 | How could the mind have a link to the necessary character of reality? [Devitt] |
| Full Idea: What non-experiential link to reality could support insights into its necessary character? | |
| From: Michael Devitt (There is No A Priori (and reply) [2005], 4) | |
| A reaction: The key to it, I think, is your theory of mind. If you are a substance dualist, then connecting to such deep things looks fine, but if you are a reductive physicalist then it looks absurdly hopeful. |
| 9353 | We explain away a priori knowledge, not as directly empirical, but as indirectly holistically empirical [Devitt] |
| Full Idea: We have no need to turn to an a priori explanation of our knowledge of mathematics and logic. Our intuitions that this knowledge is not justified in some direct empirical way is preserved. It is justified in an indirect holistic way. | |
| From: Michael Devitt (There is no a Priori [2005], §2) | |
| A reaction: I think this is roughly the right story, but the only way it will work is if we have some sort of theory of abstraction, which gets us up the ladder of generalisations to the ones which, it appears, are necessarily true. |
| 9356 | The idea of the a priori is so obscure that it won't explain anything [Devitt] |
| Full Idea: The whole idea of the a priori is too obscure for it to feature in a good explanation of our knowledge of anything. | |
| From: Michael Devitt (There is no a Priori [2005], §3) | |
| A reaction: I never like this style of argument. It would be nice if all the components of all our our explanations were crystal clear. Total clarity about anything is probably a hopeless dream, and we may have to settle for murky corners in all explanations. |
| 19564 | Some knowledge must be empirical; naturalism implies that all knowledge is like that [Devitt] |
| Full Idea: It is overwhelmingly plausible that some knowledge is empirical. The attractive thesis of naturalism is that all knowledge is; there is only one way of knowing. | |
| From: Michael Devitt (There is No A Priori (and reply) [2005], 1) | |
| A reaction: How many ways for us to know seems to depend on what faculties we have. We lump our senses together under a single heading. The arrival of data is not the same as the arrival of knowledge. I'm unconvinced that naturalists like me must accept this. |
| 17371 | Some kinds are very explanatory, but others less so, and some not at all [Devitt] |
| Full Idea: Explanatory significance, hence naturalness, comes in degrees: positing some kinds may be very explanatory, positing others, only a little bit explanatory, positing others still, not explanatory at all. | |
| From: Michael Devitt (Natural Kinds and Biological Realism [2009], 4) | |
| A reaction: He mentions 'cousin' as a natural kind that is not very explanatory of anything. It interests us as humans, but not at all in other animals, it seems. ...Nice thought, though, that two squirrels might be cousins... |
| 21202 | The strong force has a considerably greater range than the weak force [Martin,BR] |
| Full Idea: The strong nuclear force has a range of 10^-15 m, considerably larger than the range of the weak force. | |
| From: Brian R. Martin (Particle Physics [2011], 01) | |
| A reaction: This is because the bosons transmitting the weak force (W+, W-, W°) are much heavier than the gluons of the strong force. |
| 21211 | If an expected reaction does not occur, that implies a conservation law [Martin,BR] |
| Full Idea: If some reaction is not observed when there is apparently nothing to prevent it occurring, it is an indication that a conservation law is in operation. | |
| From: Brian R. Martin (Particle Physics [2011], 07) |
| 21209 | Electron emit and reabsorb photons, which create and reabsorb virtual electrons and positrons [Martin,BR] |
| Full Idea: In QED an electron constantly emits and reabsorbs virtual photons and these photons constantly create and reabsorb pairs of virtual electrons and positrons, and so on. | |
| From: Brian R. Martin (Particle Physics [2011], 06) | |
| A reaction: 'And so on'! These virtual particles have energy, and hence mass. |
| 21212 | The Higgs field, unlike others, has a nozero value in a state without particles [Martin,BR] |
| Full Idea: The Higgs field has the property of having a nonzero value in a state without particles, the vacuum state. Other fields are assumed to have a value zero in a vacuum state. | |
| From: Brian R. Martin (Particle Physics [2011], 09) | |
| A reaction: This seems to make a big difference to our concept of a field, since it has a measurable reality even when there are no particles. So it isn't just a geometrical frame for locating particles. |
| 21201 | A 'field' is just a region to which points can be assigned in space and time [Martin,BR] |
| Full Idea: The word 'field' is simply a shorthand way of saying that a physical property is assigned to the points of space and time in a region. | |
| From: Brian R. Martin (Particle Physics [2011], 01) | |
| A reaction: This is disappointing because I had begun to think that fields were foundational for modern ontology. Turns out they are operational abstractions (according to Martin). Note that a field extends over time. |
| 21205 | Many physicists believe particles have further structure, if only we could see it [Martin,BR] |
| Full Idea: Although standard particles are assumed to be structureless, many physicists believe that if distances could be probed down to 10^-35 m structures would be discovered. | |
| From: Brian R. Martin (Particle Physics [2011], 01) | |
| A reaction: Such probing is said to be probably impossible. And does the division then come to a halt? Aristotle's meditations on this are not irrelevant. |
| 21203 | Uncertainty allows very brief violations of energy conservation - even shorter with higher energies [Martin,BR] |
| Full Idea: The uncertainty principle states that energy conservation can be violated, but only for a limited period of time. As the energy violation increases, the time period within which 'borrowed' energy has to be 'paid back' decreases. | |
| From: Brian R. Martin (Particle Physics [2011], 01) | |
| A reaction: This is the only reason modern physicists ever seem to mention the uncertainty principle. You can ask why this debt must be paid, but it seems to be hidden where the laws of physics may not even apply. |
| 21207 | The Exclusion Principle says no two fermions occupy the same state, with the same numbers [Martin,BR] |
| Full Idea: The 'exclusion principle' initially stated that no two electrons in a system could simultaneously occupy the same quantum state and thus have the same set of quantum numbers. The principle actually applies to all fermions, but not to bosons. | |
| From: Brian R. Martin (Particle Physics [2011], 02) | |
| A reaction: This principle is said to be at the root of atomic structure, making each element unique. What exactly is a 'system'? Why does this principle hold? How do you ensure two women don't wear the same dress at a party? |
| 21204 | The standard model combines theories of strong interaction, and electromagnetic and weak interaction [Martin,BR] |
| Full Idea: As presently formulated, the standard model is two theories. One operates in the sector of strong interaction, and the other in the sector of the electromagnetic and weak interactions. | |
| From: Brian R. Martin (Particle Physics [2011], 01) | |
| A reaction: The first is Quantum Chomodynamics (QCD). The second is Quantum Electrodynamics (QED). Interesting that the weak interaction is included in the latter, which (I take it) means there is an electro-weak union. Interactions are the heart of the model. |
| 21208 | Eletrons don't literally 'spin', because they are point-like [Martin,BR] |
| Full Idea: The picture of a particle spinning like a top is sometime useful, but it is not consistent with the idea of the electron being point-like. In fact there is no analogy for spin in non-quantum physics. | |
| From: Brian R. Martin (Particle Physics [2011], 02) | |
| A reaction: If we take this stuff literally then it blow traditional metaphysics to bits, because an electron has properties without being a substance. In what sense can an electron 'have' properties if it is a point? In interactions they cease to be points. Eh? |
| 21210 | Virtual particles surround any charged particle [Martin,BR] |
| Full Idea: A cloud of virtual particles always surrounds a charged particle. | |
| From: Brian R. Martin (Particle Physics [2011], 06) | |
| A reaction: Here's a nice fact for aspiring Buddhists to meditate on. |
| 21206 | The properties of a particle are determined by its quantum numbers and its mass [Martin,BR] |
| Full Idea: In quantum theory, the full set of quantum numbers defines the state of the particle and, along with its mass, determines its properties. | |
| From: Brian R. Martin (Particle Physics [2011], 02) |
| 21213 | String theory only has one free parameter (tension) - unlike the standard model with 19 [Martin,BR] |
| Full Idea: Unlike the standard model, with its 19 free parameters (including the masses of quarks, coupling constants and mixing angles), string theories have a single free paramater: the string tension. | |
| From: Brian R. Martin (Particle Physics [2011], 10) | |
| A reaction: This must be one feature in favour of string theory, despite its problems. |
| 21200 | An 'element' is what cannot be decomposed by chemistry [Martin,BR] |
| Full Idea: In the modern sense 'element' means a substance that cannot be decomposed by the methods of chemistry. | |
| From: Brian R. Martin (Particle Physics [2011], 01) |
| 17369 | We name species as small to share properties, but large enough to yield generalisations [Devitt] |
| Full Idea: Our explanatory purposes in introducing a name for a species demand that we draw the lines around a group that is small enough to share a whole lot of important properties and large enough to yield broad generalizations. | |
| From: Michael Devitt (Resurrecting Biological Essentialism [2008], 10 'Arb') | |
| A reaction: Grist to my mill. In this reaction slot (16th Oct 2013) I launch my new metaphysical school - welcome to EXPLANATIONISM! Folk metaphysics, and the best philosophical metaphysics, is entirely driven by the needs of explanation. |
| 17367 | Species are phenetic, biological, niche, or phylogenetic-cladistic [Devitt, by PG] |
| Full Idea: The four main concepts of a species are 'phenetic' (similarity of traits), 'biological species' (interbreeding and isolated), 'ecological niche' (occupying an adaptive zone), or 'phylogenetic-cladistic' (start and finish at splits in lineage) | |
| From: report of Michael Devitt (Resurrecting Biological Essentialism [2008], 4) by PG - Db (ideas) | |
| A reaction: [my summary of Devitt's list] Devitt attacks the whole lot, in favour of essentialism - the species being fixed by its underlying explanatory mechanisms. |
| 17372 | The higher categories are not natural kinds, so the Linnaean hierarchy should be given up [Devitt] |
| Full Idea: The signs are that the higher categories are not natural kinds and so the Linnaean hierarchy must be abandoned. ...This is not abandoning a hierarchy altogether, it is not abandoning a tree of life. | |
| From: Michael Devitt (Natural Kinds and Biological Realism [2009], 6) | |
| A reaction: Devitt's underlying point is that the higher and more general kinds do not have an essence (a specific nature), which is the qualification to be a natural kind. They explain nothing. Essence is the hallmark of natural kinds. Hmmm. |
| 17373 | Species pluralism says there are several good accounts of what a species is [Devitt] |
| Full Idea: Species pluralism is the view that there are several equally good accounts of what it is to be a species. | |
| From: Michael Devitt (Natural Kinds and Biological Realism [2009], 7) | |
| A reaction: Devitt votes for it, and cites Dupré, among many other. Given the existence of rival accounts, all making good points, it is hard to resist this view. |